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EDUCATION:

Ph.D in Physics and Mathematics. Yerevan State, University, Republic of Armenia,  USSR.
MS in Electrical Engineering. Department of Electrical Engineering, Texas A&M University, USA.
MS in Imaging Science. Faculty of Computer Science, Moscow Institute of Physics and Technology, Moscow, USSR.
MS in Mathematics. Faculty of Mechanics and Mathematics, Yerevan State University, Armenia, USSR.

Personal page with research 

Google Academy Citations

Journal Publications (73)

Published in Peer Reviewed Journals

2019-1. A.M. Grigoryan, S.S. Agaian, “Paired Quantum Fourier Transform with log2N Hadamard Gates,” Quantum Information Processing, p.26, (May 25, 2019) 18: 217 (view in QIP).

2019-2. A.M. Grigoryan, S.S. Agaian, “Evidence of Golden and Aesthetic Proportions in Colors of Paintings of the Prominent Artists,” in press in IEEE MultiMedia, p.6, 2019 (view in IEEE).

2018-1. A.M. Grigoryan, S.S. Agaian, “Color image enhancement via combine homomorphic ratio and histogram equalization approaches: Using underwater images as illustrative examples,”  vol. 4, Issue 5, International Journal on Future Revolution in Computer Science & Communication Engineering, pp. 36 – 47, May 18, 2018 (view at IJFRSCE).

2018-2. A.M. Grigoryan, S.S. Agaian, “Image enhancement by elliptic discrete Fourier transforms,”  vol. 4, Issue 2, International Journal on Future Revolution in Computer Science & Communication Engineering, pp. 378 – 387, February 18, 2018 (view at IJFRSCE).

2018-3. A.M. Grigoryan, A. John, S.S. Agaian, “Alpha-rooting color image enhancement method by two-side 2D-quaternion discrete Fourier transform followed by spatial transformation,” International Journal of Applied Control, Electrical and Electronics Engineering, vol. 6, no. 1, p.21, February 2018 (view at IJACEEE)

2017-1. A.M. Grigoryan, S.S. Agaian, Image Processing Contrast Enhancement,” Wiley Encyclopedia of Electrical and Electronics Engineering, 22p, Published Online: 15 May 2017 (DOI: 10.1002/047134608X.W5525.pub2) (view at Wiley Online Library)

2017-2. A.M. Grigoryan, A. John, S.S. Agaian, “Modified alpha-rooting color image enhancement method on the two-side 2-D quaternion discrete Fourier transform and the 2-D discrete Fourier transform,” Applied Mathematics and Sciences: An International Journal (MathSJ), vol. 4, no. 1/2, p. 16, June 2017 (doi: 10.5121/mathsj.2017.4201) (view at MathSJ).

2017-3.  A.M. Grigoryan, A. John, S.S. Agaian, “A Novel color image enhancement method by the transformation of color images to 2-D grayscale images,” International Journal of Signal Processing and Analysis, vol. 2, no. 1, p. 18, 2017 (view at IJSPA)

2016-1. A.M. Grigoryan, S.S. Agaian, New look on q2^r-point fast Fourier transforms,” IEEE Transactions on Signal Processing , vol. 62, Issue 22, pp. 5972-5980, November 2016, (doi: 10.1109/TSP.2016.2598325)

2016-2.   R. Narayanam, A.M. Grigoryan, P.A. Patel, B. Tushara, “Paired faster FFT: Grigoryan FFT implementation and performance on XILINX FPGAS and TMS DSPS,” International Journal of Engineering Sciences & Research Technology, vol. 5, no. 6, pp. 431-444, June, 2016. (doi: 10.5281/zenodo.55536) (view at IJESRT)

2016-3.  A.M. Grigoryan, “Solution of the problem on image reconstruction in computed tomography,”Journal of Mathematical Imaging and Vision, vol. 54, Issue 1, pp. 35-63, January 2016. (doi: 10.1007/s10851-015-0588-6) (view at JMIV).

2016-4.   A.M. Grigoryan, E.R. Dougherty, S.S. Agaian, “Optimal Wiener and Homomorphic Filtration: Review,” Signal Processing, vol. 121, pp. 111-138, April 2016, (doi:10.1016/j.sigpro.2015.11.006) (view at SP).

2015-1.    A.M. Grigoryan, S.S. Agaian, “Tensor transform-based quaternion Fourier transform algorithm, Information Sciences (2015), vol. 320, pp. 62–74, 1 November 2015, (doi: http://dx.doi.org/10.1016/j.ins.2015.05.018) (view at IS).

2015-2.    A.M. Grigoryan, S.S. Agaian, “Monotonic sequences for image enhancement and segmentation,” Digital Signal Processing (2015), vol. 41, pp. 70–89, June 2015, (doi:10.1016/j.dsp.2015.02.011) (view at DSP).

2015-3.    A.M. Grigoryan, J. Jenkinson, S.S. Agaian, Quaternion Fourier transform based alpha-rooting method for color image measurement and enhancement,” Signal Processing, vol. 109, pp. 269-289, April 2015, (doi:10.1016/j.sigpro.2014.11.019) (view at SP).

2014-1.    A.M. Grigoryan, “New method of Givens rotations for triangularization of square matrices,”Journal of Advances in Linear Algebra & Matrix Theory (ALAMT) , vol. 4, no. 2, pp. 65-78, June 2014 (view at ALAMT).

2014-2.    A.M. Grigoryan and S.S. Agaian, “Retooling of color imaging in the quaternion algebra, Applied Mathematics and Sciences: An International Journal (MathSJ), vol. 1, no. 3, pp. 23-39, December 2014 (view at MathSJ).

2014-3.    A.M. Grigoryan, S.P.K. Devieni, “New method of signal denoising by the paired transform,” Applied Mathematics and Sciences: An International Journal (MathSJ), vol. 1, no. 2, pp. 1-20, August 2014 (view at MathSJ).

2014-4.    A.M. Grigoryan, M. Hajinoroozi, “Image and audio signal filtration with discrete Heap transforms,” Applied Mathematics and Sciences: An International Journal (MathSJ), vol. 1, no. 1, pp. 1-18, May 2014 (view at MathSJ).

1.    A.M. Grigoryan, “Image reconstruction from finite number of projections: Method of transferring geometry,” IEEE Trans. on Image Processing, vol. 22, no. 12, pp. 4738-4751, December 2013 (view at IEEE).

2.    N. Ranganadh, A.M. Grigoryan, P.A. Patel, B. Tushara, “Implementation and performance evaluation of paired transform based Faster FFT: Grigoryan FFT on Xilinx FPGAs and TMS DSPs using MATLAB: SIMULINK and CC Studio,” International Journal of Scientific and Engineering Research, IJSER NASA Astrophysics Database Systems French international journal, vol. 4, no. 8, pp. 373-383, August 2013 (view at IJSER).

3.    N. Ranganadh, A.M. Grigoryan, B. Tushara D, “Implementation of FFT by using MATLAB: SIMULINK on Xilinx Virtex-4 FPGAs: Performance of a Paired Transform Based FFT,” International Journal of Advanced Computer Research, vol. 3, no. 2, issue 10, pp. 72-78, June-2013 (view at IJACR).

4.    N. Ranganadh, P.A. Patel, A.M. Grigoryan, “Case study of Grigoryan FFT onto FPGAs and DSPs,” IJFCC – International Journal of Future Computer and Communication, vol. 2, no. 6, pp. 678-681. December 2013 (view at IJFCC).

4a-related.     N. Ranganadhm, N.R. Dhanavath, “A TMS DSP processor based case study of Grigoryan FFT performance over Cooley-Tukey FFT (TMS320C5416, TMS320C5515),” Asian Journal of Current Engineering and Maths, vol 2, no 1, pp. 50-52, January-February 2013 (view at Innovative Journal).

4b-related.     N. Ranganadh and B.D. Tushara, “Performance evaluations of Grigoryan FFT and Cooley-Tukey FFT onto Xilinx Virtex-II Pro and Virtex-5 FPGAs,” International Conference on Signal, Image Processing and Pattern Recognition , AIRCC-Springer-SIPP-2013, February-2013, Bangalore, India.

4c-related.     N. Ranganadh and M. Guravaiah, “Performance Case study of Grigoryan FFT over Cooley-Tukey FFT using TMS DSP Processors,” International Journal of Advanced Computer Research, vol. 2, no 4, issue 6, pp. 452-457, December 2012 (view at IJACR).

5.    N. Ranganadh, P.A. Patel, A.M. Grigoryan “Case study of Grigoryan FFT onto FPGAs and DSPs”, TMS320C6X DSPs and Virtex II Pro FPGAs,” International Journal of Future Computer and Communication (IJFCC), 2012.

6.    R. Narayanam, P. Parimal, A.M. Grigoryan, “Performances of Texas Instruments DSP and Xilinx FPGAs for Cooley-Tukey and Grigoryan FFT algorithms,” SOURCE Journal of Engineering & Technology, vol. 1, Issue 2, p.83, July 2011 (view at EBSCO).

7.    A.M. Grigoryan, “Two classes of elliptic discrete Fourier transforms: Properties and examples,” Journal of Mathematical Imaging and Vision (0235), vol. 39, pp. 210-229, January 2011 (view at Springer).

8.    A.M. Grigoryan, Nan Du, Principle of superposition by direction images,” IEEE Trans. on Image Processing, vol. 20, no. 9, pp. 2531-2541, September 2011 (view at IEEE).

9.    A.M. Grigoryan, Nan Du, “Comments on “Generalised finite Radon transform for N×N images”,” IMAVIS, vol. 29, no 11, pp. 797-801, November 2011. (view at Image and Vision Computing)

10.    A.M. Grigoryan, “Comments on “The discrete periodic Radon transform”,” IEEE Trans. on Signal Processing, vol. 58, no. 11, pp. 5962-5963, Nov 2010 (view at IEEE)

11.    A.M. Grigoryan and Nan Du, “2-D images in frequency-time representation: Direction images and resolution map,” Journal of Electronic Imaging, vol. 19, no. 3 (033012), July-September 2010 (view at JEI)

12.    Nan Du, A.M. Grigoryan, “Paired transform method of image reconstruction from projections,” in book Object Modeling, Algorithms and Applications, Editors: R.P. Barneva. V. Brimkov, R.M. Natal Jorge, and J.R.S. Tavares, Research Publishing, June 18, 2010 (view at PRS)

13.    S. Dursun and A.M. Grigoryan, “Nonlinear L2-by-3 transform for PAPR reduction in OFDM systems,” Computer and Electrical Engineering, vol. 36 (6), pp. 1055-1065, November 2010 (view at CEE)

14.    A.M. Grigoryan, “16-point reversible integer discrete Fourier transform with 12 control bits,” IEEE Trans. on Signal Processing, vol. 58, no. 2, pp. 912-916, February 2010 (view at IEEE)

15.    A.M. Grigoryan and K. Naghdali, “On a method of paired representation: Enhancement and decomposition by series direction images,” Journal of Mathematical Imaging and Vision, vol. 34, no. 2, pp. 185-199, June 2009 (view at Springer)

16.    A.M. Grigoryan, M.M. Grigoryan, “Discrete signal induced unitary transforms,” in book Computer and Simulation in Modern Science (Editor-in-Chief: Prof. Nikos Mastorakis), vol. 1, pp. 26-31, Mathematics and Computers in Science and Engineering, A series of Reference Books and Textbooks, WSEAS Press, 2008.

17.    A.M. Grigoryan, “Novel reversible integer Fourier transform with control bits,” IEEE Trans. on Signal Processing, Nov. 2007, vol. 55, no. 11, pp. 5267-5276 (view at IEEE)

18.    F.T. Arslan, A.M. Grigoryan, “Fast splitting alpha-rooting method of image enhancement: Tensor representation,” IEEE Trans. on Image Processing, Nov. 2006, vol. 15, no. 11, pp. 3375-3384 (view at IEEE)

19.    A.M. Grigoryan, “Representation of the Fourier transform by Fourier series,” Journal of Mathematical Imaging and Vision, vol. 25, no. 1, pp. 87-105, July 2006 (view at Springer)

20.    A.M. Grigoryan, “Fourier transform representation by frequency-time wavelets,” IEEE Trans. on Signal Processing, July 2005, vol. 53, no. 7, pp. 2489-2497 (view at IEEE )

21.    A.M. Grigoryan, “An algorithm for calculation of the discrete cosine transform by paired transform,” IEEE Trans. on Signal Processing, January 2005, vol. 53, no. 1, pp. 265-273 (view at IEEE )

21(a).    ———, “Author Corrections to “An algorithm for calculation of the discrete cosine transform by paired transform”,” ECE Dept. UTSA, Aug. 25, 2005. (View pdf-file 29kB)

22.  A.M. Grigoryan, V.S. Bhamidipati, “Method of flow graph simplification for the 16-point discrete Fourier transform,” ECE Dept. UTSA, Dec. 12, 2018. (Renewed pdf-file 147kB

22.    A.M. Grigoryan, V.S. Bhamidipati, “Method of flow graph simplification for the 16-point discrete Fourier transform,” IEEE Trans. on Signal Processing, January 2005, vol. 53, no. 1, pp. 384-389 (view at IEEE)

23.    A.M. Grigoryan, “A novel algorithm for computing the 1-D discrete Hartley transform,” IEEE Signal Processing Letters, vol. 11, no. 2, pp. 156-159, Feb. 2004 (view at IEEE)

24.    A.M. Grigoryan, “Method of paired transforms for reconstruction of images from projections: Discrete model,” IEEE Trans. on Image Processing, Sep. 2003, vol. 12, no. 9, pp. 985-994 (<a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1221753&isnumber=27440&punumber=83&k2dockey=1221753@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=3″>view at IEEE )

25.    A.M. Grigoryan, “Efficient algorithms for computing the 2-D hexagonal Fourier transforms,” IEEE Transaction on Signal Processing, June 2002, vol. 50, no. 6, pp. 1438-1448 (view at IEEE)

26.    A.M. Grigoryan, G. Hostetter, O.P. Kallioniemi, and E.R. Dougherty, “Simulation toolbox for 3D-FISH spot counting algorithms,” Real Time Imaging, vol. 8, no 3, pp. 203-212, June 2002.

27.    A.M. Grigoryan, E.R. Dougherty, J. Kononen, L. Bubendorf, G. Hostetter, and O.P. Kallioniemi,  “Morphological spot counting from stacked images for automated analysis of gene copy numbers by fluorescence in situ hybridization,” Biomedical Optics, January 2002, vol. 7, no. 1, pp. 109-122 (view at SPIE)

28.    A.M. Grigoryan, E.R. Dougherty, “Bayesian robust optimal linear filters,” Signal Processing, vol. 81, no. 12, pp 2503-2521, December 2001.

29.    C.L. Andersen, G.H. Hostetter, A.M. Grigoryan, G. Sauter, A. Kallioniemi, “Improved procedure for fluorescence in situ hybridization on tissue microarrays,” Cytometry 2001, 45, pp. 83-86. 

30.    A.M. Grigoryan, E.R. Dougherty, “Optimization of linear filters under power-spectral-density stabilization,” IEEE Transaction on Signal Processing, October 2001, vol. 49, no. 10, pp. 2292-2300 (<a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=950785&k2dockey=950785@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=5″>view at IEEE)

31.    A.M. Grigoryan, S.S. Agaian, “Shifted Fourier transform based tensor algorithms for 2-D DCT,” IEEE Transaction on Signal Processing, Sep. 2001, vol. 49, no. 9, pp. 2113-2126 ( <a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=942639&k2dockey=942639@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=8″>view at IEEE)

32.    A.M. Grigoryan, “2-D and 1-D multi-paired transforms: frequency-time type wavelets,” IEEE Transaction on Signal Processing, February 2001, vol. 49, no. 2, pp. 344-353 ( <a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=902116&k2dockey=902116@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=7″>view at IEEE)

33.    S.S.Agaian, K.P. Lentz, and A.M. Grigoryan, “Transform-based image enhancement algorithms,” IEEE Transaction on Image Processing, March 2001, vol. 10, no. 3, pp. 367-382 ( <a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=908502&k2dockey=908502@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=6″>view at IEEE)

34a.    A.M. Grigoryan, S.S. Agaian, “Method of fast 1-D paired transforms for computing the 2-D discrete Hadamard transform,” IEEE Transactions on Circuits and Systems II, January 2001, vol. 48, no. 1 ( <a href=”http://search.ieeexplore.ieee.org/search97/s97is.vts?Action=Search&queryText=%28Grigoryan%20%20A.%20M.au%20)&SearchPage=authors.jsp&ResultTemplate=lpadv_crst.hts&Filter=fld_sch.hts&ViewTemplate=lpdocview.hts&SortField=pyr&SortOrder=desc&ResultCount=15″>view at IEEE)

34c.    A.M. Grigoryan, S.S. Agaian, “Efficient algorithm for computing the 2-D discrete Hadamard transform,” IEEE Transactions on Circuits and Systems II, December 2000, vol. 47, no. 12, pp. 1399-1404.

34b.    A.M. Grigoryan, S.S. Agaian, “Method of fast 1-D paired transforms for computing the 2-D discrete Hadamard transform,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, October 2000, vol. 47, no. 10, pp. 1098-1103.

35.    A.M. Grigoryan, S.S. Agaian, “Efficient algorithm for computing the 2-D discrete Hadamard transform,” IEEE Transactions on Circuits and Systems II, October 2000, vol. 47, no. 10, pp. 1098-1103 ( <a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=877152&k2dockey=877152@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=2″>view at IEEE)

36.    A.M. Grigoryan, S.S. Agaian, “Split manageable efficient algorithm for Fourier and Hadamard transforms,” IEEE Transaction on Signal Processing, January 2000, vol. 48, no. 1, pp. 172-183. (<a href=”http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=815487&k2dockey=815487@ieeejrns&query=(grigoryan%20a.%20%20m.au%20)&pos=9″>view at IEEE)

37.    A.M. Grigoryan, E.R. Dougherty, “Design and analysis of robust binary filters in the context of a prior distribution for the states of nature,” Journal of Mathematical Imaging and Vision 11, pp. 239-254, 1999. (view at Springer )

38.    A.M. Grigoryan, “Mixed median filters and their properties”, Selected SPIE Papers on CD-ROM series, vol. 8: Mathematical Imaging and Vision/ edited by Dr. Gerhard Ritter, Univ. of Florida, SPIE, December 1999.

39.    A.M. Grigoryan, E.R. Dougherty, “Robustness of optimal filters,” Journal of Electronic Imaging, vol. 7, no. 1, pp. 117-126, January 1998.

40.    A.M. Grigoryan, “Quasilinear spaces,” Reports of Armenian National Academy of Science (in Russian), Yerevan, 1997, no 1. 

41.    A.M. Grigoryan, “Vectorial algorithms for computing the two-dimensional discrete Hartley transform,” Reports of Armenian National Academy of Science (in Russian), Yerevan, 1995, no 1, pp. 6-9.

42.    A.M. Grigoryan, “Efficient method of linear filtration,” Reports of Armenian National Academy of Science (in Russian), Yerevan, 1995, no 2, pp. 79-81.

43.    A.M. Grigoryan, S.S. Agaian, “Discrete unitary transforms and their relation to coverings of fundamental periods. Part-I,” In Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications, USA. 1994, vol. 1, no 1, pp. 16-22.

44.    A.M. Grigoryan, S.S. Agaian, “Discrete unitary transforms and their relation to coverings of fundamental periods. Part-II,” In Pattern Recognition and Image Analysis. Advances in Mathematical Theory and Applications, USA. 1994, vol. 1, no 2, pp. 23-31.

45.    A.M. Grigoryan, “An algorithm for computing a two-dimensional discrete Fourier transform of arbitrary order,” USSR Computational Mathematics and Mathematical Physics, 1991, vol. 31, no 10, pp. 112-117. (View original pdf-file 1.91MB)

46.    A.M. Grigoryan, “An algorithm of computation of the one-dimensional discrete Hadamard transform,” Izvestiya VUZov SSSR Radioelectronica, USSR, Kiev, 1991, vol. 34, no 8, pp. 100-103.

47.    A.M. Grigoryan, “An algorithm of computation of the one-dimensional discrete Fourier transform,” Izvestiya VUZov SSSR, Radioelectronica. USSR, Kiev, 1988, vol. 31, no 5, pp. 47-52.

48.    A.M. Grigoryan and M.M. Grigoryan, “Algorithm of computerized tomography,” Electronoe Modelirovanie (in Russian), AS USSR, Kiev, 1990, vol. 12, no 4, pp. 96-98.

49.    A.M. Grigoryan and M.M. Grigoryan, “Two-dimensional Fourier transform in the tensor presentation and new orthogonal functions,” Avtometria, AS USSR Siberian section, Novosibirsk, 1986, no 1, pp. 21-27. (View original pdf-file 2.22MB)

50.    A.M. Grigoryan and M.M. Grigoryan, “A new method of image reconstruction from projections,” Electronnoe Modelirovanie (in Russian), AS USSR, Kiev, 1986, vol. 8, no 6, pp. 74-77.

51.    A.M. Grigoryan, “New algorithms for calculating discrete Fourier transforms,” USSR Computational Mathematics and Mathematical Physics, 1986, vol. 26, no 5, pp. 84-88. (view original)

52.    A.M. Grigoryan, “An optimal algorithm for computing the two-dimensional discrete Fourier transform,” Izvestiya VUZov SSSR, Radioelectronica. USSR, Kiev, 1986, vol. 29, no 12, pp. 20-25. (View pdf-file 1.88MB)

53.    A.M. Grigoryan, “Arrangement of zeros in the spectrum of a discrete signal,” Radiotexnika, USSR, Moscow, 1986, no 11, pp. 78-79.

54.    A.M. Grigoryan, “An algorithm of the two-dimensional Fourier transform,” Izvestiya VUZov SSSR, Radioelectronica, USSR, Kiev, 1984, vol. 27, No. 10, pp. 52-57. (View pdf-file 1.91MB)

Articles in Proceedings (102)

1 – 2019.    A.M. Grigoryan, S.S. Agaian, Gradient based histogram equalization in grayscale image enhancement,” Proc. of SPIE, Defense + Commercial Sensing, Mobile Multimedia/Image Processing, Security, and Applications 2019, vol. 10993, p. 11, Baltimore, Maryland, 4-18 April 2019.

2 – 2019.    A.M. Grigoryan, S.S. Agaian,Asymmetric and symmetric gradient operators with application in face recognition in Renaissance portrait art,” Proc. of SPIE, Defense + Commercial Sensing, Mobile Multimedia/Image Processing, Security, and Applications 2019, vol. 10993, p. 12, Baltimore, Maryland, 4-18 April 2019.

3 – 2019.    A.M. Grigoryan, A. John, S.S. Agaian, “Quaternion alpha-rooting image enhancement of grayscale images,” Proc. of SPIE, Defense + Commercial Sensing, Mobile Multimedia/Image Processing, Security, and Applications 2019, vol. 10993, p. 8, Baltimore, Maryland, 4-18 April 2019.

1 – 2018.    A.M. Grigoryan, Re-Coloring of grayscale images: Models with Aesthetic and Golden proportions,” Proceedings of SPIE, Defense + Commercial Sensing, Mobile Multimedia/Image Processing, Security, and Applications, vol. 10668, p. 11, Orlando, Florida, 16-17 April 2018.

2 – 2018.    A.M. Grigoryan, A. John, S.S. Agaian, “A novel image enhancement method of 3-D medical images by transforming the 3-D images to 2-D grayscale images,” Proceedings of SPIE, Defense + Commercial Sensing, Mobile Multimedia/Image Processing, Security, and Applications, vol. 10668, p. 10, Orlando, Florida, 16-17 April 2018.

3 – 2018.    A.M. Grigoryan, S.S. Agaian, “Color visibility images and measures of image enhancement,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems, 28 Jan.-2 Feb., Burlingame, CA, 2018.

4 – 2018.    A.M. Grigoryan, S.S. Agaian, “Color facial image representation with new quaternion gradients,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems, 28 Jan.-2 Feb., Burlingame, CA, 2018.

5 – 2018.    A.M. Grigoryan, A. John, S.S. Agaian, “Enhancement of underwater color images by two-side 2-D quaternion discrete Fourier transform,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems, 28 Jan.-2 Feb., Burlingame, CA, 2018.

6 – 2018.    A.M. Grigoryan, S.S. Agaian, “Two general models for gradient operators in imaging,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems, 28 Jan.-2 Feb., Burlingame, CA, 2018.

1 – 2017.    A.M. Grigoryan, S.S. Agaian, “2-D Octonion discrete Fourier transform: Fast algorithms,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems XV, 29 Jan.-2 Feb., Burlingame, CA, 2017.

2 – 2017.    A.M. Grigoryan, S.S. Agaian, “Alpha-rooting method of gray-scale image enhancement in the quaternion frequency domain,” Proceedings of IS&T International Symposium, Electronic Imaging: Algorithms and Systems XV, 29 Jan.-2 Feb., Burlingame, CA, 2017.

3 – 2017.    A.M. Grigoryan, A. John, S.S. Agaian, “Color image enhancement of medical images using alpha-rooting and zonal alpha-rooting methods on 2-D QDFT,” Proceedings of SPIE Medical Imaging Symposium, Image Perception, Observer Performance, and Technology Assessment conference, 12 – 13 Feb., Orlando, FL, 2017, (doi http://dx.doi.org/10.1117/12.2254889).

1 – 2016.    A.M. Grigoryan, S.S. Agaian, “2D hexagonal quaternion Fourier transform in color image processing,” Proceedings of SPIE, 2016 Mobile Multimedia/Image Processing, Security, and Applications, April 17-21, Baltimore, Maryland, 2016.

2 – 2016.    A.M. Grigoryan, S.S. Agaian, “2-D Left-side quaternion discrete Fourier transform fast algorithms,” Proceedings of IS&T International Symposium, 2016 Electronic Imaging: Algorithms and Systems XIV, February 14-18, San Francisco, California, 2016.

3 – 2016.    A.M. Grigoryan, A. John, S. Agaian, “Zonal-alpha-rooting color image enhancement by the two-side 2D quaternion discrete Fourier transform,” Proceedings of IS&T International Symposium, 2016 Electronic Imaging: Algorithms and Systems XIV, February 14-18, San Francisco, California, 2016.

4 – 2016.    M. Hajinoroozi, A. Grigoryan, S. Agaian, “Image enhancement with weighted histogram equalization and heap transforms,” Proceedings of Conference: 2016 World Automation Congress (WAC), p. 1-6, July 2016 (DOI: 10.1109/WAC.2016.7582992)

1 – 2015.    A.M. Grigoryan, “Fourier transform with rotations on circles and ellipses in signal and image processing,” [9411-25], Proceedings of SPIE vol. 9411, 2015 Electronic Imaging: Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, February 10-11, San Francisco, California, 2015.

2 – 2015.    A.M. Grigoryan, “Fast Heap transform-based QR-decomposition of real and complex matrices: Algorithms and codes,” [9411-21], Proceedings of SPIE vol. 9411, 2015 Electronic Imaging: Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, February 10-11, San Francisco, California, 2015.

3 – 2015.    A.M. Grigoryan, S.S. Again, “Tensor representation of color images and fast 2-D quaternion discrete Fourier transform,” [9399-16], Proceedings of SPIE vol. 9399, 2015 Electronic Imaging: Image Processing: Algorithms and Systems XIII, February 10-11, San Francisco, California, 2015.

4 – 2015.    A.M. Grigoryan, S.S. Again, A.M. Gonzales, “Fast Fourier transform-based retinex and alpha-rooting color image enhancement,” [9497-29], Proc. SPIE Conf., Mobile Multimedia/Image Processing, Security, and Applications, 20 – 24 April 2015, Baltimore, Maryland United States.

5- 2015.    A.M. Grigoryan, B.A. Wiatrek, S.S. Again, “Image encryption by redirection and cyclical shift,” [9497-13], Proc. SPIE Conf., Mobile Multimedia/Image Processing, Security, and Applications, 20 – 24 April 2015, Baltimore, Maryland United States.

6 – 2015.    A.M. Grigoryan and S.S. Agaian, “Optimal color image restoration: Wiener filter and quaternion Fourier transform,” [9411-24], Proceedings of SPIE vol. 9411, 2015 Electronic Imaging: Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, February 10-11, San Francisco, California, 2015.

7 – 2015.    A.M. Gonzales, A.M. Grigoryan “Fast Retinex for color Image enhancement: Methods and Algorithms,” [9411-14], Proceedings of SPIE vol. 9411, 2015 Electronic Imaging: Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, February 10-11, San Francisco, California, 2015.

8 – 2015.    A.M. Grigoryan, S.S. Agaian, “New 2-D discrete Fourier transforms in image processing,” [9399-35], Proceedings of SPIE vol. 9399, 2015 Electronic Imaging: Image Processing: Algorithms and Systems XIII, February 10-11, San Francisco, California, 2015.

9 – 2015.    A.M. Grigoryan, S.S. Agaian, “Algorithms of the q^2r×q^2r-point 2-D discrete Fourier transform,” [9399-17], Proceedings of SPIE vol. 9399, 2015 Electronic Imaging: Image Processing: Algorithms and Systems XIII, February 10-11, San Francisco, California, 2015.

10 – 2015.    J. Jenkinson, A.M. Grigoryan, S.S. Agaian, “Enhancement of galaxy images for improved classification,” [9399-32], Proceedings of SPIE vol. 9399, 2015 Electronic Imaging: Image Processing: Algorithms and Systems XIII, February 10-11, San Francisco, California, 2015.

11 – 2015.    A.M. Grigoryan, S.S. Agaian, J. Jenkinson, “Innovating Engineering Education Through Teaching Image Processing In Texas,” 2015 ASEE-GSW Annual Conference University of Texas at San Antonio College of Engineering, March 26, Texas 2015.

1.    J. Jenkinson, A. Grigoryan, M. Hajinoroozi, et al., “Machine learning and image processing in astronomy with sparse data sets,” In proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (SMC2014), pp. 200-203.San Diego, California, October 5-8, 2014. (view at IEEE )

2.    A.M. Grigoryan and Nan Du, “Novel tensor transform-based method of image reconstruction from limited-angle projection data,” [9020-14], SPIE proceedings, 2014 Electronic Imaging: Computational Imaging XII, February 2-6, San Francisco, California, 2014.

3.    A.M. Grigoryan and M. Hajinoroozi, “A novel method of filtration by the discrete heap transforms,” [9019-2], SPIE proceedings, 2014 Electronic Imaging: Image Processing: Algorithms and Systems XII, February 2-6, San Francisco, California, 2014.

4.    A.M. Grigoryan and S.S. Agaian, “Alpha-rooting method of color image enhancement by discrete quaternion Fourier transform,” [9019-3], SPIE proceedings, 2014 Electronic Imaging: Image Processing: Algorithms and Systems XII, February 2-6, San Francisco, California, 2014.

5.    A.M. Grigoryan and S.S. Agaian, “Fibonacci thresholding: Signal representation and morphological filters,” [9019-30], SPIE proceedings, 2014 Electronic Imaging: Image Processing: Algorithms and Systems XII, February 2-6, San Francisco, California, 2014.

6.    A.M, Grigoryan and Nan Du, “Method of field transformation of G-particles for image reconstruction from a finite number of projections,” SPIE proceedings, SPIE Electronic Imaging, February 3-7, Burlingame, California, 2013.

7.    Nan Du, Y. Feng, and A.M, Grigoryan, “ Reconstruction of the image on the Cartesian latticefrom a finite number of projections in computed-tomographic imaging,” SPIE proceedings, SPIE Electronic Imaging, February 3-7, Burlingame, California, 2013.

8.    Nan Du, Y. Feng, and A.M, Grigoryan, “Image reconstruction from limited-angle range projections,” SPIE proceedings, SPIE Medical Imaging, February 9-14, Florida, 2013.

9.    N. Ranganadh, P.A. Patel, and A.M. Grigoryan “Case study of Grigoryan FFT onto FPGAs and DSPs,” TMS320C6X DSPs and Virtex II Pro FPGAs. IEEE proceedings, IEEE 4th International Conference on Electronics Computer Technology (ICECT 2012), pp. 423-426. Kanyakumari, India, April 6-8, 2012.

10.    Joao Donacien N. Nsingui and A.M. Grigoryan, “Elliptic discrete Fourier transform and its application in signal and image processing,” in Proceedings of the National Conference On Undergraduate Research (NCUR) 2012, Weber State University, Ogden Utah, March 29-31, 2012 (view pdf file (147 kB) )

11.    T. Nagaraju and A.M. Grigoryan, “Fast discrete Fourier transform in FPGA by using the method of fast paired transform,” in Proceedings of the 2011 ASEE Gulf-Southwest Annual Conference, University Houston, p. 8, 2011 (view pdf file (605 kB) )

12.    S. Dursun, Nan Du, and A.M, Grigoryan, “Paired transform slice theorem of 2-D image reconstruction from projections,” presented in the 20th International Conference on Pattern Recognition (ICPR), August 23-26, Istanbul, 2010. (view at IEEE )

13.    S. Dursun and A.M, Grigoryan, “Reversible integer 2-D discrete Fourier transform by control bits,” presented in the 20th International Conference on Pattern Recognition (ICPR), August 23-26, Istanbul, 2010. (view at IEEE )

14.    A.M. Grigoryan, “Elliptic discrete Fourier transforms of Type II,” presented in 2009 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2009), pp. 954-959, San Antonio, Texas, USA, October 11-14, 2009 (view at IEEE or see the presentation in Slides and Posters)

15.    K. Naghdali, R. Raghunath, and A.M. Grigoryan, “Fast signal-induced transforms in image enhancement,” presented in 2009 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2009), pp. 565-570, San Antonio, Texas, USA, October 11-14, 2009 (view at IEEE or see the presentation in Slides and Posters)

16.    A.M. Grigoryan and Nan Du, “New formula for image reconstruction from projections by the 2-D paired transformation,” presented in 2009 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2009), pp. 153-156, San Antonio, Texas, USA, October 11-14, 2009 (view at IEEE or see the presentation in Slides and Posters)

17.    Nan Du,, S. Devineni, and A.M. Grigoryan, “Mixed Fourier transforms and image encryption,” presented in 2009 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2009), pp. 547-552, San Antonio, Texas, USA, October 11-14, 2009 (view at IEEE or see the presentation in Slides and Posters)

18.    A.M. Grigoryan and K. Naghdali, “Fast unitary heap transforms: Theory and application in cryptography,” [7351-16], International Conference Mobile Multimedia/Image Processing, Security, and Applications 2009, DSS09 SPIE Defense, Security, and Sensing 2009, Orlando, FL, USA, April 13-17, 2009. (view at SPIE or see the presentation in Slides and Posters)

19.    A.M. Grigoryan, “Decomposition by series direction images: Image reconstruction and enhancement” [7245A-25], International Conference: Electronic Imaging, Science and technology, IS&T/SPIE 21st Annual Symposium, San Diego, CA, 18-22 January, 2009. (view at SPIE)

20.    A.M. Grigoryan and M.M. Grigoryan, “Discrete integer Fourier transform in real space: Elliptic Fourier transform” [7245A-1], International Conference: Electronic Imaging, Science and technology, IS&T/SPIE 21st Annual Symposium, San Diego, CA, 18-22 January, 2009. (view at SPIE)

21.    E. Gonzalez and A.M. Grigoryan, “Reversible integer 2-D Fourier transform,” [7245A-2], International Conference: Electronic Imaging, Science and technology, IS&T/SPIE 21st Annual Symposium, San Diego, CA, 18-22 January, 2009. (view at SPIE)

22.    A.M. Grigoryan and M.M. Grigoryan, “Discrete signal induced unitary transforms,” (paper number: 577-827), in ISI Book (Thomson) published by American Conference on Applied Mathematics, WSEAS 2008, Cambridge, MA, March 24-26, 2008.

23.    F.T. Arslan and A.M. Grigoryan, “Enhancement of medical images by the paired transform,” in Proceedings of the 14th IEEE International Conference on Image Processing, vol. 1, pp. 537-540, San Antonio, Texas, September 16-19, 2007. (view at IEEE )

24.    A.M. Grigoryan and M.M. Grigoryan, “Discrete unitary transforms generated by moving waves” [6701-78], in the Proceedings of the International Conference: Wavelets XII, SPIE: Optics+Photonics 2007, San Diego, CA, 27-29 August, 2007. (view at SPIE )

25.    A.M. Grigoryan and M.M. Grigoryan, “New discrete unitary Haar-type heap transforms” [6701-79], in the Proceedings of the International Conference: Wavelets XII, SPIE: Optics+Photonics 2007, San Diego, CA, 27-29 August, 2007. (view at SPIE )

26.    A.M. Grigoryan and M.M. Grigoryan, “Nonlinear approach of construction of fast unitary transforms,” in the Proceedings of the 40th Annual Conference on Information Sciences and Systems (CISS 2006), Princeton Univ., pp. 1073-1078, March 22-24, 2006, Princeton. (view at IEEE )

27.    A.M. Grigoryan, S. Dursun, and M.M. Grigoryan, “Method of sliding norm transforms for peak-to-average power reduction in OFDM systems,” 2006 IEEE International Symposium on Industrial Electronics ISIE’06, June 9-13, Montreal, Canada. (view at IEEE )

28.    J.U. Anugom and A.M. Grigoryan, “Method of splitting signals by the paired transform,” 2006 IEEE International Symposium on Industrial Electronics ISIE’06, June 9-13, Montreal, Canada. (view at IEEE )

29.    S. Alla and A.M. Grigoryan, “Method of reconstruction of 3-D PET images from projections,” IEEE Region 5 Technical, Professional, and Student Conference (TPS 2006), April 6-8, San Antonio, TX, (view pdf file (1.9 MB) )

30.    F.T. Arslan, A.K. Chan, and A.M. Grigoryan, “Directional denoising of aerial images by splitting-signals,” IEEE Region 5 Technical, Professional, and Student Conference (TPS 2006), April 6-8, San Antonio, TX, (view pdf file (987 KB) )

31.    J.U. Anugom and A.M. Grigoryan, “Multiresolution signal processing by Fourier transform time-frequency correlation analysis,” IEEE Region 5 Technical, Professional, and Student Conference (TPS 2006), April 6-8, San Antonio, TX, (view pdf file (1.3 MB) )

32.    R.N. Raghunath, J.M. Moreno, and A.M. Grigoryan, “The novel Arc low-pass filter,” IEEE Region 5 Technical, Professional, and Student Conference (TPS 2006), April 6-8, San Antonio, TX, (view pdf file (599 KB) )

33.    F.T. Arslan and A.M. Grigoryan, “Alpha-rooting image enhancement by paired splitting-signals,” in the Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging: from Macro to Nano, ISBI 2006, pp. 968-971, April 6-9, 2006, Arlington, VA ( view at IEEE )

34.    S. Alla, M.J. Moreno, and A.M. Grigoryan, “Novel method of tensor representation for reconstruction of 3D PET images from projections,” in Proceedings of SPIE — Volume 6246, Visual Information Processing XV, April 18-19, 2006 (view at SPIE )

35.    F.T. Arslan, J.M. Moreno, and A.M. Grigoryan, “Paired directional transform-based methods of image enhancement,” in Proceedings of SPIE — Volume 6246, Visual Information Processing XV, April 18-19, 2006 (view at SPIE )

36.    A.M. Grigoryan and S. Dursun, “Multiresolution of the Fourier transform,” in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005 (ICASSP ’05), vol. 4, pp. 577–580, March 18-23, 2005, Philadelphia, PA ( view at IEEE )

37.    F.T. Arslan and A.M. Grigoryan, “Method of image enhancement by splitting-signals,” in the Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005 (ICASSP ’05), vol. 4, pp. 177–180, March 18-23, 2005 ( view at IEEE )

38.    F.T. Arslan, A.M. Grigoryan, and A.C. Chan, “Method of tensor transform for directional clutter removal of aerial digital images,” DCDIS 4th International Conference on Engineering Applications and Computational Algorithms, Ontario, Canada, July 27-29, 2005.

39.    F.T. Arslan, J.M. Moreno, and A.M. Grigoryan, “New Methods of Image Enhancement” Quantum Information and Computation III. Edited by Donkor, Eric J.; Pirich, Andrew R.; Brandt, Howard E. Proceedings of the SPIE, Volume 5817, pp. 225-236, the International Conference of SPIE Defense and Security Symposium, Orlando, FL, March 29-31, 2005 (view at SPIE )

40.    A.M. Grigoryan, V.S. Bhamidipati, S. Alla, “New method of calculation of reversible integer 1D DCTs” [5672-24], presented by Phani Sagiraju in the International Conference: Image Processing: Algorithm and Systems IV, IS\&T/SPIE’s Annual Symposium, Electronic Imaging, San Jose, CA, 16-20 January, 2005 (view at SPIE )

41.    N. Ranganadh, P. Patel, and A.M. Grigoryan, “Implementation of the DFT using radix-2 and paired transform algorithms,” 17th International Conference on Computer Applications in Industry and Engineering, CAINE-2004, Orlando, Florida USA, Nov. 17-19, 2004.

42.    A.M. Grigoryan and S.-C. Liu, “New method of image reconstruction from projections,” Proceedings, IEEE International Symposium on Biomedical Imaging: from Macro to Nano, ISBI 2004, pp. 776-779, April 2004, Arlington, VA ( view at IEEE )

43.    A.M. Grigoryan and F.T. Arslan, “Image enhancement by the tensor transform,” Proceedings, IEEE International Symposium on Biomedical Imaging: from Macro to Nano, ISBI 2004, pp. 816-819, April 2004, Arlington, VA ( view at IEEE )

44.    A.M. Grigoryan, S. Dursun, and E.E Regentova, “Lossless Encoding Based on Redistribution of Statistics,” Proceedings of IEEE International Conference on Information Technology: Coding and Computing, ITCC-2004, vol. 2, pp. 620-624, Las Vegas, Nevada, USA, April 5-7, 2004.  (view at IEEE )

45.    V. S. Bhamidipati and A.M. Grigoryan, “Parametrized reversible integer discrete cosine transforms,” [EI 5298-2] Proceedings of SPIE-IS\&T, Electronic Imaging, SPIE vol. 5298, pp. 13-24, San Jose, CA, 19-21 January, 2004. (view at SPIE )

46.    F.T. Aslan, J.G. Vital, and A.M. Grigoryan, “Method of arithmetical thresholding of images,” [EI 5298-24] Proceedings of SPIE-IS\&T, Electronic Imaging, SPIE vol. 5298, pp. 200-211, San Jose, CA, 19-21 January, 2004). (view at SPIE )

47.    A.M. Grigoryan, S. Agaian, A.R. Manukyan, “A novel method of splitting the 3-D discrete Hartley transform,” in Proceedings of the IEEE International Conference on Image Processing, ICIP-2003, vol. 1, pp. 1009-1012, Sept. 14-17, 2003. ( view at IEEE )

48.    A.M. Grigoryan, “Nontraditional cross sections and morphological operations,” [5014-18] (Image Processing: Algorithms and Systems II, Electronic Imaging, Science and Technology 2003, IS&T/SPIE 15 Annual Symposium, Santa Clara, CA, January 20-24, 2003). (view at SPIE )

49.    A.M. Grigoryan and S.S. Agaian, “Tensor form of image representation: Enhancement by image-signals,” [5014-26] (Image Processing: Algorithms and Systems II, Electronic Imaging, Science and Technology 2003, IS&T/SPIE 15 Annual Symposium, Santa Clara, CA, January 20-24, 2003) (view at SPIE )

50.    A.M. Grigoryan, “Paired algorithm of the 1-D discrete Hartley transform,” (The International Signal Processing Conference (ISPC) and Global Signal Processing Expo (GSPx), Dallas, March 31-April 3, 2003).

51.    A.M. Grigoryan, P.A. Patel, and N. Ranganadh, “Novel algorithm of the Haar transform,” (ISPC & GSPx, Dallas, March 31-April 3, 2003).

52.    A.M. Grigoryan and E.E Regentova, “A New Optimal Encoding Method,” (accepted to the 36th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, November 3-6, 2002.)

53.    A.M. Grigoryan and E.E Regentova, “A new method of optimal coding,” Processing of Third IEEE International Conference on Information Technolgy: Coding and Computing, ITCC-2002, pp. 378-382, Las Vegas, Nevada, USA, April 8-10, 2002,  ( view at IEEE )

54.    A.M. Grigoryan and E.R. Dougherty, “Automatic counting of illuminated spheres in a random Boolean model,”[4667-21] Processing of SPIE, Image Processing: Algorithms and Systems Conference, Electronic Imaging 2002, IS&T/SPIE 13 International Symposium, San Jose, January 21-23 2002. (view at SPIE )

55.    A.M. Grigoryan and E.R. Dougherty, “Morphological counting of illuminated 3D bodies,” [4304-06] Processing of SPIE, “Nonlinear Image Processing and Pattern Analysis XII” Conference, Electronic Imaging 2001, IS&T/SPIE 13 International Symposium, San Jose, January 22-23 2001. (view at SPIE )

56.    A.M. Grigoryan, S.S. Agaian, and E.R. Dougherty, “Splitting of the 2-D Hexagonal DFT,” Processing of the conference Pattern Recognition and Information Processing – PRIP’2001, Belarus, 2001.

57.    S. Agaian, K.A. Panetta, and A. Grigoryan, “A new measure of image enhancement,” IASTED International Conference on Signal Processing and Communications, pp. 19-22, July 3-6, 2000, Rhodes, Greece.

58.    G.H. Hostetter, A.M. Grigoryan, C.L. Andersen, L. Bubendorf, J. Kononen, E.R.  Dougherty, and O.P. Kallioniemi, “Towards Automated Spot Counting of Interphase FISH Experiments on Tissue Microarray” [2849] 2001 Annual Meeting of American Association for Cancer Research, New Orleans, March 24-29, 2001.

59.    G.H. Hostetter, A.M. Grigoryan, C.L. Andersen, L. Bubendorf, J. Kononen, E.R.  Dougherty, and O. Kallioniemi, “Design of an Automated Spot Counting Program for Interphase FISH on the Tissue Microarray” [318] 50th Annual Meeting of the American Society of Human Genetics, Philadelphia, October 3 – 7, 2000.

60.    L. Bubendorf, A.M. Grigoryan, J. Kononen, M. Barlund, O. Monni, A. Kallioniemi, G. Sauter, E.R. Dougherty, and O. Kallioniemi, “FISH on tissue microarrays: Towards automated analysis of genetic alterations in thousands of tumors with multiple probes,” The Eighth International Workshop on Chromosomes in Solid Tumors, Tucson, AZ, January 30 – February 1, 2000.

61.    A. M. Grigoryan, E.R. Dougherty, L. Bubendorf, J. Kononen, and O. Kallioniemi, “Rapid analysis of gene copy numbers by FISH and automatic spot counting from stacked confocal images” [3924-21] BIOS 2000, International Biomedical Optics Symposium, Conference Molecular Imaging: Reporters, Dyes, Markers, Instrumentation II, San Jose, California, January 2000.( view at SPIE )

62.    L. Bubendorf, J. Kononen, M. Barlund, A. Kallioniemi, A. Grigoryan, G. Sauter, E. R. Dougherty, and O.-P. Kallioniemi, “Tissue microarray FISH and digital imaging: towards automated analysis of thousands of tumors with thousands of probes” [316] Cancer Genetics, 49th Annual Meeting of the American Society of Human Genetics, Moscone Center in San Francisco, California, October 19 – 23, 1999. (The authors have received Postdoctoral Translation Research Award at ASHG)

63.    A.M. Grigoryan, S.S. Agaian, and E.R. Dougherty, “Fibonacci thresholding, signal representation, and morphological filters,” EUSIPCO-2000, X European Signal Processing Conference, Tampere, Finland, Sept. 2000, pp. 2393-2396.

64.    A.M. Grigoryan and S.S. Agaian, “Three algorithms for computing the 2-D discrete Hartley transform,” ICIP 2000 Conference on Image Processing, 359-362 (Sep. 2000), Canada. ( view at IEEE )

65.    E.R. Dougherty, A.M. Grigoryan, J. Barrera, and N.S.T. Hirata, “Binary filter design: Optimization, Prior information, and Robustness [3475-24],” SPIE’s International Symposium on Optical Science, Engineering and Instrumentation: Mathematical Modeling and Estimation Techniques in Computer Vision, 23 July 1998, San Diego, California, USA. ( view at SPIE )

66.    A.M Grigoryan and E.R. Dougherty, “Designing Robust Binary Filters [3304-02],” in Proc. SPIE’s Symposium on Electronic Imaging: Science and Technology, January 1998, San Jose,USA. 

67.    E.R. Dougherty and A.M. Grigoryan, “Robustness of Optimal Binary Filters. [3167-12],” in Proc. SPIE’s International Symposium on Optic Science, Engineering, and Instrumentation: Statistical and Stochastic Methods in Image Processing II, 130-138 (July-August 97), San Diego, USA. ( view at SPIE )

68.    A.M. Grigoryan, “Mixed Median Filters and Their Properties [3026-03],” in Proc. SPIE’s Symposium on Electronic Imaging: Science and Technology, February 1997, San Jose, USA. (view at SPIE )

69.    A.M. Grigoryan and S.S. Agaian, “New Models and Nonlinear Filters for Image Restoration [2662-19],” in Proc. SPIE’s Symposium on Electronic Imaging: Science and Technology, 118-128 (February-January 96), San Jose, USA. [ view at SPIE )

70.    G.H. Sarukhanyan and A.M. Grigoryan, “Decomposition of the Hadamard matrices by orthogonal vectors; The paired algorithm for 1-D Hadamard transform,” in Proc. ISCIS IX Int. Symposium on Computer and Information Sciences, 10p, November 1996, Antalya, Turkey, 

71.    A.M. Grigoryan, S.S. Agaian, and J. Astola, “Quasilinear Spaces: A General Framework For Nonlinear Filtering [2424A-19],” in Proc. SPIE’s Symposium on Electronic Imaging: Science and Technology, 176-186 (February 95), San Jose, USA. (view at SPIE )

72.    A.M. Grigoryan, “New models of image restoration,” 6th International Conference CAIP’95: Computer Analysis of Images and Patterns, September 1995, Prague, Czech Republic.

73.    A.M. Grigoryan, “General two-cascade median quasilinear systems with second structural elements,” in Proc. CSIT’97 Conference on Computer Science and Information Technologies, September 97, Yerevan, Armenia.

74.    A.M. Grigoryan, “Efficient algorithms of the two-dimensional Hartley transform,” in Proc. CSIT’97 Conference on Computer Science and Information Technologies, September 97, Yerevan, Armenia.

75.    A.M. Grigoryan, “An algorithm for computing the two-dimensional Fourier transform of equal orders,” In Proc. On IX All-Union Conference on Coding, Part 2, pp. 42-52, Odessa 88, USSR.

Research

Research in Digital Signal and Image Processing, Fast Transforms:

Quantum Computing: Algorithms of the quantum Fourier transform, quantum image processing.

Quaternion Imaging: Image enhancement, quaternion gradient, quaternion  2-D convolution, quaternion optimal filters (quaternion Wiener filter).

Fast algorithms: Quaternion discrete Fourier transforms. 1-D and 2-D discrete Fourier, Hartley, Hadamard, and cosine transforms.

Tensor and paired representations: 2-D tensor and paired transforms. Image and signal representation by splitting-signals. Fast 1-D paired transform. These transforms I developed and first published in 1984-1986s, are called in many publications by different names, such as “discrete, finite, periodic, orthogonal, and generalized Radon, and mojette transforms.”

Fourier analysis and Multiresolution: Resolution map, image compression. Color image enhancement and optimal filtration. Image cryptography.

Methods of Computed Tomography: Image reconstruction from parallel projections, solution of the problem with a finite number of projections. Principle of superposition by direction images.

Elliptic discrete Fourier transforms: Two classes of transforms which generalize the known concept of the DFT and rotate data around the elipses, not circles.

Signal-induced Heap transforms: Fast unitary transforms which are generated by given signals. Angular representation.


Teaching

Classes and Students 

Fall 2019
  • Mathematics in Signals and Systems – EE 3423 

Required Text-Book:
Signals, Systems, and Transforms,
Charles L. Philips, John M. Park, and Eve A. Riskin  (Prentice Hall, 5th edit. 2014).

  • Discrete Signals and Systems – EE 3523 

Required Text-Book:
Signals, Systems, and Transforms,
Charles L. Philips, John M. Park, and Eve A. Riskin  (Prentice Hall, 5th edit. 2014), Chapters 9-12.

My brief notes of lectures can be downloaded:

       15 Lectures: Math in Signals and Systems (formerly Signals and Systems I)
       10 Lectures: Discrete Signals and Systems (formerly Signals and Systems II) 

  • 4663: Digital Image Processing / EE 5353: Topic 1: Digital Image Processing
    Books:
    1. Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, Second or Third Edition Prentice Hall, 2002, … . (Required).
    2. R.C. Gonzalez, R.E. Woods, S.L. Eddins, Digital Image Processing Using MATLAB, Prentice Hall; 1st edition, 2003. (Recommended).
    3. A.M. Grigoryan. My notes for DIP with all topics and MATLAB codes discussed in the class will be posted in BB.

* My lectures and many codes in Digital Signal Processing (DSP) and digital Image Processing (DIP) are posted in the personal web page by the address: (http://www.fasttransfroms.com)

Supervision of students

PhD in EE (8):

1. Aparna John, “2-D Quaternion Discrete Fourier Transform in Color Image Enhancement,” Graduated in December 2017.
2. John Jekinson, “Enhancement of galaxy images,” 2014-2017.
3.
Nan Du, “Tensor Transform Based Method of Image Reconstruction by Projections,” Graduated in August 2013.
4. Sree Phani Kishore Devineni, “Methods of Paired Representation in Signal Denoising,” Graduated in Fall 2013.
5. Khalil Naghdali, “Discrete Signal-Induced Fast Transforms and Their Applications Image Processing,” Graduated in Fall 2013.
6. Tilak Nagaraju, “Design and Architectural Implementation of the Fast Fourier Transform in FPGA”
7. Serkan Dursun, “Peak-to-Average Power Ratio Reduction in Multi-Carrier Communication Systems,” Graduated in May 2010.

8. Fatma Arslan, “Image Enhancement and Directional Denoising by Paired Transform,” Graduated in March 2007.

BS with Honor in EE:
Joao, Nsingui, “Elliptic Discrete Fourier Transforms and Their application,” Graduated in May 2012.

MS in EE (21):

1. Richard Down, “Intersection Monitoring Tool Using Computer Vision and Machine Learning Techniques,” Graduated in December 2018.

2. Anusha Cherukuri (/ Dr. Sos Agaian), “To Develop a Financial Data Analytics and Prediction System by Combining Multiple data Sources,” Graduated in December 2017.
3. Venkata Parameswada R. Boddu (/ Dr. Sos Agaian) , “Parametric Transfer Learning Analysis wuth Prostate and Breast Cancer,” Graduated in December 2017.
4. Venkata Parameswada R. Boddu, “A Novel Reversible Watermarking Method based on Adaptive Thresholding and Companding Technique,” Graduated in May 2016.

5. Sai Krishna Papineni, “Facial Expression Recognition System using Hog Features and Cross Validation,” Graduated in May 2016.
6. Pranita B. Panta, “Retinex Using Fast Fourier Transform,” Graduated in May 2016.
7. Ramya Y. Kavuda “ Mineral Image Enhancement,” Graduated in May 2016. 
8. Bryan A. Wiatrek, “Image Encryption by Redirection and Cyclic Shift,” Graduated in May 2015. 
9. Analysa M. Gonzales, “Fast Multiscale RETINEX and a-Rooting, Fusion for Post Processing,” Graduated in May 2015. 
10. John Jenkinson, “Enhancement Classification of Galaxy Images,” Graduated in December 2014. 
11. Mehdi Hajinoroozi, “Image and Signal Processing with Discrete Signal-Induced Heap Transform,” Graduated in May 2014. 
12. Hassan Alshwaf, “Seismic Signal Processing Techniques and algorithms,” Graduated in August 2013. 
13. Ahmad Turki, “Overview on Different Medical Image Enhancement Algorithms,” Graduated in August 2013.
14. Julian, Anugom, “Multiresolution Signal Processing by Fourier Transform Time-Frequency Correlation Analysis,” Graduated in May 2006.
15. Alla Srikrishna, “Novel Method of Image Reconstruction Using Tensor Representation – Its Applications in Positron Emission Tomography,” Graduated in Dec. 2005.
16. Shih-Chia Liu, “Method of Tensor Representation for Reconstruction of Image from Projections,” Graduated in May 2005.
17. Jung-Hua Liao, “New Methods of Filtering for 1-D Signals by the Paired Transform,” Graduated in May 2005.
18. Veerabhadrasam S. Bhamidipati, “New Methods of Calculation of Reversible Integer Discrete Cosine Transform,” Graduated in Dec. 2004.
19. Ranganadh Narayaham, ( / Dr. Patel Parimal) “Implementation and Performance Evaluation of the fast DFT by Using Radix-2 and the Paired Transform Algorithms,” Graduated in August 2004.
20. Larry Stephen Lamoureux, ( / Dr. Sos Agaian) “Image De-noising via Local Information Based Fuzzy Filters,” Graduated in May 2002.
21. Ashish Dinanath, Graduated in May 2002.

  • Other Classes (from 2001-2018):   
    Topics in DSP: Biomedical Imaging – BME 6703-01
    Advanced Topics in Signal Processing – EE 6363 001 
    Topics in DSP: Biomedical Image Processing – EE 5263-01
    Topics in DSP: Digital Image Processing – EE 5263-01
    Digital Signal Processing – EE 5163 
    Discrete Signals and Systems (Signals and Systems II) EE 3523 
    Math in Signals and Systems – EE 3424, EE 3423 (Signals and Systems I)
    Network Theory – EE 2423
    Statics and Dynamics – ERG 2213 
    Digital Image Processing – EE 4663 
    Topics: Digital Image Processing – EE 5353 
    Digital Signal Processing – EE 4643 
    Topics in Multimedia Signal Processing – EE 5353 
    Topics in DSP – EE 4453 
    Applied Engineering Analysis I – EGR 2323 
    Applied Engineering Analysis II – EGR 3323