# 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.