Research in Signal and Image Processing, Fast Transforms:

Quantum Computing: Quantum signal/image representation and processing. Algorithms of the quantum Fourier transform, quantum image gradients.

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

Quaternion Commutative (2,2)-model:  Quaternion algebra and DSP fundamental properties: Quaternion convolution, correlation, and Fourier transform .

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.

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

Tensor and paired representations: New methods of image and signal representations and processing by splitting-signals. Fast 1-D paired transform. These transforms I developed and first published in 1984-1986s and 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.

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

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