**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.