{"id":13,"date":"2017-07-07T20:21:07","date_gmt":"2017-07-07T20:21:07","guid":{"rendered":"http:\/\/utsaengineer.wpengine.com\/faculty-page-example\/?page_id=13"},"modified":"2025-06-21T09:32:21","modified_gmt":"2025-06-21T14:32:21","slug":"research","status":"publish","type":"page","link":"https:\/\/ceid.utsa.edu\/agrigoryan\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

Research<\/strong> in Signal and Image Processing, Theory and Methods:<\/span><\/p>\n

Quantum Computing in Image Processing<\/strong><\/em><\/a>: Quantum signal\/image representation and processing. Algorithms of the quantum Fourier transform, quantum image gradients.<\/span><\/p>\n

Quantum Multi-Qubit Operations \/ Gates<\/strong><\/em><\/a>: New arithmetic on qubits – multiplication and division of qubits. The quantum circuits of any gate without permutations and CNOTs, effective QR-decompositions of unitary matrices.<\/span><\/p>\n

Quaternion Imaging<\/strong><\/em><\/a>: Image enhancement, quaternion gradients, quaternion\u00a0 2-D convolution. Quaternion optimal filters (quaternion Wiener filter).<\/span><\/p>\n

Quaternion Commutative (2,2)-model<\/strong><\/em><\/a>:\u00a0 Quaternion algebra and DSP fundamental properties, commutative quaternions: Quaternion convolution, correlation, and Fourier transform .<\/span><\/p>\n

Methods of Computed Tomography<\/a>:<\/i><\/b> Image reconstruction from parallel projections, Solution of the problem<\/a> with a finite number of projections. Principle of superposition by direction images.<\/span><\/p>\n

Fast algorithms:<\/b><\/i> Quantum Fourier Transform<\/a>, Quaternion 1-D and 2-D discrete Fourier transforms. Fast Fourier, Hartley, Hadamard, and cosine transforms.<\/span><\/p>\n

Tensor and paired representations<\/a>:<\/b><\/i> 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 were used in many publications by different names, such as “discrete, finite, periodic, orthogonal, and generalized Radon, and mojette transforms.”<\/i><\/span><\/p>\n

Fourier analysis and Multiresolution<\/a>:<\/i><\/b> Resolution map, image compression. Robust optimal filters<\/a>. Optimal (Wiener) filtration<\/a>. Image cryptography.<\/span><\/p>\n

Image enhancement<\/a>:<\/strong><\/em> Grayscale and color image enhancement in different color model, including in the quaternion space. Measures of image enhancement.\u00a0<\/span><\/p>\n

Elliptic discrete Fourier transforms<\/a>:<\/i><\/b> Two classes of transforms which generalize the known concept of the DFT and rotate data around the ellipses, not circles.<\/span><\/p>\n

Signal-induced Heap transforms<\/a>:<\/i><\/b> Fast unitary transforms which are generated by given signals. Angular representation. Triangularization of square matrices. QR-decomposition of real<\/a> and complex<\/a> matrices.<\/span><\/p>\n

Golden ratio function<\/a>:<\/strong><\/em> Theory of the golden ratio, the golden equation, and similarity fields in the multi-dimension vector space.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Research in Signal and Image Processing, Theory and Methods: Quantum Computing in Image Processing: Quantum signal\/image representation and processing. Algorithms of the quantum Fourier transform, quantum image gradients. Quantum Multi-Qubit Operations \/ Gates: New arithmetic on qubits – multiplication and division of qubits. The quantum circuits of any gate without permutations and CNOTs, effective QR-decompositions … <\/p>\n

Continue reading “Research”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-13","page","type-page","status-publish","hentry"],"yoast_head":"\nResearch - Artyom (Art) Grigoryan<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ceid.utsa.edu\/agrigoryan\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Artyom (Art) Grigoryan\" \/>\n<meta property=\"og:description\" content=\"Research in Signal and Image Processing, Theory and Methods: Quantum Computing in Image Processing: Quantum signal\/image representation and processing. 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