{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T21:49:11Z","timestamp":1781819351126,"version":"3.54.5"},"reference-count":60,"publisher":"SPIE","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,3,16]]},"DOI":"10.1117\/12.2083389","type":"proceedings-article","created":{"date-parts":[[2015,3,16]],"date-time":"2015-03-16T12:59:36Z","timestamp":1426510776000},"page":"939910","source":"Crossref","is-referenced-by-count":3,"title":["New 2D discrete Fourier transforms in image processing"],"prefix":"10.1117","volume":"9399","author":[{"given":"Artyom M.","family":"Grigoryan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sos S.","family":"Agaian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"189","reference":[{"key":"c1","article-title":"Fundamentals of digital image processing","author":"Jain","year":"1989"},{"key":"c2","article-title":"Theory and application of digital signal processing","author":"Rabiner","year":"1975"},{"issue":"1168","key":"c3","article-title":"Hadamard matrices and their applications","author":"Agaian","year":"1985"},{"key":"c4","doi-asserted-by":"publisher","DOI":"10.1117\/3.890094"},{"key":"c5","doi-asserted-by":"crossref","DOI":"10.1201\/9781482276329","article-title":"Multidimensional Discrete Unitary Transforms: Representation, Partitioning and Algorithms","author":"Grigoryan","year":"2003"},{"key":"c6","first-page":"1073","article-title":"Nonlinear approach of construction of fast unitary transforms","author":"Grigoryan","year":"2006, Princeton"},{"key":"c7","first-page":"236","article-title":"New method of calculation of reversible integer 1D DCTs","author":"Grigoryan","year":"2005"},{"key":"c8","doi-asserted-by":"publisher","DOI":"10.1117\/12.728383"},{"key":"c9","first-page":"24","article-title":"Discrete signal induced unitary transforms","author":"Grigoryan","year":"2008"},{"key":"c10","doi-asserted-by":"publisher","DOI":"10.1117\/12.728386"},{"key":"c11","first-page":"2","article-title":"A novel method of filtration by the discrete heap transforms","author":"Grigoryan","year":"2014"},{"issue":"1","key":"c12","first-page":"1","article-title":"Image and audio signal filtration with discrete Heap transforms","volume":"1","author":"Grigoryan","year":"2014"},{"issue":"2","key":"c13","first-page":"1","article-title":"New method of signal denoising by the paired transform","volume":"1","author":"Grigoryan","year":"2014"},{"key":"c14","first-page":"565","article-title":"Fast signal-induced transforms in image enhancement","author":"Naghdali","year":"Oct 2009"},{"key":"c15","first-page":"73510H","article-title":"Fast unitary heap transforms: theory and application in cryptography","author":"Grigoryan","year":"2009"},{"key":"c16","article-title":"Fast algorithms for digital signal processing","author":"Blahut","year":"1985"},{"key":"c17","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(90)90158-U"},{"key":"c18","first-page":"26","article-title":"An one-dimensional unitary transformation computation","author":"Grigoryan","year":"1994"},{"issue":"8","key":"c19","first-page":"100","article-title":"Algorithm of computing the 1-D discrete Hadamard transform","volume":"34","author":"Grigoryan","year":"1991"},{"issue":"9","key":"c20","first-page":"1407","article-title":"New algorithms for calculating discrete Fourier transforms","volume":"26","author":"Grigoryan","year":"1986"},{"issue":"1","key":"c21","first-page":"21","article-title":"Two-dimensional Fourier transform in the tensor presentation and new orthogonal fonctions","author":"Grigoryan","year":"1986"},{"key":"c22","first-page":"49","article-title":"An algorithm for computing the two-dimensional Fourier transform of equal orders","author":"Grigoryan","year":"1988"},{"issue":"10","key":"c23","first-page":"1576","article-title":"An algorithm for computing the discrete Fourier transform with arbitrary orders","volume":"30","author":"Grigoryan","year":"1991"},{"issue":"1","key":"c24","first-page":"16","article-title":"Discrete Unitary Transforms and Their Relation to Coverings of Fundamental Periods: Parts-1,2","volume":"1","author":"Grigoryan","year":"1994"},{"key":"c25","doi-asserted-by":"publisher","DOI":"10.1109\/78.815487"},{"key":"c26","doi-asserted-by":"publisher","DOI":"10.1109\/78.902116"},{"key":"c27","doi-asserted-by":"publisher","DOI":"10.1201\/9781439801383"},{"key":"c28","doi-asserted-by":"publisher","DOI":"10.1117\/1.3483906"},{"key":"c29","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-006-5150-0"},{"key":"c30","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2007.898784"},{"key":"c31","first-page":"359","article-title":"Three algorithms for computing the 2-D discrete Hartley transform","volume":"2","author":"Grigoryan","year":"2000"},{"key":"c32","article-title":"Implementation of FFT by using MATLAB: SIMULINK on Xilinx Virtex-4 FPGAs: Performance of a Paired Transform Based FFT","author":"Narayanam","year":"2013"},{"issue":"10","key":"c33","first-page":"72","article-title":"Implementation of FFT by using MATLAB: SIMULINK on Xilinx Virtex-4 FPGAs: Performance of a Paired Transform Based FFT","volume":"3","author":"Ranganadh","year":"2013"},{"key":"c34","first-page":"423","article-title":"Case study of Grigoryan FFT onto FPGAs and DSPs, TMS320C6X DSPs and Virtex II Pro FPGAs","author":"Ranganadh","year":"2012"},{"key":"c35","doi-asserted-by":"publisher","DOI":"10.1109\/ICSMC.2009.5346084"},{"key":"c36","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0235-1"},{"key":"c37","first-page":"4436","article-title":"Reversible Integer 2-D Discrete Fourier Transform by Control Bits","author":"Dursun","year":"2010"},{"key":"c38","doi-asserted-by":"publisher","DOI":"10.1201\/CRCELEENGHBK"},{"key":"c39","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2011.2128334"},{"key":"c40","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-009-0141-6"},{"key":"c41","doi-asserted-by":"publisher","DOI":"10.1201\/b13007"},{"key":"c42","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456326"},{"key":"c43","first-page":"97","article-title":"Generalized orthogonal Haar systems. Synthesis, metric and computing Properties","volume":"1","author":"Agaian","year":"1987"},{"issue":"5","key":"c44","first-page":"647","article-title":"Relations between Haar and Walsh\/Hadamard transforms","volume":"60","author":"Fino","year":"1972"},{"key":"c45","doi-asserted-by":"publisher","DOI":"10.1109\/45.666645"},{"key":"c46","unstructured":"Kai, Hwang, Advanced Computed Architecture: Parallelism, Scalability, Programmahility."},{"issue":"3","key":"c47","first-page":"146","article-title":"Advances and Problems of the Fast Orthogonal Transforms for Signal-Images Processing Applications (part 1)","author":"Agaian","year":"1990"},{"key":"c48","unstructured":"L. Rabiner and B. Gold, Theory and application of digital signal processing, Prentice-Hall Inc., 1975."},{"key":"c49","doi-asserted-by":"publisher","DOI":"10.1109\/83.908502"},{"key":"c50","first-page":"19","article-title":"A new measure of image enhancement","author":"Agaian","year":"2000"},{"key":"c51","doi-asserted-by":"publisher","DOI":"10.1016\/S1076-5670(04)30002-9"},{"key":"c52","doi-asserted-by":"publisher","DOI":"10.1117\/12.473063"},{"key":"c53","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2006.881927"},{"key":"c54","doi-asserted-by":"publisher","DOI":"10.1117\/12.669674"},{"key":"c55","doi-asserted-by":"publisher","DOI":"10.1117\/1.1428292"},{"key":"c56","article-title":"FISH on tissue microarrays: Towards automated analysis of genetic alterations in thousands of tumors with multiple probes","author":"Bubendorf","year":"January 30 - February 1, 2000"},{"key":"c57","first-page":"1830","article-title":"Quaternion-Fourier transforms for analysis of 2-dimensional linear time-invariant partial differential systems","volume":"1-4","author":"Ell","year":"1993"},{"key":"c58","first-page":"12","article-title":"Alpha-rooting method of color image enhancement by discrete quaternion Fourier transform","author":"Grigoryan","year":"2014"},{"issue":"3","key":"c59","first-page":"23","article-title":"Retooling of color imaging in the quaternion algebra","volume":"1","author":"Grigoryan","year":"2014"},{"key":"c60","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2014.11.019"}],"event":{"name":"IS&T\/SPIE Electronic Imaging","location":"San Francisco, California, United States"},"container-title":["SPIE Proceedings","Image Processing: Algorithms and Systems XIII"],"original-title":[],"deposited":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T18:22:05Z","timestamp":1538504525000},"score":1,"resource":{"primary":{"URL":"http:\/\/proceedings.spiedigitallibrary.org\/proceeding.aspx?doi=10.1117\/12.2083389"}},"subtitle":[],"editor":[{"given":"Karen O.","family":"Egiazarian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]},{"given":"Sos S.","family":"Agaian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]},{"given":"Atanas P.","family":"Gotchev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2015,3,16]]},"references-count":60,"URL":"https:\/\/doi.org\/10.1117\/12.2083389","relation":{},"ISSN":["0277-786X"],"issn-type":[{"value":"0277-786X","type":"print"}],"subject":[],"published":{"date-parts":[[2015,3,16]]}}}