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The number of splitting-signals is 3N\u22122, and they have different durations, carry the spectral information of the image in disjoint subsets of frequency points, and can be calculated from the projection data along one of 3N\/2 angles. The paired representation leads to the image composition by a set of 3N\u22122 direction images, which defines the directed multiresolution and contains periodic components of the image. We also introduce the concept of the resolution map, as a result of uniting all direction images into log2 N series. In the resolution map, all different periodic components (or structures) of the image are packed into a N\u00d7N matrix, which can be used for image processing in enhancement, filtration, and compression<\/jats:p>","DOI":"10.1117\/1.3483906","type":"journal-article","created":{"date-parts":[[2010,8,31]],"date-time":"2010-08-31T18:19:56Z","timestamp":1283278796000},"page":"1-14","source":"Crossref","is-referenced-by-count":19,"title":["Two-dimensional images in frequency-time representation: direction images and resolution map"],"prefix":"10.1117","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6683-0064","authenticated-orcid":false,"given":"Artyom M.","family":"Grigoryan","sequence":"first","affiliation":[{"name":"The Univ. of Texas at San Antonio"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nan","family":"Du","sequence":"additional","affiliation":[{"name":"The Univ. of Texas at San Antonio"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"189","reference":[{"key":"10.1117\/1.3483906_r1","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1966.4920"},{"key":"10.1117\/1.3483906_r2","doi-asserted-by":"crossref","unstructured":"S. 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