Sparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transforms
buir.contributor.author | Haldun M. Özaktaş | |
dc.citation.epage | 255 | en_US |
dc.citation.spage | 247 | en_US |
dc.citation.volumeNumber | 77 | en_US |
dc.contributor.author | Koç A. | |
dc.contributor.author | Bartan, B. | |
dc.contributor.author | Gundogdu, E. | |
dc.contributor.author | Çukur, T. | |
dc.contributor.author | Özaktaş, Haldun M. | |
dc.date.accessioned | 2018-04-12T11:12:14Z | |
dc.date.available | 2018-04-12T11:12:14Z | |
dc.date.issued | 2017 | en_US |
dc.department | Department of Electrical and Electronics Engineering | en_US |
dc.department | National Magnetic Resonance Research Center (UMRAM) | en_US |
dc.description.abstract | Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider two- and three-dimensional images, and investigate various multi-dimensional transforms in terms of the compressibility of the resultant coefficients. Specifically, we compare the fractional Fourier (FRT) and linear canonical transforms (LCT), which are generalized versions of the Fourier transform (FT), as well as Hartley and simplified fractional Hartley transforms, which differ from corresponding Fourier transforms in that they produce real outputs for real inputs. We also examine a cascade approach to improve transform-domain sparsity, where the Haar wavelet transform is applied following an initial Hartley transform. To compare the various methods, images are recovered from a subset of coefficients in the respective transform domains. The number of coefficients that are retained in the subset are varied systematically to examine the level of signal sparsity in each transform domain. Recovery performance is assessed via the structural similarity index (SSIM) and mean squared error (MSE) in reference to original images. Our analyses show that FRT and LCT transform yield the most sparse representations among the tested transforms as dictated by the improved quality of the recovered images. Furthermore, the cascade approach improves transform-domain sparsity among techniques applied on small image patches. | en_US |
dc.description.provenance | Made available in DSpace on 2018-04-12T11:12:14Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2017 | en |
dc.embargo.release | 2019-07-01 | en_US |
dc.identifier.doi | 10.1016/j.eswa.2017.01.046 | en_US |
dc.identifier.issn | 0957-4174 | |
dc.identifier.uri | http://hdl.handle.net/11693/37395 | |
dc.language.iso | English | en_US |
dc.publisher | Elsevier Ltd | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1016/j.eswa.2017.01.046 | en_US |
dc.source.title | Expert Systems with Applications | en_US |
dc.subject | Compressibility | en_US |
dc.subject | Fractional fourier transform | en_US |
dc.subject | Haar wavelet transform | en_US |
dc.subject | Image representation | en_US |
dc.subject | Linear canonical transforms | en_US |
dc.subject | Simplified fractional hartley transform | en_US |
dc.subject | Sparsifying transforms | en_US |
dc.subject | Transform domain coding | en_US |
dc.title | Sparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transforms | en_US |
dc.type | Article | en_US |
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