Sparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transforms

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage255en_US
dc.citation.spage247en_US
dc.citation.volumeNumber77en_US
dc.contributor.authorKoç A.
dc.contributor.authorBartan, B.
dc.contributor.authorGundogdu, E.
dc.contributor.authorÇukur, T.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2018-04-12T11:12:14Z
dc.date.available2018-04-12T11:12:14Z
dc.date.issued2017en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.departmentNational Magnetic Resonance Research Center (UMRAM)en_US
dc.description.abstractSparse 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.embargo.release2019-07-01en_US
dc.identifier.doi10.1016/j.eswa.2017.01.046en_US
dc.identifier.issn0957-4174
dc.identifier.urihttp://hdl.handle.net/11693/37395
dc.language.isoEnglishen_US
dc.publisherElsevier Ltden_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.eswa.2017.01.046en_US
dc.source.titleExpert Systems with Applicationsen_US
dc.subjectCompressibilityen_US
dc.subjectFractional fourier transformen_US
dc.subjectHaar wavelet transformen_US
dc.subjectImage representationen_US
dc.subjectLinear canonical transformsen_US
dc.subjectSimplified fractional hartley transformen_US
dc.subjectSparsifying transformsen_US
dc.subjectTransform domain codingen_US
dc.titleSparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transformsen_US
dc.typeArticleen_US

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Department of Electrical and Electronics Engineering
National Magnetic Resonance Research Center (UMRAM)