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

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      Embargo Lift Date: 2019-07-01
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      Author
      Koç A.
      Bartan, B.
      Gundogdu, E.
      Çukur, T.
      Haldun M. Özaktaş
      Date
      2017
      Source Title
      Expert Systems with Applications
      Print ISSN
      0957-4174
      Publisher
      Elsevier Ltd
      Volume
      77
      Pages
      247 - 255
      Language
      English
      Type
      Article
      Item Usage Stats
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      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.
      Keywords
      Compressibility
      Fractional fourier transform
      Haar wavelet transform
      Image representation
      Linear canonical transforms
      Simplified fractional hartley transform
      Sparsifying transforms
      Transform domain coding
      Permalink
      http://hdl.handle.net/11693/37395
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.eswa.2017.01.046
      Collections
      • Department of Electrical and Electronics Engineering 3632
      • National Magnetic Resonance Research Center (UMRAM) 202
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