Sparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transforms
Author
Koç A.
Bartan, B.
Gundogdu, E.
Çukur, T.
Haldun M. Özaktaş
Date
2017Source Title
Expert Systems with Applications
Print ISSN
0957-4174
Publisher
Elsevier Ltd
Volume
77
Pages
247 - 255
Language
English
Type
ArticleItem 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
CompressibilityFractional fourier transform
Haar wavelet transform
Image representation
Linear canonical transforms
Simplified fractional hartley transform
Sparsifying transforms
Transform domain coding
Permalink
http://hdl.handle.net/11693/37395Published Version (Please cite this version)
http://dx.doi.org/10.1016/j.eswa.2017.01.046Collections
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