Image compression using fractal multiwavelet transform

Abstract

Multiwavelets occur in wavelet theory for more general multiresolution analysis (MRA) using several scaling functions. The muliwavelets feature orthogonality, short support, symmetry, approximation order and regularity at a time which is not possible by using only a single wavelet system. In the present work, theory of MRA and wavelet using several scaling functions is reviewed to define Discrete Multiwavelet Transform and Fractal Multiwavelet Transform in matrix form, using a multifilter. As an application the defined transforms are applied to an image for its compression and the resulting entropy and PSNR values are compared with those occurring with earlier used transforms like Haar and D4 transforms.

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Correspondence to Md. Nasim Akhtar.

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Akhtar, M.N., Guru Prem Prasad, M. & Kapoor, G.P. Image compression using fractal multiwavelet transform. J Anal 28, 769–789 (2020). https://doi.org/10.1007/s41478-019-00198-w

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Keywords

  • Fractal interpolation functions
  • Multiresolution analysis
  • Multiwavelets
  • Image compression

Mathematics Subject Classification

  • 28A80
  • 42C40
  • 94A08