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Patch-ordering-based wavelet frame and its use in inverse problems.

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This study introduces a redundant tree-based wavelet transform (RTBWT) for image processing. RTBWT acts as a powerful regularizer, achieving state-of-the-art results in image denoising and deblurring.

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Area of Science:

  • Image processing
  • Signal processing
  • Applied mathematics

Background:

  • Redundant Tree-Based Wavelet Transform (RTBWT) was previously developed for high-dimensional data.
  • RTBWT was shown to be an effective image-adaptive transform robust to corruptions.

Purpose of the Study:

  • To utilize RTBWT as a sparsity-promoting regularizer in inverse image processing problems.
  • To analyze RTBWT as a frame expansion and derive its operators.
  • To demonstrate the effectiveness of RTBWT in image denoising and deblurring.

Main Methods:

  • Application of RTBWT as a regularizer in inverse problems.
  • Derivation of analysis and synthesis operators for the RTBWT frame expansion.
  • Implementation and evaluation of RTBWT for image denoising and deblurring.

Main Results:

  • The image representation using RTBWT is confirmed as a frame expansion.
  • RTBWT-based regularization yields state-of-the-art performance in image denoising.
  • RTBWT-based regularization achieves state-of-the-art performance in image deblurring.

Conclusions:

  • RTBWT is a powerful tool for inverse problems in image processing.
  • The derived frame operators enable effective image restoration.
  • RTBWT offers significant improvements for image denoising and deblurring tasks.