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An hybrid denoising algorithm based on directional wavelet packets

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Abstract

The paper presents an image denoising algorithm by combining a method that is based on directional quasi-analytic wavelet packets (qWPs) with the popular BM3D algorithm. The qWP-based denoising algorithm (qWPdn) consists of decomposition of the degraded image, application of adaptive localized soft thresholding to the transform coefficients using the Bivariate Shrinkage methodology, and restoration of the image from the thresholded coefficients from several decomposition levels. The combined method consists of several iterations of qWPdn and BM3D algorithms, where at each iteration the output from one algorithm updates the input to the other. The proposed methodology couples the qWPdn capabilities to capture edges and fine texture patterns even in the severely corrupted images with utilizing the sparsity in real images and self-similarity of patches in the image that is inherent in the BM3D. Multiple experiments, which compared the proposed methodology performance with the performance of six state-of-the-art denoising algorithms, confirmed that the combined algorithm was quite competitive.

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Notes

  1. The index n refers to the number of filters in the underlying one-dimensional complex tight framelet filter bank.

  2. \(s_{+}{\mathop {=}\limits ^{{\textit{def}}}}\max \{s, 0\}\).

  3. $$\begin{aligned}&{\textit{PSNR}}(\mathbf {x},{\tilde{\mathbf {x}}}){\mathop {=}\limits ^{{\textit{def}}}}10\log _{10}\left( \frac{K\,255^2}{\sum _{k=1}^K(x_{k}-\tilde{x}_{k})^2}\right) \; dB. \end{aligned}$$
    (3.2)

  4. For the “Seismic” image upqWP instead of upBM3D

  5. Averaged results from upBM3D are almost identical to those from hybrid algorithm.

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Acknowledgements

This research was partially supported by the Israel Science Foundation (ISF, 1556/17), Blavatnik Computer Science Research Fund Israel Ministry of Science and Technology 3-13601 and 3-14481.

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel

    Amir Averbuch, Valery Zheludev & Moshe Salhov

  2. Faculty of Mathematical Information Technology, University of Jyväskylä, Agora, Jyväskylä, Finland

    Pekka Neittaanmäki

  3. School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel

    Jonathan Hauser

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  1. Amir Averbuch
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Correspondence to Amir Averbuch.

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Appendix: Matlab code for calculation of number of different orientations of real qWPs

Appendix: Matlab code for calculation of number of different orientations of real qWPs

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Averbuch, A., Neittaanmäki, P., Zheludev, V. et al. An hybrid denoising algorithm based on directional wavelet packets. Multidim Syst Sign Process 33, 1151–1183 (2022). https://doi.org/10.1007/s11045-022-00836-w

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