Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm

Hariony Bienvenu Rakotonirina; Sarobidy Nomenjanahary Razafitsalama Fin Luc; Marie Emile Randrianandrasana

doi:doi:10.11648/j.cssp.20251201.12

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Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm

Hariony Bienvenu Rakotonirina^*

, Sarobidy Nomenjanahary Razafitsalama Fin Luc

, Marie Emile Randrianandrasana

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 12, Issue 1)

Received: 1 October 2025 Accepted: 14 October 2025 Published: 31 October 2025

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Abstract

This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.

Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 12, Issue 1)
DOI	10.11648/j.cssp.20251201.12
Page(s)	8-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Compressive Sensing, Reverse Biorthogonal, CoSaMP, SP; ALISTA, Wavelet Transform

References

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[2]	Chen, X., Liu, J., Wang, Z., & Yin, W. Theoretical linear convergence of unfolded ISTA and its practical weights and thresholds. Advances in Neural Information Processing Systems, 2018, 31, 9061–9071. https://doi.org/10.48550/arXiv.1809.04137
[3]	Mallat, S. G. A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press, 2009. https://doi.org/10.1016/B978-0-12-374370-1.00001-0
[4]	Strang, G., & Nguyen, T. Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996. ISBN: 0-9614088-3-4
[5]	Zhang, J., Liu, Y., & Zhang, W. (2023). Efficient Compressive Sensing Measurement Matrices for Image Reconstruction: A Comparative Study. IEEE Transactions on Computational Imaging, 9, 412–425. https://doi.org/10.1109/TCI.2023.3267891
[6]	Chen, X., Liu, J., Wang, Z., & Yin, W. (2023). ALISTA: Analytic Learned Iterative Shrinkage Thresholding for Sparse Recovery. IEEE Transactions on Signal Processing, 71, 1285–1299. https://doi.org/10.1109/TSP.2023.3267452
[7]	Zhang, J., Liu, Y., & Zhang, W. (2024). Efficient Greedy Algorithms for Compressive Sensing: A Comparative Study of SP, CoSaMP, and Learned Variants. Signal Processing, 215, 109287. https://doi.org/10.1016/j.sigpro.2023.109287
[8]	Zhang, Y., Wang, L., & Liu, H. (2024). Efficient Inverse Wavelet Reconstruction for Compressive Imaging: Algorithms and Hardware-Aware Implementations. IEEE Transactions on Image Processing, 33, 1125–1138. https://doi.org/10.1109
[9]	Chen, M., Li, X., & Zhao, D. (2023). Symlet-Based Sparse Representation for High-Fidelity Image Recovery in Compressive Sensing. Signal Processing: Image Communication, 118, 116932. https://doi.org/10.1016/j.image.2023.116932
[10]	Wang, Y., Liu, Z., & Chen, H. (2024). Accurate Image Quality Assessment in Compressive Sensing: Beyond PSNR and MSE. IEEE Transactions on Image Processing, 33, 2105–2118. https://doi.org/10.1109/TIP.2024.3372109
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[12]	Liu, Y., Zhang, H., & Wang, Q. (2024). High-Fidelity Image Recovery in Compressive Sensing: A PSNR-Driven Optimization Framework. IEEE Transactions on Multimedia, 26, 3012–3025. https://doi.org/10.1109/TMM.2024.3368421
[13]	Patel, R., Gupta, S., & Mehta, K. (2023). Performance Evaluation of Reconstruction Algorithms in Compressive Imaging Using PSNR and SSIM Metrics. Journal of Visual Communication and Image Representation, 94, 103857. https://doi.org/10.1016
[14]	Wang, Z., & Bovik, A. C. (2023). Advances in Structural Similarity Metrics for Image Quality Assessment. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(8), 10212–10227. https://doi.org/10.1109/TPAMI.2023.3267890
[15]	Li, H., Liu, Y., & Zhang, J. (2024). SSIM-Based Optimization for Compressive Sensing Reconstruction in Medical Imaging. Medical Image Analysis, 92, 102987. https://doi.org/10.1016/j.media.2023.102987

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Rakotonirina, H. B., Luc, S. N. R. F., Randrianandrasana, M. E. (2025). Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Science Journal of Circuits, Systems and Signal Processing, 12(1), 8-15. https://doi.org/10.11648/j.cssp.20251201.12

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ACS Style

Rakotonirina, H. B.; Luc, S. N. R. F.; Randrianandrasana, M. E. Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Sci. J. Circuits Syst. Signal Process. 2025, 12(1), 8-15. doi: 10.11648/j.cssp.20251201.12

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AMA Style

Rakotonirina HB, Luc SNRF, Randrianandrasana ME. Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Sci J Circuits Syst Signal Process. 2025;12(1):8-15. doi: 10.11648/j.cssp.20251201.12

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@article{10.11648/j.cssp.20251201.12,
  author = {Hariony Bienvenu Rakotonirina and Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana},
  title = {Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm
},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {12},
  number = {1},
  pages = {8-15},
  doi = {10.11648/j.cssp.20251201.12},
  url = {https://doi.org/10.11648/j.cssp.20251201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20251201.12},
  abstract = {This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.
},
 year = {2025}
}

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TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm

AU  - Hariony Bienvenu Rakotonirina
AU  - Sarobidy Nomenjanahary Razafitsalama Fin Luc
AU  - Marie Emile Randrianandrasana
Y1  - 2025/10/31
PY  - 2025
N1  - https://doi.org/10.11648/j.cssp.20251201.12
DO  - 10.11648/j.cssp.20251201.12
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20251201.12
AB  - This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.

VL  - 12
IS  - 1
ER  -

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Author Information

Hariony Bienvenu Rakotonirina

Department of Telecommunication, High School Polytechnic of Antsirabe, Antsirabe, Madagascar

Contact Email

http://orcid.org/0009-0004-5054-736X
Sarobidy Nomenjanahary Razafitsalama Fin Luc

Department of Signal, Doctoral School of Engineering and Innovation Sciences and Techniques, Antananarivo, Madagascar

Contact Email

http://orcid.org/0009-0007-6451-1925
Marie Emile Randrianandrasana

Department of Telecommunication, High School Polytechnic of Antsirabe, Antsirabe, Madagascar

Contact Email

http://orcid.org/0009-0007-2595-5857

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Plain Text BibTeX RIS

APA Style

Rakotonirina, H. B., Luc, S. N. R. F., Randrianandrasana, M. E. (2025). Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Science Journal of Circuits, Systems and Signal Processing, 12(1), 8-15. https://doi.org/10.11648/j.cssp.20251201.12

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ACS Style

Rakotonirina, H. B.; Luc, S. N. R. F.; Randrianandrasana, M. E. Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Sci. J. Circuits Syst. Signal Process. 2025, 12(1), 8-15. doi: 10.11648/j.cssp.20251201.12

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AMA Style

Rakotonirina HB, Luc SNRF, Randrianandrasana ME. Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm. Sci J Circuits Syst Signal Process. 2025;12(1):8-15. doi: 10.11648/j.cssp.20251201.12

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@article{10.11648/j.cssp.20251201.12,
  author = {Hariony Bienvenu Rakotonirina and Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana},
  title = {Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm
},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {12},
  number = {1},
  pages = {8-15},
  doi = {10.11648/j.cssp.20251201.12},
  url = {https://doi.org/10.11648/j.cssp.20251201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20251201.12},
  abstract = {This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm

AU  - Hariony Bienvenu Rakotonirina
AU  - Sarobidy Nomenjanahary Razafitsalama Fin Luc
AU  - Marie Emile Randrianandrasana
Y1  - 2025/10/31
PY  - 2025
N1  - https://doi.org/10.11648/j.cssp.20251201.12
DO  - 10.11648/j.cssp.20251201.12
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 8
EP  - 15
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20251201.12
AB  - This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.

VL  - 12
IS  - 1
ER  -

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