Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) 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.ajcst.20250804.14

Research Article |

| Peer-Reviewed

Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm

Hariony Bienvenu Rakotonirina^*

, Sarobidy Nomenjanahary Razafitsalama Fin Luc

, Marie Emile Randrianandrasana

Published in American Journal of Computer Science and Technology (Volume 8, Issue 4)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This work proposes an efficient image reconstruction method based on compressive sensing (CS), combining the level-4 Daubechies 4 (db4) discrete wavelet transform with three iterative reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach follows four key steps: (1) decomposing the original image via the db4 wavelet transform to obtain a sparse representation, (2) performing compressed sampling using a random measurement matrix, (3) reconstructing the sparse signal from the reduced measurements using one of the three optimization algorithms, and (4) recovering the final image through the inverse wavelet transform. Experimental evaluation uses the standard Lena image (200 × 200 pixels) and compares the performance of the three algorithms according to two criteria: reconstruction quality (measured by SSIM) and computational cost (reconstruction time in minutes), across sampling rates ranging from 10% to 60%. Results show that all three methods achieve very similar SSIM scores (up to >0.96 at 60%), indicating high structural fidelity regardless of the algorithm chosen. However, ALISTA stands out significantly for its temporal efficiency, particularly at low sampling rates (<0.1 minute at 10%), while CoSaMP exhibits high and unstable computation times (peaking at ~35 minutes at 40%). SP offers a stable, nearly linear increase in runtime but remains consistently slower than ALISTA. These results demonstrate that ALISTA provides the best trade-off between quality and speed. Thus, this study validates the value of coupling the db4 wavelet basis with modern, learned optimization algorithms for practical CS applications in image processing, where computational efficiency is as critical as reconstruction accuracy.

Published in	American Journal of Computer Science and Technology (Volume 8, Issue 4)
DOI	10.11648/j.ajcst.20250804.14
Page(s)	206-213
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, Daubechies, CoSaMP, SP, ALISTA, Wavelet Transform

References

[1]	Needell, D., & Tropp, J. A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 2009, 26(3), 301–321. https://doi.org/10.1016/j.acha.2008.07.002
[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.
[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
[11]	Gupta, A., & Singh, R. (2023). Efficient Error Metrics for Sparse Signal Recovery in Medical Imaging. Signal Processing, 212, 109145. https://doi.org/10.1016/j.sigpro.2023.109145
[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

Cite This Article

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 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. American Journal of Computer Science and Technology, 8(4), 206-213. https://doi.org/10.11648/j.ajcst.20250804.14

Copy | Download

ACS Style

Rakotonirina, H. B.; Luc, S. N. R. F.; Randrianandrasana, M. E. Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. Am. J. Comput. Sci. Technol. 2025, 8(4), 206-213. doi: 10.11648/j.ajcst.20250804.14

Copy | Download

AMA Style

Rakotonirina HB, Luc SNRF, Randrianandrasana ME. Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. Am J Comput Sci Technol. 2025;8(4):206-213. doi: 10.11648/j.ajcst.20250804.14

Copy | Download

@article{10.11648/j.ajcst.20250804.14,
  author = {Hariony Bienvenu Rakotonirina and Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana},
  title = {Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm
},
  journal = {American Journal of Computer Science and Technology},
  volume = {8},
  number = {4},
  pages = {206-213},
  doi = {10.11648/j.ajcst.20250804.14},
  url = {https://doi.org/10.11648/j.ajcst.20250804.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajcst.20250804.14},
  abstract = {This work proposes an efficient image reconstruction method based on compressive sensing (CS), combining the level-4 Daubechies 4 (db4) discrete wavelet transform with three iterative reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach follows four key steps: (1) decomposing the original image via the db4 wavelet transform to obtain a sparse representation, (2) performing compressed sampling using a random measurement matrix, (3) reconstructing the sparse signal from the reduced measurements using one of the three optimization algorithms, and (4) recovering the final image through the inverse wavelet transform. Experimental evaluation uses the standard Lena image (200 × 200 pixels) and compares the performance of the three algorithms according to two criteria: reconstruction quality (measured by SSIM) and computational cost (reconstruction time in minutes), across sampling rates ranging from 10% to 60%. Results show that all three methods achieve very similar SSIM scores (up to >0.96 at 60%), indicating high structural fidelity regardless of the algorithm chosen. However, ALISTA stands out significantly for its temporal efficiency, particularly at low sampling rates (<0.1 minute at 10%), while CoSaMP exhibits high and unstable computation times (peaking at ~35 minutes at 40%). SP offers a stable, nearly linear increase in runtime but remains consistently slower than ALISTA. These results demonstrate that ALISTA provides the best trade-off between quality and speed. Thus, this study validates the value of coupling the db4 wavelet basis with modern, learned optimization algorithms for practical CS applications in image processing, where computational efficiency is as critical as reconstruction accuracy.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) 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.ajcst.20250804.14
DO  - 10.11648/j.ajcst.20250804.14
T2  - American Journal of Computer Science and Technology
JF  - American Journal of Computer Science and Technology
JO  - American Journal of Computer Science and Technology
SP  - 206
EP  - 213
PB  - Science Publishing Group
SN  - 2640-012X
UR  - https://doi.org/10.11648/j.ajcst.20250804.14
AB  - This work proposes an efficient image reconstruction method based on compressive sensing (CS), combining the level-4 Daubechies 4 (db4) discrete wavelet transform with three iterative reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach follows four key steps: (1) decomposing the original image via the db4 wavelet transform to obtain a sparse representation, (2) performing compressed sampling using a random measurement matrix, (3) reconstructing the sparse signal from the reduced measurements using one of the three optimization algorithms, and (4) recovering the final image through the inverse wavelet transform. Experimental evaluation uses the standard Lena image (200 × 200 pixels) and compares the performance of the three algorithms according to two criteria: reconstruction quality (measured by SSIM) and computational cost (reconstruction time in minutes), across sampling rates ranging from 10% to 60%. Results show that all three methods achieve very similar SSIM scores (up to >0.96 at 60%), indicating high structural fidelity regardless of the algorithm chosen. However, ALISTA stands out significantly for its temporal efficiency, particularly at low sampling rates (<0.1 minute at 10%), while CoSaMP exhibits high and unstable computation times (peaking at ~35 minutes at 40%). SP offers a stable, nearly linear increase in runtime but remains consistently slower than ALISTA. These results demonstrate that ALISTA provides the best trade-off between quality and speed. Thus, this study validates the value of coupling the db4 wavelet basis with modern, learned optimization algorithms for practical CS applications in image processing, where computational efficiency is as critical as reconstruction accuracy.

VL  - 8
IS  - 4
ER  -

Copy | Download

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

Download PDF

Submit an Article

Sections

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 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. American Journal of Computer Science and Technology, 8(4), 206-213. https://doi.org/10.11648/j.ajcst.20250804.14

Copy | Download

ACS Style

Rakotonirina, H. B.; Luc, S. N. R. F.; Randrianandrasana, M. E. Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. Am. J. Comput. Sci. Technol. 2025, 8(4), 206-213. doi: 10.11648/j.ajcst.20250804.14

Copy | Download

AMA Style

Rakotonirina HB, Luc SNRF, Randrianandrasana ME. Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm. Am J Comput Sci Technol. 2025;8(4):206-213. doi: 10.11648/j.ajcst.20250804.14

Copy | Download

@article{10.11648/j.ajcst.20250804.14,
  author = {Hariony Bienvenu Rakotonirina and Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana},
  title = {Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) Discrete Wavelet Transform And SP, CoSaMP and ALISTA Algorithm
},
  journal = {American Journal of Computer Science and Technology},
  volume = {8},
  number = {4},
  pages = {206-213},
  doi = {10.11648/j.ajcst.20250804.14},
  url = {https://doi.org/10.11648/j.ajcst.20250804.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajcst.20250804.14},
  abstract = {This work proposes an efficient image reconstruction method based on compressive sensing (CS), combining the level-4 Daubechies 4 (db4) discrete wavelet transform with three iterative reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach follows four key steps: (1) decomposing the original image via the db4 wavelet transform to obtain a sparse representation, (2) performing compressed sampling using a random measurement matrix, (3) reconstructing the sparse signal from the reduced measurements using one of the three optimization algorithms, and (4) recovering the final image through the inverse wavelet transform. Experimental evaluation uses the standard Lena image (200 × 200 pixels) and compares the performance of the three algorithms according to two criteria: reconstruction quality (measured by SSIM) and computational cost (reconstruction time in minutes), across sampling rates ranging from 10% to 60%. Results show that all three methods achieve very similar SSIM scores (up to >0.96 at 60%), indicating high structural fidelity regardless of the algorithm chosen. However, ALISTA stands out significantly for its temporal efficiency, particularly at low sampling rates (<0.1 minute at 10%), while CoSaMP exhibits high and unstable computation times (peaking at ~35 minutes at 40%). SP offers a stable, nearly linear increase in runtime but remains consistently slower than ALISTA. These results demonstrate that ALISTA provides the best trade-off between quality and speed. Thus, this study validates the value of coupling the db4 wavelet basis with modern, learned optimization algorithms for practical CS applications in image processing, where computational efficiency is as critical as reconstruction accuracy.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using The Level 4 Daubechies 4 (db4) 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.ajcst.20250804.14
DO  - 10.11648/j.ajcst.20250804.14
T2  - American Journal of Computer Science and Technology
JF  - American Journal of Computer Science and Technology
JO  - American Journal of Computer Science and Technology
SP  - 206
EP  - 213
PB  - Science Publishing Group
SN  - 2640-012X
UR  - https://doi.org/10.11648/j.ajcst.20250804.14
AB  - This work proposes an efficient image reconstruction method based on compressive sensing (CS), combining the level-4 Daubechies 4 (db4) discrete wavelet transform with three iterative reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach follows four key steps: (1) decomposing the original image via the db4 wavelet transform to obtain a sparse representation, (2) performing compressed sampling using a random measurement matrix, (3) reconstructing the sparse signal from the reduced measurements using one of the three optimization algorithms, and (4) recovering the final image through the inverse wavelet transform. Experimental evaluation uses the standard Lena image (200 × 200 pixels) and compares the performance of the three algorithms according to two criteria: reconstruction quality (measured by SSIM) and computational cost (reconstruction time in minutes), across sampling rates ranging from 10% to 60%. Results show that all three methods achieve very similar SSIM scores (up to >0.96 at 60%), indicating high structural fidelity regardless of the algorithm chosen. However, ALISTA stands out significantly for its temporal efficiency, particularly at low sampling rates (<0.1 minute at 10%), while CoSaMP exhibits high and unstable computation times (peaking at ~35 minutes at 40%). SP offers a stable, nearly linear increase in runtime but remains consistently slower than ALISTA. These results demonstrate that ALISTA provides the best trade-off between quality and speed. Thus, this study validates the value of coupling the db4 wavelet basis with modern, learned optimization algorithms for practical CS applications in image processing, where computational efficiency is as critical as reconstruction accuracy.

VL  - 8
IS  - 4
ER  -

Copy | Download