Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms

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

doi:doi:10.11648/j.ajcst.20250804.15

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Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms

Sarobidy Nomenjanahary Razafitsalama Fin Luc

, Marie Emile Randrianandrasana

, Hariony Bienvenu Rakotonirina^*

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

Received: 20 October 2025 Accepted: 3 November 2025 Published: 9 December 2025

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Abstract

This paper proposes an efficient image reconstruction method in compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) with the Daubechies 7 (db7) wavelet and three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT), whose implementation relies on computationally expensive convolution operations, the LWT enables a faster sparse representation while preserving the sparsity properties essential for reconstruction. The proposed methodology is based on a key observation: among the four subbands generated by the LWT: approximation (CA) and detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Consequently, compression is applied exclusively to these detail components, while the approximation subband is kept intact, thereby preserving critical low-frequency information. Experiments were conducted on two types of images a natural image (Lena) and a medical image (MRI) across various resolutions (from 200×200 to 512×512 pixels) and sampling rates (from 10% to 80%). Performance was evaluated using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently show that ALISTA significantly outperforms SP and CoSaMP in both reconstruction quality and speed. At 80% sampling, ALISTA achieves an SSIM of 0.9936 for Lena and 0.9764 for MRI, compared to approximately 0.975 and 0.934 for the other methods, respectively. Moreover, ALISTA maintains extremely low reconstruction times under 4 seconds even for 512×512-pixel images. This research confirm that the ALISTA + LWT/db7 combination achieves the best quality–speed trade-off and exhibits robustness regardless of image type or size.

Published in	American Journal of Computer Science and Technology (Volume 8, Issue 4)
DOI	10.11648/j.ajcst.20250804.15
Page(s)	214-227
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, 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]	Sweldens, W. The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets. Applied and Computational Harmonic Analysis, vol. 3, no. 2, pp. 186-200, 1996. https://doi.org/10.1006/acha.1996.0015
[4]	Daubechies, I.; Sweldens, W. Factoring Wavelet Transforms into Lifting Steps. Journal of Fourier Analysis and Applications, vol. 4, no. 3, pp. 247-269, 1998. https://doi.org/10.1007/BF02476026
[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]	Claypoole, R. L., Davis, G. M., Sweldens, W., and Baraniuk, R. G. Nonlinear Wavelet Transforms for Image Coding via Lifting. IEEE Transactions on Image Processing, 12(12): 1449-1459, 2003. https://doi.org/10.1109/TIP.2003.819865
[9]	Arivazhagan, S., Prema, G., (2025) Novel Image Fusion based on Hybrid DWT and LWT Transform, Journal of Advanced Research in Dynamical and Control Systems, https://doi.org/10.5373/JARDCS/V12SP5/20201800
[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]	Simoes, W., De Sa, M., (2024). PSNR and SSIM: Evaluation of the Imperceptibility Quality of Images Transmitted over Wireless Networks. https://doi.org/10.1016/j.procs.2024.11.134
[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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APA Style

Luc, S. N. R. F., Randrianandrasana, M. E., Rakotonirina, H. B. (2025). Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. American Journal of Computer Science and Technology, 8(4), 214-227. https://doi.org/10.11648/j.ajcst.20250804.15

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ACS Style

Luc, S. N. R. F.; Randrianandrasana, M. E.; Rakotonirina, H. B. Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. Am. J. Comput. Sci. Technol. 2025, 8(4), 214-227. doi: 10.11648/j.ajcst.20250804.15

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AMA Style

Luc SNRF, Randrianandrasana ME, Rakotonirina HB. Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. Am J Comput Sci Technol. 2025;8(4):214-227. doi: 10.11648/j.ajcst.20250804.15

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@article{10.11648/j.ajcst.20250804.15,
  author = {Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana and Hariony Bienvenu Rakotonirina},
  title = {Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms},
  journal = {American Journal of Computer Science and Technology},
  volume = {8},
  number = {4},
  pages = {214-227},
  doi = {10.11648/j.ajcst.20250804.15},
  url = {https://doi.org/10.11648/j.ajcst.20250804.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajcst.20250804.15},
  abstract = {This paper proposes an efficient image reconstruction method in compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) with the Daubechies 7 (db7) wavelet and three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT), whose implementation relies on computationally expensive convolution operations, the LWT enables a faster sparse representation while preserving the sparsity properties essential for reconstruction. The proposed methodology is based on a key observation: among the four subbands generated by the LWT: approximation (CA) and detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Consequently, compression is applied exclusively to these detail components, while the approximation subband is kept intact, thereby preserving critical low-frequency information. Experiments were conducted on two types of images a natural image (Lena) and a medical image (MRI) across various resolutions (from 200×200 to 512×512 pixels) and sampling rates (from 10% to 80%). Performance was evaluated using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently show that ALISTA significantly outperforms SP and CoSaMP in both reconstruction quality and speed. At 80% sampling, ALISTA achieves an SSIM of 0.9936 for Lena and 0.9764 for MRI, compared to approximately 0.975 and 0.934 for the other methods, respectively. Moreover, ALISTA maintains extremely low reconstruction times under 4 seconds even for 512×512-pixel images. This research confirm that the ALISTA + LWT/db7 combination achieves the best quality–speed trade-off and exhibits robustness regardless of image type or size.},
 year = {2025}
}

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TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms
AU  - Sarobidy Nomenjanahary Razafitsalama Fin Luc
AU  - Marie Emile Randrianandrasana
AU  - Hariony Bienvenu Rakotonirina
Y1  - 2025/12/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ajcst.20250804.15
DO  - 10.11648/j.ajcst.20250804.15
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  - 214
EP  - 227
PB  - Science Publishing Group
SN  - 2640-012X
UR  - https://doi.org/10.11648/j.ajcst.20250804.15
AB  - This paper proposes an efficient image reconstruction method in compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) with the Daubechies 7 (db7) wavelet and three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT), whose implementation relies on computationally expensive convolution operations, the LWT enables a faster sparse representation while preserving the sparsity properties essential for reconstruction. The proposed methodology is based on a key observation: among the four subbands generated by the LWT: approximation (CA) and detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Consequently, compression is applied exclusively to these detail components, while the approximation subband is kept intact, thereby preserving critical low-frequency information. Experiments were conducted on two types of images a natural image (Lena) and a medical image (MRI) across various resolutions (from 200×200 to 512×512 pixels) and sampling rates (from 10% to 80%). Performance was evaluated using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently show that ALISTA significantly outperforms SP and CoSaMP in both reconstruction quality and speed. At 80% sampling, ALISTA achieves an SSIM of 0.9936 for Lena and 0.9764 for MRI, compared to approximately 0.975 and 0.934 for the other methods, respectively. Moreover, ALISTA maintains extremely low reconstruction times under 4 seconds even for 512×512-pixel images. This research confirm that the ALISTA + LWT/db7 combination achieves the best quality–speed trade-off and exhibits robustness regardless of image type or size.
VL  - 8
IS  - 4
ER  -

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Author Information

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
Hariony Bienvenu Rakotonirina

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

Contact Email

http://orcid.org/0009-0004-5054-736X

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APA Style

Luc, S. N. R. F., Randrianandrasana, M. E., Rakotonirina, H. B. (2025). Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. American Journal of Computer Science and Technology, 8(4), 214-227. https://doi.org/10.11648/j.ajcst.20250804.15

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ACS Style

Luc, S. N. R. F.; Randrianandrasana, M. E.; Rakotonirina, H. B. Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. Am. J. Comput. Sci. Technol. 2025, 8(4), 214-227. doi: 10.11648/j.ajcst.20250804.15

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AMA Style

Luc SNRF, Randrianandrasana ME, Rakotonirina HB. Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms. Am J Comput Sci Technol. 2025;8(4):214-227. doi: 10.11648/j.ajcst.20250804.15

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@article{10.11648/j.ajcst.20250804.15,
  author = {Sarobidy Nomenjanahary Razafitsalama Fin Luc and Marie Emile Randrianandrasana and Hariony Bienvenu Rakotonirina},
  title = {Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms},
  journal = {American Journal of Computer Science and Technology},
  volume = {8},
  number = {4},
  pages = {214-227},
  doi = {10.11648/j.ajcst.20250804.15},
  url = {https://doi.org/10.11648/j.ajcst.20250804.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajcst.20250804.15},
  abstract = {This paper proposes an efficient image reconstruction method in compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) with the Daubechies 7 (db7) wavelet and three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT), whose implementation relies on computationally expensive convolution operations, the LWT enables a faster sparse representation while preserving the sparsity properties essential for reconstruction. The proposed methodology is based on a key observation: among the four subbands generated by the LWT: approximation (CA) and detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Consequently, compression is applied exclusively to these detail components, while the approximation subband is kept intact, thereby preserving critical low-frequency information. Experiments were conducted on two types of images a natural image (Lena) and a medical image (MRI) across various resolutions (from 200×200 to 512×512 pixels) and sampling rates (from 10% to 80%). Performance was evaluated using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently show that ALISTA significantly outperforms SP and CoSaMP in both reconstruction quality and speed. At 80% sampling, ALISTA achieves an SSIM of 0.9936 for Lena and 0.9764 for MRI, compared to approximately 0.975 and 0.934 for the other methods, respectively. Moreover, ALISTA maintains extremely low reconstruction times under 4 seconds even for 512×512-pixel images. This research confirm that the ALISTA + LWT/db7 combination achieves the best quality–speed trade-off and exhibits robustness regardless of image type or size.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Image Reconstruction in Compressive Sensing Using Daubechies 7 (db7) and Lifting Wavelet Transforms with SP, CoSaMP, and ALISTA Algorithms
AU  - Sarobidy Nomenjanahary Razafitsalama Fin Luc
AU  - Marie Emile Randrianandrasana
AU  - Hariony Bienvenu Rakotonirina
Y1  - 2025/12/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ajcst.20250804.15
DO  - 10.11648/j.ajcst.20250804.15
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  - 214
EP  - 227
PB  - Science Publishing Group
SN  - 2640-012X
UR  - https://doi.org/10.11648/j.ajcst.20250804.15
AB  - This paper proposes an efficient image reconstruction method in compressive sensing (CS) that combines the Lifting Wavelet Transform (LWT) with the Daubechies 7 (db7) wavelet and three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). Unlike the conventional Discrete Wavelet Transform (DWT), whose implementation relies on computationally expensive convolution operations, the LWT enables a faster sparse representation while preserving the sparsity properties essential for reconstruction. The proposed methodology is based on a key observation: among the four subbands generated by the LWT: approximation (CA) and detail coefficients (LH, HL, HH) only the latter three are inherently sparse. Consequently, compression is applied exclusively to these detail components, while the approximation subband is kept intact, thereby preserving critical low-frequency information. Experiments were conducted on two types of images a natural image (Lena) and a medical image (MRI) across various resolutions (from 200×200 to 512×512 pixels) and sampling rates (from 10% to 80%). Performance was evaluated using the Structural Similarity Index (SSIM) and reconstruction time. Results consistently show that ALISTA significantly outperforms SP and CoSaMP in both reconstruction quality and speed. At 80% sampling, ALISTA achieves an SSIM of 0.9936 for Lena and 0.9764 for MRI, compared to approximately 0.975 and 0.934 for the other methods, respectively. Moreover, ALISTA maintains extremely low reconstruction times under 4 seconds even for 512×512-pixel images. This research confirm that the ALISTA + LWT/db7 combination achieves the best quality–speed trade-off and exhibits robustness regardless of image type or size.
VL  - 8
IS  - 4
ER  -

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