Abstract
The theory of compressed sensing asserts that one can recover signals in \(\mathbb {R}^n\) from far fewer samples or measurements, if the signal has a sparse representation in some orthonormal basis; from non-adaptive linear measurements by solving a \(\mathbb {L}_1\) norm minimisation problem. The non-adaptive measurements have the character of random linear combinations of the basis or frame elements. However, for large-scale 2D image signals, the randomized sensing matrix consumes enormous computational resources that makes it impractical. The problem has been addressed in the paper as a block compressed sensing (BCS) with sparsity normalization in the transformed domain in the preprocessing stage. The blocks obtained are converted to non-adaptive measurements using identically independent weighted Gaussian random matrices. The feasibility of reconstruction is verified using orthogonal matching pursuit. Simulation results show that better reconstruction performance can be achieved by the proposed technique in comparison with the existing BCS approaches.






Similar content being viewed by others
References
Baraniuk, R.G.: Compressive sensing [lecture notes]. IEEE Signal Process. Mag. 24(4), 118–121 (2007)
Baron, D., Duarte, M.F., Wakin, M.B., Sarvotham, S., and Baraniuk, R.G.: Distributed compressive sensing. CoRR, arXiv: 0901.3403 (2009)
Candes, E., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies? Appl. Comput. Math. 52(12), 5406–5425 (2006)
Candès, E.J., Wakin, M.B.: An introduction to compressive sampling [a sensing/sampling paradigm that goes against the common knowledge in data acquisition]. IEEE Signal Process. Mag. 25(2), 21–30 (2008)
Cao, Y., Gong, W., Zhang, B., Zeng, F., Bai, S.: Optimal permutation based block compressed sensing for image compression applications. IEICE Trans. Inf. Syst. 101(1), 215–224 (2018)
Chen, C., Tramel, E.W., Fowler, J.E.: Compressed-sensing recovery of images and video using multihypothesis predictions. In: 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), pp. 1193–1198. IEEE (2011)
Donoho, D.L.: Optimally sparse representation from overcomplete dictionaries via L1-norm minimization. Proc. Nat. Acad. Sci. U. S. A. 100, 2197–2002 (2003)
Duarte, M.F., Baraniuk, R.G.: Kronecker compressive sensing. IEEE Trans. Image Process. 21(2), 494–504 (2012)
Douze, M., Jegou, H., Schmid, C.: Hamming embedding and weak geometry consistency for large scale image search. In: Proceedings of the 10th European Conference on Computer Vision (2008)
Fowler, J.E., Mun, S., Tramel, E.W.: Multiscale block compressed sensing with smoothed projected landweber reconstruction. In: 2011 19th European Signal Processing Conference, pp. 564–568. IEEE (2011)
Gan, L.: Block compressed sensing of natural images. In: 2007 15th International Conference on Digital Signal Processing, pp. 403–406. IEEE (2007)
Kingsbury, N.: Complex wavelets for shift invariant analysis and filtering of signals. Appl. Comput. Harmon. Anal. 10(3), 234–253 (2001)
Kutyniok, G.: Theory and applications of compressed sensing. GAMM-Mitteilungen 36(1), 79–101 (2013)
Li, R., Liu, H., Zeng, Y., Li, Y.: Block com-pressed sensing of images using adaptive granular reconstruction. Adv. MultiMedia 2016, 1–9 (2016)
Mun, S., Fowler, J.E.: Block compressed sensing of images using directional transforms. In: 2009 16th IEEE international Conference on Image Processing (ICIP), pp. 3021–3024. IEEE (2009)
Rebollo-Neira, L., Sasmal, P.: Low memory implementation of orthogonal matching pursuit like greedy algorithms: analysis and applications. arXiv preprint arXiv:1609.00053 (2016)
The INRIA Holidays dataset. http://lear.inrialpes.fr/people/jegou/data.php. Accessed 12 Jan 2020
Trocan, M., Maugey, T., Tramel, E.W., Fowler, J.E., Pesquet-Popescu, B.: Multistage compressed-sensing reconstruction of multiview images. In: 2010 IEEE International Workshop on Multimedia Signal Processing, pp. 111–115 (2010)
Unde, A.S., Deepthi, P.P.: Block compressive sensing. J. Vis. Commun. Image Represent. 44(C), 187–197 (2017)
USC-SIPI Image Database. http://sipi.usc.edu/database/. Accessed 12 Jan 2020
Yang, Y., Au, O.C., Fang, L., Wen, X., Tang, W.: Reweighted compressive sampling for image compression. In: 2009 Picture Coding Symposium, pp. 1–4. IEEE (2009)
Zhou, Y., Guo, H.: Collaborative block compressed sensing reconstruction with dual-domain sparse representation. Inf. Sci. 472, 77–93 (2019)
Acknowledgements
The research was funded by PURSE Scheme of the Department of Science and Technology, Govt. of India awarded to the CSE Department, University of Kalyani, WB, India. The authors would like to thank the anonymous reviewers for their helpful comments on the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Das, S., Mandal, J.K. An enhanced block-based Compressed Sensing technique using orthogonal matching pursuit. SIViP 15, 563–570 (2021). https://doi.org/10.1007/s11760-020-01777-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-020-01777-2