Abstract
Recent development in data compression emphasizes compressed sensing technique as a widely applied one for compression and reconstruction of images and videos by projecting the pixel values into smaller dimensional measurements. These compressed measurements are reconstructed at the receiver using suitable reconstruction algorithms, generally the greedy algorithms. Greedy algorithms are time consuming and complex processes, giving rise to a trade-off between reconstruction performance and algorithmic performance. This work proposes a non-iterative method, non-iterative pseudo inverse based recovery algorithm (NIPIRA), for reconstruction of compressively sensed images and videos that exhibits small complexity and time requirement along with preservation of reconstruction quality. Mathematical proofs for NIPIRA’s accuracy and optimality provide additional theoretical support to the algorithm. NIPIRA gives a minimum PSNR of 32 dB for very few measurements, accuracy of above 97 and 92% decrease in elapsed time compared with other iterative algorithms. The complexity of NIPIRA is \(O(MN)\) which is \(s\) times less than OMP and StOMP.
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References
Dana, M. (2009). Compressed sensing makes every pixel count. Journal of What Happens in Mathematical Science, 7(2009), 114–127.
Masiero, R., Quer, G., Rossi, M., & Zorzi, M. (2009). A Bayesian analysis of compressive sensing data recovery in wireless sensor networks. In Proceedings of international conference on ultra-modern telecommunications & workshops (pp. 1–6). October 12–14, 2009.
Candes, E., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2), 489–509.
Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.
Drori, I. (2008) Compressed video sensing. In BMVA symposium on 3D video—Analysis, display, and applications.
Patel, V. M., & Chellappa, R. (2013). Sparse representation and compressive sensing for imaging and vision. Berlin: Springer.
Fazel, M., Candes, E., Recht, B., & Parrilo, P. (2007). Compressed sensing and robust recovery of low rank matrices. In 42nd Asilomar conference on signals, systems and computers (pp. 1043–1047). October 26–29, 2008.
Candes, E. (2008). The restricted isometry property and its implications. Journal Comptes Rendus Mathematique, 346(9–10), 589–592.
Tony, Cai T., & Wang, Lie. (2011). Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Transactions on Information Theory, 57(7), 4680–4688.
Donoho, D. L., Tsaig, Y., Drori, I., & Starck, J.-L. (2012). Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (StOMP). IEEE Transactions of Information Theory, 58(2), 1094–1121.
Zhi-xue, L., Gang, L., Hao, Z., & Xi-qin, W. (2012). Sparse-driven SAR imaging using MMV-StOMP. In Proceedings of 1st international workshop on compressed sensing applied to radar. IEEE Press, May 14–16.
Needell, D., & Tropp, J. A. (2009). CoSaMP: Iterative signal recovery from incomplete and inaccurate sample. Journal of Applied and Computational Analysis, 26(3), 301–321.
Blumensath, T., & Davies, M. E. (2009). Iterative hard thresholding for compressed sensing. Journal of Applied and Computational Harmonic Analysis, 27(3), 265–274.
Eldar, Y. C., & Kutyniok, G. (2012). Compressed sensing: Theory and applications. Cambridge: Cambridge University Press.
Kutyniok, G. (2012). Theory and applications of compressed sensing. arXiv preprint arXiv:1203.3815. http://www.math.tuberlin.de/fileadmin/i26_fgkutyniok/Kutyniok/Papers/SurveyCompressedSensing_Revision.pdf.
Baraniuk, R., Davenport, M., DeVore, R., & Wakin, M. (2008). A simple proof of the restricted isometry property for random matrices. Constructive Approximation, 28(3), 253–263.
Florence Gnana Poovathy, J., & Radha, S. (2015). Non-iterative threshold based recovery algorithm (NITRA) for compressively sensed images and videos. KSII Transactions on Internet and Information Systems, 9(10), 4160–4176.
http://sipi.usc.edu/database/database.php?volume=misc. Accessed on December 2015.
http://see.xidian.edu.cn/vipsl/database_Video.html. Accessed on November 2014.
Mrak, M., Grgic, S., & Grgic M. (2003). Picture quality measures in image compression systems. In EUROCON 2003. Computer as a Tool. The IEEE Region 8 (Vol. 1, pp. 233–236). IEEE.
Kratochvil, T., & Simicek, P. (2005). Utilization of MATLAB for picture quality evaluation. Brno: Institute of Radio Electronics, Brno University of Technology.
Lauterjung, J. (1998). Picture quality measurement. In International broadcasting convention (pp. 413–417). Amsterdam, London: IEE. September 11–15, 1998.
Knapp-Cordes, M., & McKeeman, B. (2011). Improvements to tic and toc functions for measuring absolute elapsed time performance in MATLAB. Matlab Digest. mathworks.com.
Hutter, Frank, Lin, Xu, Hoos, Holger H., & Leyton-Brown, Kevin. (2014). Algorithm runtime prediction: Methods and evaluation. Artificial Intelligence, 206(2014), 79–111.
Sen, S. (2013). Lecture notes for algorithm analysis and design. November 6, 2013. http://www.cse.iitd.ernet.in/~ssen/csl356/root.pdf.
Sturm, B. L., & Græsbøll Christensen, M. (2010). Comparison of orthogonal matching pursuit implementations. In 20th European signal processing conference (EUSIPCO 2012). Romania, August 27–31.
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Florence Gnana Poovathy, J., Radha, S. Non-iterative Pseudo Inverse Based Recovery Algorithm (NIPIRA) for Compressively Sensed Images and Videos. Wireless Pers Commun 95, 4947–4966 (2017). https://doi.org/10.1007/s11277-017-4134-2
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DOI: https://doi.org/10.1007/s11277-017-4134-2