VLSI Design and Test pp 35-43 | Cite as
Computational Functions’ VLSI Implementation for Compressed Sensing
Conference paper
Abstract
Compressed Sensing (CS) is found to be promising method for sparse signal recovery and sampling. The paper proposes the architecture for computing various computational functions useful in realizing CS recovery consisting of Singular Value Decomposition (SVD) using Bi-diagonalization method; L1 norm of vector, L2 norm of vector calculations. This is one of the early VLSI implementation attempt for CS recovery. We have verified the design for speed and accuracy of results on FPGA.
Keywords
Compressed Sensing Compressive Sensing ArchitecturePreview
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References
- 1.Maleki, A.: Approximate Message Passing Algorithms for compressed sensing, PhD Thesis, Stanford University (September 2011)Google Scholar
- 2.Kim, S.-J., Koh, K., Lustig, M., Boyd, S.: An Interior-Point Method for Large Scale l1-Regularized Least Squares. IEEE Journal of Selected Topics in Signal Processing 1(4), 606–617 (2007)CrossRefGoogle Scholar
- 3.Kim, S.-J., Koh, K., Lustig, M., Boyd, S.: An Efficient Method For Compressed Sensing. In: IEEE International Conference on Image Processing, vol. 3, pp. III-117-III-120, http://www.stanford.edu/~boyd/l1_ls/
- 4.Hale, E.T., Yin, W., Zhang, Y.: A Fixed Point Continuation method for l1-Regularized Minimization with Applications to Compressed Sensing, CAAM Technical Report TR07-07, Dept of Computational and Applied Mathematics, Rice University, Houstan, Texas (July 7, 2007)Google Scholar
- 5.Baraniuk, R., Davenport, M.A., Duarte, M.F., Hegde, C.: An Introduction to Compressive Sensing. In: Connexions. Rice University, Houston (2011)Google Scholar
- 6.Maleki, A., Donoho, D.L.: Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing. IEEE Journal of Selected Topics in Signal Processing 4(2) (April 2010)Google Scholar
- 7.Maechler, P., Studer, C., Bellasi, D.E., Maleki, A., Burg, A., Felber, N., Kaeslin, H., Baraniuk, R.G.: VLSI Implementation of Approximate Message Passing for Signal Restoration and Compressive Sensing. Submitted to IEEE Journal on Emerging and Selected Topics in Circuits and SystemsGoogle Scholar
- 8.Xu, L., Liang, Q.: Compressive Sensing Using Singular Value Decomposition. In: Pandurangan, G., Anil Kumar, V.S., Ming, G., Liu, Y., Li, Y. (eds.) WASA 2010. LNCS, vol. 6221, pp. 338–342. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 9.Peng, Y., He, Y.: A Reconstruction Algorithm for Compressed Sensing Noise Signal. Journal of Computational Information Systems 8(14), 6025–6031 (2012)Google Scholar
- 10.Yu, Y., Hong, M., Liu, F., Wang, H., Crozier, S.: Compressed Sensing MRI Using Singular Value Decomposition based Sparsity Basis. In: 33rd Annual International Conference of the IEEE EMBS, Boston, Massachusetts USA, August 30-September 3 (2011)Google Scholar
- 11.Ahmedsaid, A., et al.: Improved SVD systolic array and implementation on FPGA. In: Proceedings of the 2003 IEEE International Conference on Field-Programmable Technology, FPT (2003)Google Scholar
- 12.Ma, W., et al.: An FPGA based Singular Value Decomposition processor. In: IEEE Canadian Conference on Electrical and Computer Engineering, CCECE 2006 (2006)Google Scholar
- 13.Rahmati, M., et al.: FPGA Based Singular Value Decomposition for Image Processing Applications. In: IEEE International Conference on Application-Specific Systems, Architectures and Processors, ASAP 2008 (2008)Google Scholar
- 14.Szecówka, P.M., et al.: CORDIC and SVD Implementation in Digital Hardware. In: IEEE 17th International Conference on Mixed Design of Integrated Circuits and Systems, MIXDES 2010, Wrocław, Poland, June 24-26 (2010)Google Scholar
- 15.Ledesma-Carrillo, L.M.: Reconfigurable FPGA-Based Unit for Singular Value Decomposition of Large m × n Matrices. In: IEEE 2011 International Conference on Reconfigurable Computing and FPGAs (2011)Google Scholar
- 16.Numerical Recipes- The Art of Scientific Computing, 3rd edn. Cambridge University PressGoogle Scholar
- 17.Golub, Reinsch: Singular Value Decomposition and Least Squares Solutions. Handbook Series Linear Algebra, Numer. Math. 14, 403–420 (1970)MATHMathSciNetGoogle Scholar
- 18.Strang, G.: Linear Algebra and its Applications, 4th edn. Cengage LearningGoogle Scholar
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