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Table 1. SVD results
Matrix Size Xilinx ISE value Matlab value Time
4x4 4 4 41.330 us 2
4x4 2 2 18.130 us
4X4 1.999999 2 49.750 us
32x16 16 16 1.969 ms
32x32 22.62739 22.6274 4.578 ms
96x96 67.88227 67.8823 50.904 ms
128x128 90.50966 90.5097 90.869 ms
(The timing values given above can be 1/3 rd if minimum clock period of 3ns is
used)
5
Conclusion
In this paper we have implemented and synthesized the computational functions
required for doing compressive sensing recovery. We believe ours is one the early
attempts to carry out VLSI implementation and synthesis of computational functions
for compressive sensing recovery. We could not get any reference for L 1 norm of
vector and L 2 norm of vector implementations and could not do comparison.
Similarly, Bi-diagonalization architecture is also our contribution. Our SVD
implementation has been found to be faster and more accurate compared to
implementations done in [15].
We also studied algorithms (second order methods) like interior point method
which can be solved in the polynomial time (O( N 3 )) and it uses preconditioned
conjugate gradient (PCG) method to approximately solve linear systems in a truncated
Newton framework. Iteration methods ( first order) are studied for L 1 -minimization
and literature has compared iterative algorithms (Hard /Soft, IST/IHT) along with its
tuning. For certain very large matrices it can rapidly apply and without representing
as a full matrix and in such settings, the work required scales very favorably with N.
In future we plan to consider implementation of SVD based method/ first order
method, along with calculation of power and present compressive sensing recovery
architecture.
References
[1] Maleki, A.: Approximate Message Passing Algorithms for compressed sensing, PhD
Thesis, Stanford University (September 2011)
[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)
[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/
2
The timing corresponds to the same input that was also used for bi-diagonalization testing.
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