Computational Functions’ VLSI Implementation for Compressed Sensing - VLSI Design and Test - page 35

Computational Functions' VLSI Implementation
for Compressed Sensing

Shrirang Korde, Amol Khandare, Raghavendra Deshmukh, and Rajendra Patrikar

Electronics Engineering Department, VNIT, SA Road, Nagpur-440010
{shrirang.korde,amolkhandare2}@gmail.com,
[e-mail], [e-mail]

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; L 1 norm of vector, L 2 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, Architecture.

1 Introduction

Compressed Sensing (CS) has been receiving a lot of interest as a promising method
for sparse signal recovery and sampling. As a general principle, a sparse solution x to
an under-determined linear system of equations “Ax = y” may be obtained by
minimizing the L1 norm of x. Minimizing ||x||1 is recognized as a practical avenue for
obtaining sparse solutions x. If the "observation" y is contaminated with noise, then
an appropriate norm of the residual (Ax - y) should be minimized. If there is noise in
y, the L1-regularized least square problem (LSP) [1-4]

minimize||Ax - y|| 2 2 + ʻ ||x|| 1 (1)

ʻ >0, ||x|| 1  L 1 norm, ||Ax - y|| 2  L 2 norm

Numerous schemes have been proposed for obtaining sparse solutions of
underdetermined systems of linear equations; popular methods have been developed
from many viewpoints: L1-minimization, convex regularization and nonconvex
optimization [2-5], matching pursuit [2-5], iterative thresholding methods and
subspace methods [6-7], Singular Value Decomposition (SVD) methods [8-10]. These
specific proposals are often tailored to different viewpoints, ranging from formal
analysis of algorithmic properties to particular application requirements.
As per our review, Patrick et al [7] work is an early paper proposing VLSI
Implementation for CS recovery using message passing/iterative methods. Yeyang et
al [10] proposes to use SVD as data-adaptive sparsity basis for compressed sensing
Magnetic Resonance (MR) images and is able to give sparser representation for