Gradient Pursuit Architecture for Reduced Complexity Sparsity Independent CS Recovery

Abstract

Compressed sensing (CS) tackles the problem of recovering information from measurements acquired at subNyquist rates. Traditional designs based on orthogonal matching pursuit (OMP) are slowed down by its serial nature and high iteration count in noisy acquisitions. Parallel pursuit strategies in the literature are drawn back by their dependence on sparsity prior and hardware complexity. To address these challenges, an improved version of the sparsity independent regularized pursuit (SIRP) algorithm is proposed in this brief that seeks to achieve a better trade-off between hardware resources and recovery speed without significantly impacting reconstruction quality. A pipelined gradient descent inspired least-mean-squares (LMS) architecture is proposed to replace the complex least squares (LS) step in SIRP and incorporates hardware-sharing for the interdependent steps of the algorithm. The proposed design implemented on a Xilinx Virtex Ultrascale device clocks at 143 MHz and reconstructs a 36-sparse signal in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$185~\mu \text{s}$ </tex-math></inline-formula> which is competitive with state-of-art designs, at significantly lower hardware consumption. Also, an alternate row LMS scheme is introduced in the design requiring no additional hardware resources, reducing the cycles per iteration to improve reconstruction speed by 28% with a slight reduction in the reconstructed signal-to-noise ratio (RSNR) compared to the full row LMS update.