FPGA Implementation of an Improved OMP for Compressive Sensing Reconstruction

Abstract

This article proposes an improved orthogonal matching pursuit (OMP) algorithm and its implementation with Xilinx Vivado high-level synthesis (HLS). We use the Gram–Schmidt orthogonalization to improve the update process of signal residuals so that the signal recovery only needs to perform the least-squares solution once, which greatly reduces the number of matrix operations in a hardware implementation. Simulation results show that our OMP algorithm has the same signal reconstruction accuracy as the original OMP algorithm. Our approach provides a fast and reconfigurable implementation for different signal sizes, different measurement matrix sizes, and different sparsity levels. The proposed design can recover a 128-length signal with measurement number $M=32$ and sparsity $K=5$ and $K=8$ in 13.2 and $21~\mu \text{s}$ , which is at least a 21.9% and 22.2% improvement compared with the existing HLS-based works; a 256-length signal with $M=64$ and $K=8$ in $20.6~\mu \text{s}$ , which is a 24% improvement compared with the existing work; and a 1024-length signal with measurement number $M=256$ and sparsity $K=12$ and $K=36$ in 150.3 and $423~\mu \text{s}$ , respectively, which are close to the results of traditional hardware description language (HDL) implementations. Our results show that our improved OMP algorithm not only offers a superior reconstruction time compared with other recent HLS-based works but also can compete with existing works that are implemented using the traditional field-programmable gate array (FPGA) design route.