FPGA Implementation of an Improved OMP for Compressive Sensing Reconstruction

• Published in: IEEE transactions on very large scale integration (VLSI) systems Vol. 29; no. 2; pp. 259 - 272
• Main Authors: Li, Jun, Chow, Paul, Peng, Yuanxi, Jiang, Tian
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Atomic measurements; Compressed sensing; Compressed sensing (CS); Field programmable gate arrays; field-programmable gate array (FPGA) implementation; Hardware; Hardware description languages; High level synthesis; Image reconstruction; Matched pursuit; Matching pursuit algorithms; orthogonal matching pursuit (OMP) algorithm; Signal processing; Signal reconstruction; Sparse matrices; sparse signal recovery; Sparsity; Vivado high-level synthesis (HLS)
• ISSN: 1063-8210; 1557-9999
• DOI: 10.1109/TVLSI.2020.3030906

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 <inline-formula> <tex-math notation="LaTeX">M=32 </tex-math></inline-formula> and sparsity <inline-formula> <tex-math notation="LaTeX">K=5 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">K=8 </tex-math></inline-formula> in 13.2 and <inline-formula> <tex-math notation="LaTeX">21~\mu \text{s} </tex-math></inline-formula>, which is at least a 21.9% and 22.2% improvement compared with the existing HLS-based works; a 256-length signal with <inline-formula> <tex-math notation="LaTeX">M=64 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">K=8 </tex-math></inline-formula> in <inline-formula> <tex-math notation="LaTeX">20.6~\mu \text{s} </tex-math></inline-formula>, which is a 24% improvement compared with the existing work; and a 1024-length signal with measurement number <inline-formula> <tex-math notation="LaTeX">M=256 </tex-math></inline-formula> and sparsity <inline-formula> <tex-math notation="LaTeX">K=12 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">K=36 </tex-math></inline-formula> in 150.3 and <inline-formula> <tex-math notation="LaTeX">423~\mu \text{s} </tex-math></inline-formula>, 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.