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 μs, 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 μs, 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 μs, 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.
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FPGA Implementation of an Improved OMP for Compressive Sensing Reconstruction
