FPGA Implementation of Staged Projection Refining Multiple Orthogonal Matching Pursuit Algorithm for Compressed Sensing

Reconstruction algorithms are an integral part of compressed sensing (CS) theory, which can reliably reconstruct the original signal from the low-dimensional compressed signal. The orthogonal matching pursuit (OMP) algorithm has been widely studied and extensively selected in hardware implementations. However, the low reconstruction success rate of the OMP algorithm under high sparsity conditions has led to the proposal and application of more reconstruction algorithms in hardware implementations. In this article, a staged projection refining multiple OMP (SPR-MOMP) algorithm is proposed based on the OMP algorithm. This algorithm improves the reconstruction accuracy by refining the support set using a staged backtracking strategy. It also employs a multiple-atom selection strategy for parallel expansion of the support set, ensuring reconstruction efficiency. The reconstruction simulation demonstrates that the SPR-MOMP algorithm achieves a higher reconstruction success rate than the OMP algorithm, with fewer iterations. A hardware architecture applying the SPR-MOMP algorithm is designed and implemented on a Virtex UltraScale+ field-programmable gate array (FPGA) with $N =1024$ , $M =256$ , and $K =36$ . The proposed architecture achieves a reconstruction signal-to-noise ratio (RSNR) of 44.27 dB, with 20-bit data width and 15-bit fractional width. The maximum clock frequency of the architecture is 200 MHz, enabling reconstruction within $276.6~\mu $ s. The proposed architecture achieves a lower dynamic power consumption of 1929 mW.