Reduced computational complexity orthogonal matching pursuit using a novel partitioned inversion technique for compressive sensing

Abstract

This paper reports a field-programmable gate array (FPGA) design of compressed sensing (CS) using the orthogonal matching pursuit (OMP) algorithm. While solving the least-squares (LS) problem in the OMP algorithm, the complexity of the matrix inversion operation at every loop is reduced by the proposed partitioned inversion that utilizes the inversion result in the previous iteration. By the proposed matrix (n × n) inversion method inside the OMP, the number of operations is reduced down from O(n3) to O(n2). The OMP algorithm is implemented with a Xilinx Kintex UltraScale. The architecture with the proposed partitioned inversion involves 722 less DSP48E compared with the conventional method. It operates with a sample period of 4 ns, signal reconstruction time of 27 µs, and peak signal to noise ratio (PSNR) of 30.26 dB.