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.
Highlights
The compressed sensing (CS) can effectively acquire and reconstruct sparse signals with significantly less samples than that required from the Nyquist–Shannon sampling theorem [1].The reconstruction process in CS finds the best solution to an underdetermined system, with a linear equation of the form y = Fx, where we know the measurement matrix, F, that model the sampling system and the measurement vector, y, while the original signal, x, remains to be determined.Various algorithms have been proposed to reconstruct the signal x from the compressively sensed samples
The Simultaneous orthogonal matching pursuit (SOMP) algorithm generally results in a high computational complexity for the LS problem, because of a very large inner product
The single measurement vector (SMV) model causes an increase of this complexity
Summary
The compressed sensing (CS) can effectively acquire and reconstruct sparse signals with significantly less samples than that required from the Nyquist–Shannon sampling theorem [1]. Two algorithms, the greedy pursuit [2,3] and the convex relaxation [4,5], are mainly selected for sparse signal reconstruction. In OMP, one of the major problems in the LS step is the matrix inversion, because it results in a high computational complexity per iteration [7]. Several inversion methods for the OMP algorithm have been proposed, such as the QR decomposition [8] and Cholesky-based factorization [7,9], to improve the computation efficiency of the matrix inversion. We propose a novel matrix inversion with a better computational efficiency, based on the incremental computation of the partitioned inversion targeting the OMP. The experiments show that the total hardware utilization is significantly reduced compared with the conventional partitioned inversion, and the reconstruction time is 27 μs.
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