  During the past decade, implementing reconstruction algorithms on hardware
has been at the center of much attention in the field of real-time
reconstruction in Compressed Sensing (CS). Orthogonal Matching Pursuit (OMP) is
the most widely used reconstruction algorithm on hardware implementation
because OMP obtains good quality reconstruction results under a proper time
cost. OMP includes Dot Product (DP) and Least Square Problem (LSP). These two
parts have numerous division calculations and considerable vector-based
multiplications, which limit the implementation of real-time reconstruction on
hardware. In the theory of CS, besides the reconstruction algorithm, the choice
of sensing matrix affects the quality of reconstruction. It also influences the
reconstruction efficiency by affecting the hardware architecture. Thus,
designing a real-time hardware architecture of OMP needs to take three factors
into consideration. The choice of sensing matrix, the implementation of DP and
LSP. In this paper, a sensing matrix, which is sparsity and contains zero
vectors mainly, is adopted to optimize the OMP reconstruction to break the
bottleneck of reconstruction efficiency. Based on the features of the chosen
matrix, the DP and LSP are implemented by simple shift, add and comparing
procedures. This work is implemented on the Xilinx Virtex UltraScale+ FPGA
device. To reconstruct a digital signal with 1024 length under 0.25 sampling
rate, the proposal method costs 0.818us while the state-of-the-art costs
238$us. Thus, this work speedups the state-of-the-art method 290 times. This
work costs 0.026s to reconstruct an 8K gray image, which achieves 30FPS
real-time reconstruction.
