Hardware Implementation of Iterative Method With Adaptive Thresholding for Random Sampling Recovery of Sparse Signals

Sparse recovery methods find extensive applications in various fields such as image and audio processing, wireless communication, and spectral estimation. In this paper, a hardware architecture of iterative method with adaptive thresholding (IMAT) is presented to recover a sparse signal from its random samples. To demonstrate the effectiveness of IMAT, a comparison is performed between the IMAT algorithm and the compressive sensing recovery method, orthogonal matching pursuit, in terms of complexity and reconstruction quality. In the context of image reconstruction, as a practical case, simulation results show the advantages of IMAT in improving the performance of the signal reconstruction via peak signal-to-noise ratio and structural similarity index metrics. Since IMAT employs discrete transform as a principal operation in each iteration, using fast or fast approximate algorithms allows more efficient implementation. In this paper, two multiplication-free transforms, Walsh–Hadamard transform (WHT) and approximate discrete cosine transform (ADCT), are used to reduce computational complexity of IMAT implementation. The IMAT recovery algorithm is implemented on Virtex6 FPGA using two above transforms, and the results are compared with respect to the hardware resource utilization, power consumption, and recovery time. The results demonstrate that using WHT for IMAT implementation is more efficient than using ADCT in terms of hardware resources. Also, the comparison implies that the performance of the hardware implementation is very close to its floating point simulated counterpart. For a block size of $32 \times 32$ , the IMAT implementation using WHT provides the reconstruction time of $185~\mu \text{s}$ and the dynamic power of 123 mW.