FPGA Implementation of an Improved ADMM for Compressive Sensing Reconstruction

The existing Compressed Sensing(CS) hardware design of reconstruction mainly adopts the greedy algorithm that only supports low-sparsity signals. In contrast, the actual physical signals often have high sparsity, which cannot meet the real-time reconstruction requirements. This article proposes an improved Alternating Direction Method of Multipliers (ADMM) algorithm and its implementation with field programmable gate array (FPGA). First, We use the Norman series approximation to simplify the matrix inversion, greatly reducing computational complexity. Then, we apply the Newton-Raphson Method to compute the reciprocal and optimize the soft threshold operator with approximate computation. Finally, The proposed design was verified on Xilinx Kintex7. The presented implementation can recover a 1024-length signal with measurement number = 64 and sparsity =36 in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$98.02 \mu \mathrm{s}$</tex>. The result shows that our design can meet the real-time reconstruction requirements.