Parallel Gibbs Sampler for Wavelet-Based Bayesian Compressive Sensing with High Reconstruction Accuracy

Bayesian compressive sensing (BCS) helps address ill-posed signal recovery problems using the Bayesian estimation framework. Gibbs sampling is a technique used in Bayesian estimation that iteratively draws samples from conditional posterior distributions, which is inherently sequential. In this work, we propose a two-stage parallel coefficient update scheme for wavelet-based BCS, where the first stage approximates the real distributions of the wavelet coefficients and the second stage computes the final estimate of the coefficients. While in the first stage, the parallel computing units share information with each other, in the second stage, the parallel units work independently. Even when the computing units share information, when the number of computing units is large, the process deviates from the sequential Gibbs sampler resulting in large reconstruction error. We propose two new coefficient re-computation schemes to reduce the reconstruction error at the cost of longer computation time. We also propose a new coefficient update scheme that updates coefficients in both stages based on data generated a few rounds ago. Such a scheme helps in relaxing the timing constraints for communication in the first stage and computations in the second stage. We design the corresponding parallel architecture and synthesize it in 7 nm technology node. For the system with 8 computing units, the proposed algorithm reduces the execution time up to 6.8× at maximum compared to the sequential implementation.