Parallel Gibbs Sampler for Wavelet-Based Bayesian Compressive Sensing with High Reconstruction Accuracy
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Parallel Gibbs Sampler for Wavelet-Based Bayesian Compressive Sensing with High Reconstruction Accuracy Jian Zhou1
· Antonia Papandreou-Suppappola1 · Chaitali Chakrabarti1
Received: 16 April 2019 / Revised: 3 January 2020 / Accepted: 29 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Gibbs sampling · Parallel implementation · Relaxed computing · Bayesian compressive sensing
1 Introduction Wavelet transform based coding has been successfully used in many image processing applications [1, 2]. Using wavelet coefficients as a sparse basis image representation, compressive sensing (CS) has been used to efficiently reconstruct images from a small number of projection measurements [3–6]. Recently, model-based CS approaches were shown to require even less measurements by exploiting the structure of the wavelet coefficients in natural images [7]. One such approach is Bayesian compressive sensing Chaitali Chakrabarti
[email protected] Jian Zhou [email protected] Antonia Papandreou-Suppappola [email protected] 1
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ, USA
(BCS) that models the structural dependencies of wavelet coefficients according to a Bayesian parametric framework [8, 9]. The BCS approach assumes that the coefficients follow a sparse prior distribution and uses sparse Bayesian learning and the relevance vector machine to compute a posterior distribution on the coefficient weights [8]. In [9], the BCS algorithm uses hierarchical
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