Multivariate Copula Spatial Dependency in One Bit Compressed Sensing

TL;DR

This paper introduces a novel multivariate copula-based Bayesian framework for one bit compressed sensing, effectively modeling wavelet coefficient dependencies to improve sparse signal reconstruction.

Contribution

It proposes a new statistical multivariate model using Gaussian copulas and a variational Bayes algorithm for better sparse signal recovery from one bit measurements.

Findings

Outperforms existing methods in numerical experiments.

Effectively models intra-scale dependencies of wavelet coefficients.

Provides closed-form solutions for posterior distributions.

Abstract

In this letter, the problem of sparse signal reconstruction from one bit compressed sensing measurements is investigated. To solve the problem, a variational Bayes framework with a new statistical multivariate model is used. The dependency of the wavelet decomposition coefficients is modeled with a multivariate Gaussian copula. This model can separate marginal structure of coefficients from their intra scale dependency. In particular, the drawable Gaussian vine copula multivariate double Lomax model is suggested. The reconstructed signal is derived by variational Bayes algorithm which can calculate closed forms for posterior of all unknown parameters and sparse signal. Numerical results illustrate the effectiveness of the proposed model and algorithm compared with the competing approaches in the literature.