Regularized Bayesian compressed sensing in ultrasound imaging

Compressed sensing has recently shown much interest for ultrasound imaging. In particular, exploiting the sparsity of ultrasound images in the frequency domain, a specific random sampling of ultrasound images can be used advantageously for designing efficient Bayesian image reconstruction methods. We showed in a previous work that assigning independent Bernoulli Gaussian priors to the ultrasound image in the frequency domain provides Bayesian reconstruction errors similar to a classical l₁ minimization technique. However, the advantage of Bayesian methods is to estimate the sparsity level of the image by using a hierarchical algorithm. This paper goes a step further by exploiting the spatial correlations between the image pixels in the frequency domain. A new Bayesian model based on a correlated Bernoulli Gaussian model is proposed for that purpose. The parameters of this model can be estimated by sampling the corresponding posterior distribution using an MCMC method. The resulting algorithm provides very low reconstruction errors even when reducing significantly the number of measurements via random sampling.