A low-complexity Bayesian approach to large-scale sparse image reconstruction with structured constraints

The known tree-structure of wavelet transform coefficients is considered for conventional sparse image reconstruction to enhance performance. However, although existing Bayesian approaches can learn the latent structures, they have two issues that potentially limit their applications to high resolution images: First, treating the wavelet coefficients of large-scale images as high-dimensional vectors leads to impractical problem dimension; Second, Bayesian learning methods based on Markov chain Monte Carlo can guarantee global optima, but they require infinite stochastic samplings and thus are of high time complexity. In this paper, we address these issues by: 1) representing the wavelet transform images as multiple-measurement vectors (MMV) to reduce the memory complexity; and 2) modifying the structured priors for the Bayesian model to derive an analytical variational Bayesian strategy which can converge with much less time complexity. Experimental results demonstrate that our proposed method provides a practical alternative to large-scale sparse image recovery with low memory and computational requirements, while exhibiting close reconstruction accuracy compared to the time-consuming exact solutions.