Variational Bayesian image restoration with multi-structured model of wavelet transform coefficients.

Recent works have demonstrated that using a properly structured prior for model-based compressive sensing (CS), can improve the recovery performance. However, there exists the low prior utilisation in previous works. Therefore, in this study, we introduce a multi-structured-wavelet Bayesian CS framework (MSW-BCS) that works for image compression with fully employing the prior knowledge. Our work can be briefly summarised by the following three aspects. Firstly, we explore the multi-structured prior knowledge, including the cluster structure and tree structure in the wavelet transform coefficients of images via statistical analyses. Secondly, a multi-variable joint recovery model is designed to describe this multi-structured prior. Finally, the detailed learning algorithm of model parameters based on variational Bayesian inference is given. The simulation experiments show that the proposed recovery model can effectively merge the different priors and achieve the superior performance compared with that of the other well-known CS algorithms under both noise-free and noisy measurement environments.