Model-Based Nonuniform Compressive Sampling and Recovery of Natural Images Utilizing a Wavelet-Domain Universal Hidden Markov Model

Behzad Shahrasbi, Nazanin Rahnavard

Abstract: In this paper, a novel model-based compressive sampling (CS) technique for natural images is proposed. Our algorithm integrates a universal hidden Markov tree (uHMT) model, which captures the relation among the sparse wavelet coefficients of images, into both sampling and recovery steps of CS. At the sampling step, we employ the uHMT model to devise a nonuniformly sparse measurement matrix Φ uHMT . In contrast to the conventional CS sampling matrices, such as dense Gaussian, Bernoulli or uniformly sparse matrices that are oblivious to the signal model and the correlation among the signal coefficients, the proposed Φ uHMT is designed based on the signal model and samples the coarser wavelet coefficients with higher probabilities and more sparse wavelet coefficients with lower probabilities. At the recovery step, we integrate the uHMT model into two state-of-the-art Bayesian CS recovery schemes. Our simulation results confirm the superiority of our proposed HMT model-based nonuniform compressive sampling and recovery, referred to as uHMT-NCS, over other model-based CS techniques that solely consider the signal model at the recovery step. This paper is distinguished from other model-based CS schemes in that we take a novel approach to simultaneously integrating the signal model into both CS sampling and recovery steps. We show that such integration greatly increases the performance of the CS recovery, which is equivalent to reducing the required number of samples for a given reconstruction quality.