Model-Based Nonuniform Compressive Sampling And Recovery Of Natural Images Utilizing A Wavelet-Domain Universal Hidden Markov Model

Keywords

Compressed sensing; image sampling; wavelet coefficients

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 ΦuHMT. 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 ΦuHMT 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.

Publication Date

1-1-2017

Publication Title

IEEE Transactions on Signal Processing

Volume

65

Issue

1

Number of Pages

95-104

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TSP.2016.2614654

Socpus ID

85020569415 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85020569415

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