Model-Based Bayesian Compressive Sensing of Non-stationary Images Using a Wavelet-Domain Triplet Markov Fields Model

Abstract

In this paper, a new model-based Bayesian compressive sensing technique for non-stationary images is proposed. Our algorithm is based on the recently addressed triplet Markov fields (TMF) model. The TMF model is well appropriate for non-stationary image processing, owing to the introduction of a third random field which reflects different non-stationarity of images. Furthermore, TMF can extract the interactions among the neighboring sites of an image in a more complete way than the classic hidden Markov models do. In this paper, the inter-scale dependencies between the wavelet coefficients is exploited explicitly in the proposed TMF model, which results in the wavelet domain TMF model. Our proposed model considers the intra- and inter-scale dependencies and the non-stationarity of images simultaneously. Also, we have developed our proposed algorithm for both Gaussian and non-Gaussian measurement noises, and we have modeled the non-Gaussianity of the noise via Laplace distribution. To approximate the posterior distributions of the hidden variables, we resort to a variational Bayesian expectation–maximization algorithm. Simulation results in both the optical and synthetic aperture radar images show that this model leads to an improvement over state-of-the-art algorithms in terms of the reconstruction error and the structural similarity.

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Torkamani, R., Sadeghzadeh, R. Model-Based Bayesian Compressive Sensing of Non-stationary Images Using a Wavelet-Domain Triplet Markov Fields Model. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01484-w

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Keywords

  • Bayesian compressive sensing
  • Triplet Markov fields
  • Non-stationary image modeling
  • Wavelet-tree structure
  • Laplacian noise
  • Variational Bayesian expectation maximization