A Bayesian compressive sensing reconstruction algorithm using wavelet-domain context modeling

A novel Bayesian compressive sensing image reconstruction algorithm based on the context modeling is proposed to solve the problem that the intrascale dependencies of image's wavelet coefficients is not fully exploited by the compressive sensing reconstruction algorithm. It is assumed that the wavelet coefficients of image obey a spike-and-slab probability model. Context vectors in the current coefficient's neighborhood are obtained through a new context modeling method. Then, the significant probability of current coefficient is estimated according to the dependencies of the context vector with the current coefficient and the state of parent coefficient. Finally, the image's wavelet coefficients is recovered from the observation vector based on the significant probabilities of the image's wavelet coefficients by using a Bayesian inference via Markov chain Monte Carlo sampling, thus, the reconstruction image is generated. Since the spike-and-slab probability model with context modeling is adaptive to the spatial changes of the images, experimental results and comparisons with Bayesian tree-structured wavelet compressive sensing algorithm which only uses the interscale dependencies show that the proposed algorithm improves the peak-signal-to-noise-ratio nearly by 2 dB at the sampling rate of 0.9.