The Study On Image Compressive Sensing Based On Compound Regularizers And Hidden Markov Tree Model

Compressed sensing (CS) is able to recover the original signal from the fewer projections using the sparse priors of it. Nowdays, the CS has been widely applied in many areas, such as compressive imaging, medical imaging, analog-to-information conversion, and so on. Recently, the theory of model-based CS has been presented, which reduces the degrees of freedom of a sparse/compressible signal by permitting only certain configurations of the large and zero/small coefficients.This paper performs the researches on the reconstruction of MRI and the image reconstruction based on model-based CS after learning the present arts, mainly including the following three aspects.First of all, Import the reconstruction method based on the smooth lB₀ form (SL0) for 1D signal to the MRI reconstruction, and aiming at lower the noises in the SL0 method, import the total variation regularization(TV). The reconstruction based on SL0 and TV is proposed. Experimental results show that the proposed methods can decrease the noises effectively, and perform well in the MRI reconstruction.Secondly, the current MRI reconstruction algorithms simply use either the sparse priors or the local smooth priors of MRI image, and result in the inferior reconstruction. Pointing at this problem, the MRI reconstruction algorithm based on the compound regularizers and compressed sensing which uses the two priors simultaneously is proposed. Applying the block-coordinate descent method, the solution to compound regularizers is turned into dealing with three simple optimization problems alternatively, which can be solved respectively. Experimental results show that the proposed algorithm is able to reconstruct the MRI image more efficiently than the current algorithms.At last, the standard CS reconstructions of image exploit simply the sparse priors of the wavelet coefficients, ignoring the structural information of the wavelet coefficients. In this paper, the Hidden Markov tree (HMT) model is integrated in the compressive sensing, which has been found successful in capturing the key features of the joint probability density of the wavelet coefficients of real-world image. What's more, a universal HMT (uHMT) model based on the dual-tree wavelet transform and its improved form are integrated to improve the reconstruction performance further, instead of the HMT model of the orthogonal wavelet transform. As the extensive experiments show, the proposed algorithm based on the improved uHMT model of the dual-tree wavelets algorithm outperforms the standard one, both visually and in peak signal-to-noise ratio.