Abstract
Existing model-based or data-driven methods have achieved a high-quality reconstruction in compressive sensing magnetic resonance imaging (CS-MRI). However, most methods are designed for a specific type of sampling mask or sampling rate while ignoring the existence of external noise, resulting in poor robustness. In this work, we propose a probabilistic model-based method based on Laplacian scale mixture (LSM) modeling and denoising based approximate message passing (D-AMP) algorithm to address this issue. Sparse coefficients of similar packed patches are modeled with LSM distribution to exploit the nonlocal self-similarity prior of MR image, and a maximum a posterior estimation problem for sparse coding is formulated. It is shown that both hidden scale parameters i.e. variances of sparse coefficients and location parameters can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. Moreover, the variance of noise is also iteratively updated based on maximum likelihood estimation. With plug-and-play prior method, the above structured sparse coding procedure can be regarded as a nonlocal filtering operation and be incorporated into D-AMP for MR image reconstruction. Owing to the power of our nonlocal filtering which takes both signal and noise estimation into account, the proposed method not only outperforms many state-of-the-art methods for most situations of observation, but also delivers the best qualitative reconstruction results with finer details and less artifacts in experiments.
Highlights
Magnetic resonance imaging (MRI) [1] is an essential medical diagnostic tool which is used for observing the tissue changes of the patients in the absence of ionizing radiation
We extend the application of the Laplacian scale mixture (LSM) model in representing the nonlocal sparsity of MR images
We propose modeling sparse coefficients related to similar patches of MR image with LSM distribution for the construction of nonlocal filtering, and incorporate it into the denoising based approximate message passing (D-AMP) method as a black-box denoiser for MR image reconstruction
Summary
Magnetic resonance imaging (MRI) [1] is an essential medical diagnostic tool which is used for observing the tissue changes of the patients in the absence of ionizing radiation. Modeling statistical dependencies among sparse coefficients can achieve more accurate reconstruction due to the reduction of uncertainty of the underdetermined system These works explore the use of more complicated and hand-designed signal models, such as tree-structured wavelet sparsity [12], [13], group sparsity [14], Gaussian scale mixtures (GSM) model [15] and nonlocal sparsity [16], [17]. We have noticed that two papers [39] (an image super-resolution method) and [40] (a denoising method) constructed the LSM model to represent the nonlocal sparsity of images they are not used in CS-MRI They are learning-based methods implying that they have exploited the information of external images. Instead of using BM3D, we incorporate our sparse coding procedure into the framework of D-AMP as a denoiser with the method of plug-and-play prior leading to a more effective method
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