A Probabilistic Model-Based Method With Nonlocal Filtering for Robust Magnetic Resonance Imaging Reconstruction

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 DAMP 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. INDEX TERMS Compressive sensing magnetic resonance imaging (CS-MRI), Laplacian scale mixture (LSM), denoising based approximate message passing (D-AMP), nonlocal filtering.

An Iterative Method With Enhanced Laplacian- Scaled Thresholding for Noise-Robust Compressive Sensing Magnetic Resonance Image Reconstruction

“…above minimization problem can be further reduced to a set of scalar minimization problems, one of which denoted by () this result are similar to the ones in our previous work (please refer to ref [5]…”

“…LSM distribution has been widely utilized in modeling sparse coefficients of signal, such as the sparse coefficients of local patches of natural images in [35], the tensor coefficients of multi-frame images in [36], and the sparse impulse noise in [43]. In our previous work [5], we have applied LSM model in describing the nonlocal sparsity of MR images. We extend the previous model to a side information-aided Laplacian-scaled model which can exploit the reference information provided by the BM3D thresholding to enhance the robustness of our method.…”

“…This objective function is similar to the one in our previous work [5], except for the second term which introduces an extra reference for the data fitting. We further simplify the objective function by translating it from ( , , )…”

“…Much research on MRI has focused on the reduction of the acquisition time and accurate reconstruction from highly undersampled k-space data, which is a pair of contradictions. Compressive sensing (CS) methods [2,3] as a fundamental developed methodology in information society are able to achieve accurate image reconstruction from very few linear measurements, and have been successfully applied to MRI, which is known as CS-MRI [4,5]. Using CS-MRI techniques one can significantly reduce the amount of kspace data and corresponding acquisition time by means of undersampling without having to sacrifice the quality of reconstructed MR images.…”

Convolutional Neural Network with a Learnable Spatial Activation Function for SAR Image Despeckling and Forest Image Analysis

“…The purpose of speckle suppression methods based on the convolutional neural network is to learn the nonlinear mapping relationships between clean images and corresponding noisy images. Since the 1980s, different methods for despeckling have been proposed based on various technologies, such as multilook processing [15][16][17][18], spatial domain filters [19][20][21][22], wavelet transform [23][24][25][26], nonlocal filtering [27][28][29][30], and total variation [31][32][33][34]. The multilook processing can suppress speckle noise simply and effectively, but this leads to reduction of resolution for SAR image.…”