Approximate Sparsity and Nonlocal Total Variation Based Compressive MR Image Reconstruction

Recent developments in compressive sensing (CS) show that it is possible to accurately reconstruct the magnetic resonance (MR) image from undersampled k-space data by solving nonsmooth convex optimization problems, which therefore significantly reduce the scanning time. In this paper, we propose a new MR image reconstruction method based on a compound regularization model associated with the nonlocal total variation (NLTV) and the wavelet approximate sparsity. Nonlocal total variation can restore periodic textures and local geometric information better than total variation. The wavelet approximate sparsity achieves more accurate sparse reconstruction than fixed wavelet l0 and l1 norm. Furthermore, a variable splitting and augmented Lagrangian algorithm is presented to solve the proposed minimization problem. Experimental results on MR image reconstruction demonstrate that the proposed method outperforms many existing MR image reconstruction methods both in quantitative and in visual quality assessment

MR Image Reconstruction Based on Iterative Split Bregman Algorithm and Nonlocal Total Variation

This paper introduces an efficient algorithm for magnetic resonance (MR) image reconstruction. The proposed method minimizes a linear combination of nonlocal total variation and least-square data-fitting term to reconstruct the MR images from undersampled k-space data. The nonlocal total variation is taken as the L1-regularization functional and solved using Split Bregman iteration. The proposed algorithm is compared with previous methods in terms of the reconstruction accuracy and computational complexity. The comparison results demonstrate the superiority of the proposed algorithm for compressed MR image reconstruction

Sparse MRI and CT Reconstruction

Sparse signal reconstruction is of the utmost importance for efficient medical imaging, conducting accurate screening for security and inspection, and for non-destructive testing. The sparsity of the signal is dictated by either feasibility, or the cost and the screening time constraints of the system. In this work, two major sparse signal reconstruction systems such as compressed sensing magnetic resonance imaging (MRI) and sparse-view computed tomography (CT) are investigated. For medical CT, a limited number of views (sparse-view) is an option for whether reducing the amount of ionizing radiation or the screening time and the cost of the procedure. In applications such as non-destructive testing or inspection of large objects, like a cargo container, one angular view can take up to a few minutes for only one slice. On the other hand, some views can be unavailable due to the configuration of the system. A problem of data sufficiency and on how to estimate a tomographic image when the projection data are not ideally sufficient for precise reconstruction is one of two major objectives of this work. Three CT reconstruction methods are proposed: algebraic iterative reconstruction-reprojection (AIRR), sparse-view CT reconstruction based on curvelet and total variation regularization (CTV), and sparse-view CT reconstruction based on nonconvex L1-L2 regularization. The experimental results confirm a high performance based on subjective and objective quality metrics. Additionally, sparse-view neutron-photon tomography is studied based on Monte-Carlo modelling to demonstrate shape reconstruction, material discrimination and visualization based on the proposed 3D object reconstruction method and material discrimination signatures. One of the methods for efficient acquisition of multidimensional signals is the compressed sensing (CS). A significantly low number of measurements can be obtained in different ways, and one is undersampling, that is sampling below the Shannon-Nyquist limit. Magnetic resonance imaging (MRI) suffers inherently from its slow data acquisition. The compressed sensing MRI (CSMRI) offers significant scan time reduction with advantages for patients and health care economics. In this work, three frameworks are proposed and evaluated, i.e., CSMRI based on curvelet transform and total generalized variation (CT-TGV), CSMRI using curvelet sparsity and nonlocal total variation: CS-NLTV, CSMRI that explores shearlet sparsity and nonlocal total variation: SS-NLTV. The proposed methods are evaluated experimentally and compared to the previously reported state-of-the-art methods. Results demonstrate a significant improvement of image reconstruction quality on different medical MRI datasets