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E.M. Eksioglu, “Decoupled Algorithm for MRI Reconstruction Using Nonlocal Block Matching Model: BM3D-MRI”, Journal of Mathematical Imaging and Vision, vol. 56, no. 3, pp. 430-440, November 2016. [pdf]
MATLAB code to realize the BM3D-MRI algorithm:
The above given BM3D-MRI toolbox should be used in conjunction with the BM3D denoising toolbox available online from the BM3D main page (http://www.cs.tut.fi/~foi/GCF-BM3D/).
Download the BM3D denoising toolbox (BM3D.zip) and put the unzipped folder “BM3D” under the main folder of the BM3D-MRI toolbox. Also download the modified BM3D denoising function here, and put it under the main folder of the BM3D-MRI toolbox.
The block matching 3D (BM3D) is an efficient image model, which has found few applications other than its niche area of denoising. We will develop a magnetic resonance imaging (MRI) reconstruction algorithm, which uses decoupled iterations alternating over a denoising step realized by the BM3D algorithm and a reconstruction step through an optimization formulation. The decoupling of the two steps allows the adoption of a strategy with a varying regularization parameter, which contributes to the reconstruction performance. This new iterative algorithm efficiently harnesses the power of the nonlocal, image-dependent BM3D model. The MRI reconstruction performance of the proposed algorithm is superior to state-of-the-art algorithms from the literature. A convergence analysis of the algorithm is also presented.
Image reconstruction, Magnetic resonance, Block matching, BM3D, Compressed sensing, Sparsity