Decoupled Algorithm for MRI Reconstruction Using Nonlocal Block Matching Model: BM3D-MRI

• Published in: Journal of mathematical imaging and vision Vol. 56; no. 3; pp. 430 - 440
• Main Author: Eksioglu, Ender M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2016; Springer Nature B.V
• Subjects: Applications of Mathematics; Computer Science; Decoupling; Image Processing and Computer Vision; Image reconstruction; Iterative algorithms; Magnetic resonance imaging; Matching; Mathematical Methods in Physics; Noise reduction; Regularization; Signal,Image and Speech Processing; BM3D; Sparsity; Magnetic resonance; Image reconstruction; Compressed sensing; Block matching
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-016-0647-7

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.