Deflated preconditioned Conjugate Gradient methods for noise filtering of low-field MR images

Deflated preconditioned Conjugate Gradient methods for noise filtering of low-field MR images

Shan, X. (TU Delft Numerical Analysis; Harbin Institute of Technology)
van Gijzen, M.B. (TU Delft Numerical Analysis)

2022

We study efficient implicit methods to denoise low-field MR images using a nonlinear diffusion operator as a regularizer. This problem can be formulated as solving a nonlinear reaction–diffusion equation. After discretization, a lagged-diffusion approach is used which requires a linear system solve in every nonlinear iteration. The choice of diffusion model determines the denoising properties, but it also influences the conditioning of the linear systems. As a solution method, we use Conjugate Gradient (CG) in combination with a suitable preconditioner and deflation technique. We consider four different preconditioners in combination with subdomain deflation. We evaluate the methods for four commonly used denoising operators: standard Laplace operator, two Perona–Malik type operators, and the Total Variation (TV) operator. We show that a Discrete Cosine Transform (DCT) preconditioner works best for problems with a slowly varying diffusion coefficient, while Jacobi preconditioning with subdomain deflation works best for a strongly varying diffusion, as happens for the TV operator. This research is part of a larger effort that aims to provide low-cost MR imaging capabilities for low-resource settings. We have evaluated the algorithms on low-field MRI images using inexpensive commodity hardware. With a suitable preconditioner for the chosen diffusion model, we are able to limit the time to denoise three-dimensional images of more than 2 million pixels to less than 15 s, which is fast enough to be used in practice.

DPCG
Image denoising
Low-field MRI
PDE

http://resolver.tudelft.nl/uuid:74704668-1da3-4564-bd19-f092bd42143a

https://doi.org/10.1016/j.cam.2021.113730

2021-12-23

0377-0427

Journal of Computational and Applied Mathematics, 400

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 X. Shan, M.B. van Gijzen