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

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