Parareal Method for Anisotropic Diffusion Denoising

This paper studies time-domain parallelisation using Parareal to speed up the computations of anisotropic diffusion filtering. We consider both explicit and implicit Euler based method for the propagation in time for Parareal. The Preconditioned Conjugate Gradient (PCG) method is used to solve the systems that arise in the implicit based...

Deflated Preconditioned Conjugate Gradients for Nonlinear Diffusion Image Enhancement

Nonlinear diffusion equations have been successfully used for image enhancement by reducing the noise in the image while protecting the edges. In discretized form, the denoising requires the solution of a sequence of linear systems. The underlying system matrices stem from a discrete diffusion operator with large jumps in the diffusion...

A Dictionary Learning Approach for Joint Reconstruction and Denoising in Low Field Magnetic Resonance Imaging

Currently, many children with hydrocephalus in East Africa and other resource-constrained countries do not have access to Magnetic Resonance Imaging (MRI) scanners, the preferred imaging tool during the disease administration and treatment. Conventional MRI scanners are costly to buy and manage, which limits their utilization in low-income...

CG Variants for General-Form Regularization with an Application to Low-Field MRI

In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the ℓ₂-regularized weighted least-squares problem. Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical...

Approximating Eigenvectors with Fixed-Point Arithmetic: A Step Towards Secure Spectral Clustering

We investigate the adaptation of the spectral clustering algorithm to the privacy preserving domain. Spectral clustering is a data mining technique that divides points according to a measure of connectivity in a data graph. When the matrix data are privacy sensitive, cryptographic techniques can be applied to protect the data. A pivotal part...

The embodiment of low-field MRI for the diagnosis of infant hydrocephalus in Uganda

Compared to other parts of the world, the incidence of hydrocephalus in children is very high in sub- Saharan Africa. Magnetic resonance imaging (MRI) would be the preferred diagnostic method for infant hydrocephaleus. However, in practice, MRI is seldom used in sub-Saharan Africa due to its high prize, low mobility, and...

Description of a low-field MRI scanner based on permanent magnets

More than 6,000 infants develop hydrocephalus in East Africa every year. Magnetic Resonance Imaging is the preferred technique to diagnose hydrocephalus. In countries such as Uganda, MRI is unaffordable at even major referral hospitals. In order to provide a sustainable diagnostic tool we are developing an inexpensive and easy-to-use MRI...

A Dictionary Learning Approach for Noise-Robust Image Reconstruction in Low-Field Magnetic Resonance Imaging

Objective: Image denoising has been considered as a separate procedure from image reconstruction which could otherwise be combined with acquisition and reconstruction. This paper discusses a joint image reconstruction and denoising algorithm in low-field MRI using a dictionary learning approach. Method: Our proposed algorithm uses a two-level...

Efficient iterative methods for multi-frequency wave propagation problems: A comparison study

In this paper we present a comparison study for three different iterative Krylov methods that we have recently developed for the simultaneous numerical solution of wave propagation problems at multiple frequencies. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed...

A class of efficient preconditioners with multilevel sequentially semiseparable matrix structure

This paper presents a class of preconditioners for sparse systems arising from discretized partial differential equations (PDEs). In this class of preconditioners, we exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. The off-diagonal blocks of MSSS matrices are of low-rank, which enables fast computations...

An induced dimension reduction algorithm to approximate eigenpairs of large nonsymmetric matrices

This work presents an algorithm to approximate eigenpairs of large, sparse and nonsymmetric matrices based on the Induced Dimension Reduction method (IDR(s)) introduced in [1]. We obtain a Hessenberg relation from IDR(s) computations and in conjunction with Implicitly Restarting and shift-and-invert techniques [2] we created a short recurrence...

Convergence bounds for preconditioned GMRES using element-by-element estimates of the field of values

By combining element-by-element estimates for the field of values of a preconditioned matrix with GMRES-convergence estimates it is possible to derive an easily computable upper bound on the GMRES-residual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The...

Convergence bounds for preconditioned GMRES using element-by-element estimates of the field of values

By combining element-by-element estimates for the field of values of a preconditioned matrix with GMRES-convergence estimates it is possible to derive an easily computable upper bound on the GMRES-residual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The...