Related papers: GMRES Methods for Tomographic Reconstruction with …
With the availability of more powerful computers, iterative reconstruction algorithms are the subject of an ongoing work in the design of more efficient reconstruction algorithms for X-ray computed tomography. In this work, we show how two…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
Magnetic resonance imaging (MRI) can present multi-contrast images of the same anatomical structures, enabling multi-contrast super-resolution (SR) techniques. Compared with SR reconstruction using a single-contrast, multi-contrast SR…
In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the authors analyzed the convergence behaviour of the Generalized Minimal Residual (GMRES) method for the least squares problem $ \min_{ {\bf x} \in {\bf R}^n} {\|…
GMRES is known to determine a least squares solution of $ A x = b $ where $ A \in R^{n \times n} $ without breakdown for arbitrary $ b \in R^n $, and initial iterate $ x_0 \in R^n $ if and only if $ A $ is range-symmetric, i.e. $ R(A^T) =…
Magnetic resonance image (MRI) reconstruction is a severely ill-posed linear inverse task demanding time and resource intensive computations that can substantially trade off {\it accuracy} for {\it speed} in real-time imaging. In addition,…
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…
Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization.…
Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of…
An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring…
Purpose: The aim of this work is to shed light on the issue of reproducibility in MR image reconstruction in the context of a challenge. Participants had to recreate the results of "Advances in sensitivity encoding with arbitrary k-space…
Reconstructing MRI from highly undersampled measurements is crucial for accelerating medical imaging, but is challenging due to the ill-posedness of the inverse problem. While supervised deep learning (DL) approaches have shown remarkable…
In image fusion tasks, the absence of real fused images as supervision signals poses significant challenges for supervised learning. Existing deep learning methods typically address this issue either by designing handcrafted priors or by…
In computed tomography, data consist of measurements of the attenuation of X-rays passing through an object. The goal is to reconstruct the linear attenuation coefficient of the object's interior. For each position of the X-ray source,…
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…
Cardiovascular magnetic resonance (CMR) imaging is the gold standard for diagnosing several heart diseases due to its non-invasive nature and proper contrast. MR imaging is time-consuming because of signal acquisition and image formation…
We consider the split-preconditioned FGMRES method in a mixed precision framework, in which four potentially different precisions can be used for computations with the coefficient matrix, application of the left preconditioner, application…
Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned…