相关论文: Accelerating CS in Parallel Imaging Reconstruction…

We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017].…

Transient simulation of linear and nonlinear circuits remains an important task in modern EDA tools. At present, SPICE-like simulators face challenges in parallelization, nonlinear convergence and linear efficiency, especially when applied…

A structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics…

In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an…

In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

In this thesis we study the preconditioning of square, non-symmetric and real Toeplitz systems. We prove theoretical results, which constitute sufficient conditions for the efficiency of the proposed preconditioners and the fast convergence…

The Cylindrical Algebraic Decomposition (CAD) algorithm is a comprehensive tool to perform quantifier elimination over real closed fields. CAD has doubly exponential running time, making it infeasible for practical purposes. We propose to…

In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…

Sparse-view Computed Tomography (CT) is an emerging protocol designed to reduce X-ray dose radiation in medical imaging. Traditional Filtered Back Projection algorithm reconstructions suffer from severe artifacts due to sparse data. In…

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…

The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…

Parallel imaging accelerates MRI data acquisition by acquiring additional sensitivity information with an array of receiver coils, resulting in fewer phase encoding steps. Because of fewer data requirements than parallel imaging, compressed…

In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…

Purpose: To develop a rapid imaging framework for balanced steady-state free precession (bSSFP) that jointly reconstructs undersampled data (by a factor of R) across multiple coils (D) and multiple acquisitions (N). To devise a…

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR data acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse…

There are variety of computational algorithms need sequential sweeping; sweeping based on specific order; on a structured grid, e.g., preconditioning (smoothing) by SOR or ILU methods and solution of eikonal equation by fast sweeping…

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…

We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…

The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…