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The treatment of the differential PDE constraint poses a key challenge in computing the numerical solution of the Serre-Green-Naghdi (SGN) equations. In this work, we introduce a constant coefficient preconditioner for the SGN constraint…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…
With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches…
Turbo compressed sensing (Turbo-CS) is an efficient iterative algorithm for sparse signal recovery with partial orthogonal sensing matrices. In this paper, we extend the Turbo-CS algorithm to solve compressed sensing problems involving more…
Blind signal separation (BSS) is an important and challenging signal processing task. Given an observed signal which is a superposition of a collection of unknown (hidden/latent) signals, BSS aims at recovering the separate, underlying…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover dynamic magnetic resonance images from undersampled measurements. We introduce a generalized formulation that is capable of handling a wide class of…
Contingency analysis (CA) plays a critical role to guarantee operation security in the modern power systems. With the high penetration of renewable energy, a real-time and comprehensive N-1 CA is needed as a power system analysis tool to…
In a recent paper (J. Chem. Theory. Comput., 2017, 13, 180-190) we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in…
We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…
We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic…
Telehealth and wearable equipment can deliver personal healthcare and necessary treatment remotely. One major challenge is transmitting large amount of biosignals through wireless networks. The limited battery life calls for low-power data…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many…
We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The ``known" part of the support, denoted T, may be…
Numerical techniques for solving partial differential equations (PDEs) are integral for many fields across science and engineering. Such techniques usually involve solving large, sparse linear systems, where preconditioning methods are…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the…