相关论文: Reverse em-problem based on Bregman divergence and…
MEG/EEG are non-invasive imaging techniques that record brain activity with high temporal resolution. However, estimation of brain source currents from surface recordings requires solving an ill-posed inverse problem. Converging lines of…
We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear,…
Calculating the capacity (with or without feedback) of channels with memory and continuous alphabets is a challenging task. It requires optimizing the directed information (DI) rate over all channel input distributions. The objective is a…
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…
The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statistics and machine learning. We establish fundamental properties…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
We propose the application of iterative regularization for the development of ensemble methods for solving Bayesian inverse problems. In concrete, we construct (i) a variational iterative regularizing ensemble Levenberg-Marquardt method…
This paper investigates the downlink communications of intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) systems. To maximize the system throughput, we formulate a joint optimization problem over the…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical…
This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
The reconstruction of the structure of biological tissue using electromyographic data is a non-invasive imaging method with diverse medical applications. Mathematically, this process is an inverse problem. Furthermore, electromyographic…
The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
Iterative learning to infer approaches have become popular solvers for inverse problems. However, their memory requirements during training grow linearly with model depth, limiting in practice model expressiveness. In this work, we propose…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…