Related papers: LINPRO: linear inverse problem library for data co…
This work concerns the direct and inverse potential problems for the stochastic diffusion equation driven by a multiplicative time-dependent white noise. The direct problem is to examine the well-posedness of the stochastic diffusion…
In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
The problem of optimization of the array size for modern discrete Fourier transform libraries is considered and reformulated as an integer linear programming problem. Acceleration of finding an optimal solution using standard freely…
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…
We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…
We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted sample points using Gaussian process regression. A heteroscedastic noise model is employed, in which additive…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
The exponential growth of data collection necessitates robust privacy protections that preserve data utility. We address information disclosure against adversaries with bounded prior knowledge, modeled by an entropy constraint $H(X) \geq…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
We formulate the loop-free, binary superoptimization task as a stochastic search problem. The competing constraints of transformation correctness and performance improvement are encoded as terms in a cost function, and a Markov Chain Monte…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…