Related papers: On deconvolution methods
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort…
We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…
The existence and structure of steady gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity…
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…
In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Higher-order singular value decomposition (HOSVD) is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete…
We investigate efficient algorithmic realisations for robust deconvolution of grey-value images with known space-invariant point-spread function, with emphasis on 1D motion blur scenarios. The goal is to make deconvolution suitable as…
Convolutions are one of the most important operations in signal processing. They often involve large arrays and require significant computing time. Moreover, in practice, the signal data to be processed by convolution may be corrupted by…
This paper studies the numerical simulation of the solution to the McKean-Vlasov equation with common noise. We begin by discretizing the solution in time using the Euler scheme, followed by spatial discretization through the particle…
This paper concerns the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this co-inversion problem can be…
In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization will recover the exact solution with high probability when the…
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to…
We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory for time series. Its components can be viewed as successive…