Related papers: A measure theoretic approach to linear inverse atm…
For quantitative seismic imaging, iterative least-squares reverse time migration is the recommended approach. The existence of an inverse of the forward modelling operator would considerably reduce the number of required iterations. In the…
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…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
We propose a method for reconstruction of the density matrix from measurable time-dependent (probability) distributions of physical quantities. The applicability of the method based on least-squares inversion is - compared with other…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…
We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering…
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…