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The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
This paper develops a novel approach to the problem of source current identification for the diffusion equation in connection with geophysical self-potential measurements. The problem is split into two subproblems: (a) the scalar source…
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for…
We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…
Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
Flow-field reconstruction from sparse sensor measurements remains a central challenge in modern fluid dynamics, as the need for high-fidelity data often conflicts with practical limits on sensor deployment. Existing deep learning-based…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
We consider an inverse problem in information diffusion modeled by random walks on combinatorial graphs. The problem concerns reconstruction of vertex centrality from the distribution of the first passage times observed on a subset of…
We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the…
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…
We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from…
We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…