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In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This…
Modern methods of environmental monitoring are deficient in the lack of ability to take measurements of energy flows since traditional readings involve capturing parameters such as temperature, pressure, and humidity without considering…
A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…
The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\Omega…
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard results for subgradients, we derive simple-to-check criteria…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…
Radio frequency sources are observed at a fusion center via sensor measurements made over slow flat-fading channels. The number of sources may be larger than the number of sensors, but their activity is sparse and intermittent with bursty…
Digital twinning offers a capability of effective real-time monitoring and control, which are vital for cost-intensive experimental facilities, particularly the ones where extreme conditions exist. Sparse experimental measurements collected…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
Remote sensors are becoming the standard for observing and recording ecological data in the field. Such sensors can record data at fine temporal resolutions, and they can operate under extreme conditions prohibitive to human access.…
This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
Given a sound field generated by a sparse distribution of impulse image sources, can the continuous 3D positions and amplitudes of these sources be recovered from discrete, bandlimited measurements of the field at a finite set of locations,…