Related papers: Shape and parameter identification by the linear s…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
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…
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
We consider the inverse medium scattering of reconstructing the medium contrast using Born data, including the full aperture, limited-aperture, and multi-frequency data. We propose data-driven basis functions for these inverse problems…
In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the…
In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
This article is written to serve as an introduction and survey of imaging with synthetic aperture radar (SAR). The reader will benefit from having some familiarity with harmonic analysis, electromagnetic radiation, and inverse problems.…
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…
We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was…
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware…
We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…