Related papers: Nonlinear Iterative Hard Thresholding for Inverse …
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship,…
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
Direct imaging methods recover the presence, position, and shape of the unknown obstacles in time-harmonic inverse scattering without a priori knowledge of either the physical properties or the number of disconnected components of the…
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…
We investigate the problem of bulk metric reconstruction in holography by leveraging the inverse scattering framework applied to boundary two-point correlation functions. We generalize our previous work of scalar field and show that…
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…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…
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…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…