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We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
Many modern iterative solvers for large-scale tomographic reconstruction incur two major computational costs per iteration: expensive forward/adjoint projections to update the data fidelity term and costly proximal computations for the…
The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered…
Many imaging technologies rely on tomographic reconstruction, which requires solving a multidimensional inverse problem given a finite number of projections. Backprojection is a popular class of algorithm for tomographic reconstruction,…
A 3D tomographic reconstruction technique is described for inversion of a set of limited-angle high-resolution 2D visible light emission projections (extended in the vertical and toroidal directions) of global MHD eigenmodes in the H-1NF…
We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lam\'e parameters) of a weakly scattering medium from full-field data of scattered waves outside…
We consider the two-dimensional multi-target detection problem of recovering a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. Motivated by the structure reconstruction…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
Ring-array ultrasound computed tomography has recently achieved sufficient maturity for clinical applications like breast imaging. Image reconstruction is achieved with state of art iterative algorithms (full waveform inversion in the…
This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…
This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…
Cosmic ray muon computed tomography ({\mu}CT) is a new imaging modality with unique characteristics that could be particularly important for diverse applications including nuclear nonproliferation, spent nuclear fuel monitoring, cargo…
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time- convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…
We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…
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…
The conformal mapping problem for the section of a channel filled with porous material under a rectangular dam onto the upper half-plane is considered. Similar problems arise in computing of fluid flow in hydraulic structures. As a solution…
In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after…
Analysis of microscope images is a tedious work which requires patience and time, usually done manually by the microscopist after data collection. Here we introduce an approach of automatic image analysis, which is based on locally applied…