Related papers: Singular Value and Frame Decomposition-based Recon…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…
The Speckle Imager via MUlti Layer Atmospheric Turbulence Object Reconstructor (SIMULATOR) is a lab-based testbed instrument developed to test for speckle correlation-based techniques in the optical regime. However, this instrument can be…
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…
Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…
The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the…
Deep learning has significantly advanced medical imaging analysis, yet variations in image resolution remain an overlooked challenge. Most methods address this by resampling images, leading to either information loss or computational…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Atmospheric turbulence characterization is crucial for technologies like free-space optical communications. Existing methods using a spatially-integrated one-dimensional (1D) orbital angular momentum (OAM) spectrum, P(m), obscure the…
We present a blind multiframe image-deconvolution method based on robust statistics. The usual shortcomings of iterative optimization of the likelihood function are alleviated by minimizing the M-scale of the residuals, which achieves more…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
Recovering images from optical interferometric observations is one of the major challenges in the field. Unlike the case of observations at radio wavelengths, in the optical the atmospheric turbulence changes the phases on a very short time…
We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares…
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
For reconstructing large tomographic datasets fast, filtered backprojection-type or Fourier-based algorithms are still the method of choice, as they have been for decades. These robust and computationally efficient algorithms have been…