14 citations · 40 across the 8 of their papers we have counts for
9 papers
Recovery of Integer Signals from Limited DFT Samples: Lattice Methods and Stability Analysis
Howard Levinson, Isaac Viviano
We analyze lattice-based algorithms for recovering integer-valued signals from partial discrete Fourier transform (DFT) measurements. These algorithms formulate signal recovery as…
Recovery of Integer Images from Minimal DFT Measurements: Uniqueness and Inversion Algorithms
Howard W Levinson, Isaac Viviano
Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior…
Inversion of band-limited discrete Fourier transforms of binary images: Uniqueness and algorithms
Howard W. Levinson, Vadim A. Markel, Nicholas Triantafillou
Conventional inversion of the discrete Fourier transform (DFT) requires all DFT coefficients to be known. When the DFT coefficients of a rasterized image (represented as a matrix)…
Structured Iterative Hard Thresholding with On- and Off-Grid Applications
Joseph S. Donato, Howard W. Levinson
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets…
Binary Discrete Fourier Transform and its Inversion
Howard W. Levinson, Vadim A. Markel
A binary vector of length has elements that are either 0 or 1. We investigate the question of whether and how a binary vector of known length can be reconstructed from a limite…
Nonlinear Iterative Hard Thresholding for Inverse Scattering
Anna C. Gilbert, Howard W. Levinson, John C. Schotland
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresh…
Imaging from the Inside Out: Inverse Scattering with Photoactivated Internal Sources
Anna C. Gilbert, Howard W. Levinson, John C. Schotland
We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering proble…
Solution of the inverse scattering problem by T-matrix completion. II. Simulations
Howard W. Levinson, Vadim A. Markel
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory a…
Nonlinear inverse problem by T-matrix completion. I. Theory
Howard W. Levinson, Vadim A. Markel
We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology and oth…