Related papers: Frames and Phaseless Reconstruction

Recently, it has been shown that a high resolution image can be obtained without the usage of a high resolution sensor. The main idea has been that a low resolution sensor is covered with a non-regular sampling mask followed by a…

Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…

This work introduces and characterizes a fast parameterless filter based on the Helgason-Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Phase retrieval is a problem encountered not only in speech and audio processing, but in many other fields such as optics. Iterative algorithms based on non-convex set projections are effective and frequently used for retrieving the phase…

Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…

We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…

The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…

Modern neural speech enhancement models usually include various forms of phase information in their training loss terms, either explicitly or implicitly. However, these loss terms are typically designed to reduce the distortion of phase…

We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…

We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

Transmission Electron Microscopy enables high-resolution imaging of materials, but the resulting images are difficult to interpret directly. One way to address this is exit wave reconstruction, i.e., the recovery of the complex-valued…

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…