相关论文: Sparse phase retrieval of one-dimensional signals …

We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m$, where $x = \Phi…

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same…

A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…

Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted as the square of the modulus of the Fourier transform of the…

Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…

This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…

Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…

Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously…

Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…

We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

We describe the relationship between different forms of linearized expressions for the spatial distribution of intensity of X-ray projection images obtained in the Fresnel region. We prove that under the natural validity conditions some of…

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…

In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…