Related papers: Universality of Linearized Message Passing for Pha…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
Approximate message passing (AMP) is a class of low-complexity, scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal from noisy, linear measurements. AMP is an iterative…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
This paper considers the generalized bilinear recovery problem which aims to jointly recover the vector $\mathbf b$ and the matrix $\mathbf X$ from componentwise nonlinear measurements ${\mathbf Y}\sim p({\mathbf Y}|{\mathbf…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
We study the problem of recovering a structured signal from independently and identically drawn linear measurements. A convex penalty function $f(\cdot)$ is considered which penalizes deviations from the desired structure, and signal…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
Approximate Message Passing (AMP) algorithms are a family of iterative algorithms based on large random matrices with the special property of tracking the statistical properties of their iterates. They are used in various fields such as…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…