Related papers: Measurement Matrix Design for Phase Retrieval Base…
We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used…
Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical…
We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…
We study a nonconvex optimization algorithmic approach to phase retrieval and the more general problem of semidefinite low-rank matrix sensing. Specifically, we analyze the nonconvex landscape of a quartic Burer-Monteiro factored…
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even…
A major challenge to implement the compressed sensing method for channel state information (CSI) acquisition lies in the design of a well-performed measurement matrix to reduce the dimension of sparse channel vectors. The widely adopted…
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
In this work, we present some new results for compressed sensing and phase retrieval. For compressed sensing, it is shown that if the unknown $n$-dimensional vector can be expressed as a linear combination of $s$ unknown Vandermonde vectors…
We consider the problem of recovering the support of a sparse signal using noisy projections. While extensive work has been done on the dense measurement matrix setting, the sparse setting remains less explored. In this work, we establish…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step…
We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…
A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the positive operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are…
We address the problem of blind gain and phase calibration of a sensor array from ambient noise. The key motivation is to ease the calibration process by avoiding a complex procedure setup. We show that computing the sample covariance…
Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating…
We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…