Related papers: Phase retrieval from noisy data based on sparse ap…
We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…
We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered…
Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the…
Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear…
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…
Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to be estimated. Recently there emerges a few…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…
This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the…
We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit…
A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation…
Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…
In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…
We continue studies on phase retrieval for continuous and discrete Fourier transforms in multidimensions. Using finite difference operators, we give a large class of unexpected examples of non-uniqueness for this problem, including examples…
In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…