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This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
In neural audio signal processing, pitch conditioning has been used to enhance the performance of synthesizers. However, jointly training pitch estimators and synthesizers is a challenge when using standard audio-to-audio reconstruction…
In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix $X$ of known low rank $K$, we present a new algorithm to estimate $X$ based on recent advances in non-convex optimization schemes. We apply this in particular to…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an…
We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system.…
We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…
We propose a novel 3D spatial representation for data fusion and scene reconstruction. Probabilistic Signed Distance Function (Probabilistic SDF, PSDF) is proposed to depict uncertainties in the 3D space. It is modeled by a joint…
We consider the recovery of sparse signals that share a common support from multiple measurement vectors. The performance of several algorithms developed for this task depends on parameters like dimension of the sparse signal, dimension of…
Phase aberration is an inherent side effect of ultrasound imaging due to the speed of sound inhomogeneity nature of human tissues, resulting in focusing error and reduced image contrast. This work introduces a phase aberration correction…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…