Related papers: Nonlinear Independent Component Analysis for Discr…
Motivated by the work of Aldroubi et al., we investigate the stability of the source term of the discrete dynamical system indexing over a non-uniform discrete set arising from spectral pairs in infinite-dimensional separable Hilbert…
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
Independent component analysis (ICA) estimates a demixing matrix that can recover statistically independent sources from linear mixtures. FastICA is a popular ICA algorithm due to its efficiency, but its performance strongly depends on a…
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…
Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
We present a new primal-dual splitting algorithm for structured monotone inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of our framework, which is motivated by image recovery applications, is to consider…
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical…
In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…
Blind methods often separate or identify signals or signal subspaces up to an unknown scaling factor. Sometimes it is necessary to cope with the scaling ambiguity, which can be done through reconstructing signals as they are received by…
This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…