Related papers: Nonparametric Sparse Representation
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…
Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…
We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace…
A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a…
Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods (MCMC). The underlying unknown noise process (possibly) exhibits…
In many scenarios, the communication system suffers from both Gaussian white noise and non-Gaussian impulsive noise. In order to design optimal signal detection method, it is necessary to estimate the parameters of mixed Gaussian-impulsive…
Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…
In this work we propose a technique to remove sparse impulse noise from hyperspectral images. Our algorithm accounts for the spatial redundancy and spectral correlation of such images. The proposed method is based on the recently introduced…