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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…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling…
{In this paper, we address the challenging problem of detecting bearing faults from vibration signals. For this, several time- and frequency-domain features have been proposed already in the past. However, these features are usually…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
Image foreground extraction is a classical problem in image processing and vision, with a large range of applications. In this dissertation, we focus on the extraction of text and graphics in mixed-content images, and design novel…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
In this paper, we propose a general collaborative sparse representation framework for multi-sensor classification, which takes into account the correlations as well as complementary information between heterogeneous sensors simultaneously…
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…
Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…
We investigate the class of quadratic detectors (i.e., the statistic is a bilinear function of the data) for the detection of poorly modeled gravitational transients of short duration. We point out that all such detection methods are…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
In the recent work of Candes et al, the problem of recovering low rank matrix corrupted by i.i.d. sparse outliers is studied and a very elegant solution, principal component pursuit, is proposed. It is motivated as a tool for video…
The increased presence of advanced sensors on the production floors has led to the collection of datasets that can provide significant insights into machine health. An important and reliable indicator of machine health, vibration signal…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Rolling element bearing faults in rotating systems are observed as impulses in the vibration signals, which are usually buried in noises. In order to effectively detect the fault of bearings, a novel spectrum searching method is proposed.…