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We study the property of the Fused Lasso Signal Approximator(FLSA) for estimating a blocky signal sequence with additive noise.We transform the FLSA to an ordinary Lasso problem. By studying the prope...
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* +...
We study sparse approximation by greedy algorithms. We prove the Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a generalization of the Weak Orthogonal Matching Pursuit to ...
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inac...
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorith...
We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorith...
We assume data independently sampled froma mixture distribution on the unit ball of RD withK+1 components: the first component is a uniform distribution on that ball representing outliers and the oth...
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 f...
In the problem of multivariate regression, a K-dimensional response vector is regressed upon a common set of p covariates, with a matrix B 2 RpK of regression coecients. We study the behavior of ...
We consider the problem of detecting edges in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the “smoot...
The problem of recovering the sparsity pattern of a fixed but unknown vector β ∈ Rp based on a set of n noisy observations arises in a variety of settings, including subset selection in regression, ...

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