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Sparsity is a naturally occurring characteristic in many real-world applications including signal denoising, outlier detection, and finance. On one hand, sparsity assumption allows people to tackle in...
We consider two alternative tests to the Higher Criticism test of Donoho and Jin (2004) for high dimensional means under the spar-sity of the non-zero means for sub-Gaussian distributed data with unkn...
We attempt to recover a high-dimensional vector observed in white noise, where the vector is known to be sparse, but the degree of sparsity is unknown. We consider three di®erent ways of deˉnin...
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
We introduce “wave atoms” as a variant of 2D wavelet packets obeying the parabolic scaling wavelength ~ (diameter)2. We prove that warped oscillatory functions, a toy model for texture, have a signifi...
We consider the problem of reconstructing a sparse signal x0 ∈ Rn from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that...
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
In the last decade, there has been considerable interest in understanding when it is possible to find structured solutions to underdetermined systems of linear equations. This paper surveys some of th...
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization paramete...
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex ...
Abstract: The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine le...
Abstract: We present a relation between sparsity and non-Euclidean isomorphic embeddings. We introduce a general restricted isomorphism property and show how it enables to construct embeddings of $\el...
We consider the problem of learning a distance metric from a limited amount of pairwise information as effectively as possible. The proposed SERAPH (SEmi-supervised metRic leArning Paradigm with Hyper...
Fusion frames have become a major tool in the implemen-tation of distributed systems. The effectiveness of fusion frame appli-cations in distributed systems is reflected in the efficiency of the end f...
We describe a connection between the identi cation problem for matrices with sparse representations in given matrix dictionaries and the problem of sparse signal recovery. This allows the application ...

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