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We introduce a new iterative algorithm to find sparse solutions of underdetermined linear systems. The algorithm, a simple combination of the Iterative Hard Thresholding algorithm and of the Compressive Sampling Matching Pursuit or Subspace Pursuit algorithms, is called Hard Thresholding Pursuit. We study its general convergence, and notice in particular… (More)

We provide sharp lower and upper bounds for the Gelfand widths of p-balls in the N-dimensional N q-space for 0 < p ≤ 1 and p < q ≤ 2. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.

Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem—e.g., in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior signal information can… (More)

MOTIVATION
Many metagenomic studies compare hundreds to thousands of environmental and health-related samples by extracting and sequencing their 16S rRNA amplicons and measuring their similarity using beta-diversity metrics. However, one of the first steps--to classify the operational taxonomic units within the sample--can be a computationally… (More)

With the decrease in cost and increase in output of whole-genome shotgun technologies, many metagenomic studies are utilizing this approach in lieu of the more traditional 16S rRNA amplicon technique. Due to the large number of relatively short reads output from whole-genome shotgun technologies, there is a need for fast and accurate short-read OTU… (More)

We provide sharp lower and upper bounds for the Gelfand widths of ℓ p-balls in the N-dimensional ℓ N q-space for 0 < p ≤ 1 and p < q ≤ 2. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.

One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary samples—only the sign of each linear measurement is maintained. Existing results in one-bit compressive sensing rely on the… (More)