• Publications
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Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse
  • D. Donoho, Y. Tsaig
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 November 2008
TLDR
In this paper, the Homotopy method, originally proposed by Osborne et al. and Efron et al., is applied to the underdetermined lscr1-minimization problem min parxpar1 subject to y=Ax, and is shown to run much more rapidly than general-purpose LP solvers when sufficient sparsity is present. Expand
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Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit
TLDR
Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Expand
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Extensions of compressed sensing
TLDR
We study the notion of compressed sensing (CS) as put forward by Donoho, Candes, Tao and others. Expand
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Automatic segmentation of moving objects in video sequences: a region labeling approach
TLDR
This paper presents a new method for automatic segmentation of moving objects in image sequences for VOP extraction using graph labeling, based on motion information. Expand
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Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
The minimum -norm solution to an underdetermined system of linear equations is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signalExpand
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Variable projection for near-optimal filtering in low bit-rate block coders
TLDR
We present an algorithm for finding optimal filters in a sampling/compression scheme. Expand
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A region-based MRF model for unsupervised segmentation of moving objects in image sequences
  • Y. Tsaig, A. Averbuch
  • Computer Science
  • Proceedings of the IEEE Computer Society…
  • 8 December 2001
TLDR
This paper addresses the problem of segmentation of moving objects in image sequences, which is of key importance in content-based applications. Expand
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Optimal framework for low bit-rate block coders
TLDR
We present an optimal framework for improving low bit-rate performance of block coders. Expand
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Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution
TLDR
We quantify the 'sufficient sparsity' condition, defining an equivalence breakdown point (EBP): the degree of sparsity of α required to guarantee equivalence to hold; this threshold depends on the matrix. Expand
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Variable projection for near-optimal filtering in low bit-rate block coders
TLDR
We show that the problem of finding optimal filters for a general, unknown, "black-box" coder can be written as a separable least squares problem in two sets of variables and solve this problem using the Variable Projection method. Expand
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