A Non-Negative and Sparse Enough Solution of an Underdetermined Linear System of Equations is Unique

  title={A Non-Negative and Sparse Enough Solution of an Underdetermined Linear System of Equations is Unique},
  author={Alfred M. Bruckstein and Michael Elad and Michael Zibulevsky},
In this paper we consider an underdetermined linear system of equations Ax = b with non-negative entries of A and b, and the solution x being also required to be nonnegative. We show that if there exists a sufficiently sparse solution to this problem, it is necessarily unique. Furthermore, we present a greedy algorithm – a variant of the matching pursuit – that is guaranteed to find this sparse solution. We also extend the existing theoretical analysis of the basis pursuit problem, i.e. min ‖x… CONTINUE READING
Highly Cited
This paper has 32 citations. REVIEW CITATIONS


Publications citing this paper.
Showing 1-10 of 22 extracted citations

On the use of sparsity for recovering discrete probability distributions from their moments

2011 IEEE Statistical Signal Processing Workshop (SSP) • 2011
View 7 Excerpts
Highly Influenced

Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing

2010 2nd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing • 2010
View 1 Excerpt

Compressive Fresnel Holography

Journal of Display Technology • 2010
View 1 Excerpt


Publications referenced by this paper.
Showing 1-10 of 29 references

Sparse representations in unions of bases

IEEE Trans. Information Theory • 2003
View 4 Excerpts
Highly Influenced

On the recovery of missing samples via sparsity conditions, M.Sc. Thesis, The Electrical Engineering department, the Technion - Israel

S. Raboi
Institute of Technology, • 2007
View 2 Excerpts

Just relax: convex programming methods for identifying sparse signals in noise

IEEE Transactions on Information Theory • 2006
View 1 Excerpt

Nonnegative Sparse PCA

NIPS • 2006
View 1 Excerpt

Thresholds for the Recovery of Sparse Solutions via L1 Minimization

2006 40th Annual Conference on Information Sciences and Systems • 2006
View 2 Excerpts

Neighborliness of randomly projected simplices in high dimensions.

Proceedings of the National Academy of Sciences of the United States of America • 2005
View 2 Excerpts

Similar Papers

Loading similar papers…