Cart (Loading....) | Create Account
Close category search window

On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Bruckstein, A.M. ; Dept. of Comput. Sci., Technion - Israel Inst. of Technol., Haifa ; Elad, M. ; Zibulevsky, M.

An underdetermined linear system of equations Ax = b with nonnegativity constraint x ges 0 is considered. It is shown that for matrices A with a row-span intersecting the positive orthant, if this problem admits a sufficiently sparse solution, it is necessarily unique. The bound on the required sparsity depends on a coherence property of the matrix A. This coherence measure can be improved by applying a conditioning stage on A, thereby strengthening the claimed result. The obtained uniqueness theorem relies on an extended theoretical analysis of the lscr0 - lscr1 equivalence developed here as well, considering a matrix A with arbitrary column norms, and an arbitrary monotone element-wise concave penalty replacing the lscr1-norm objective function. Finally, from a numerical point of view, a greedy algorithm-a variant of the matching pursuit-is presented, such that it is guaranteed to find this sparse solution. It is further shown how this algorithm can benefit from well-designed conditioning of A .

Published in:

Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 11 )

Date of Publication:

Nov. 2008

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.