Sparsest solutions of underdetermined linear systems via l(q)-minimization for 0 < q <= 1 Academic Article uri icon


  • We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal q-quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the 1-norm. We then introduce a simple numerical scheme to compute solutions with minimal q-quasinorm, and we study its convergence. Finally, we display the results of some experiments which indicate that the q-method performs better than other available methods. 2008 Elsevier Inc. All rights reserved.

published proceedings


altmetric score

  • 1

author list (cited authors)

  • Foucart, S., & Lai, M.

citation count

  • 486

complete list of authors

  • Foucart, Simon||Lai, Ming-Jun

publication date

  • January 2009