Real versus complex null space properties for sparse vector recovery Academic Article

abstract

• We identify and solve an overlooked problem about the characterization of underdetermined systems of linear equations for which sparse solutions have minimal 1-norm. This characterization is known as the null space property. When the system has real coefficients, sparse solutions can be considered either as real or complex vectors, leading to two seemingly distinct null space properties. We prove that the two properties actually coincide by establishing a link with a problem about convex polygons in the real plane. Incidentally, we also show the equivalence between stable null space properties which account for the stable reconstruction by 1-minimization of vectors that are not exactly sparse. 2010 Acadmie des sciences.

authors

• Foucart, Simon

published proceedings

• COMPTES RENDUS MATHEMATIQUE

author list (cited authors)

• Foucart, S., & Gribonval, R.

citation count

• 11

complete list of authors

• Foucart, Simon||Gribonval, Remi

publication date

• January 2010

publisher

• Elsevier  Publisher

published in

• COMPTES RENDUS MATHEMATIQUE  Journal

Digital Object Identifier (DOI)

• 10.1016/j.crma.2010.07.024

start page

• 863

end page

• 865

volume

• 348

issue

• 15-16

URL

• http://dx.doi.org/10.1016/j.crma.2010.07.024