Recovery of Short, Complex Linear Combinations Via<tex>$ell _1$</tex>Minimization
Recovery of Short, Complex Linear Combinations Via<tex>$ell _1$</tex>Minimization
This note provides a condition under which lscr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization (also known as basis pursuit) can recover short linear combinations of complex vectors chosen from fixed, overcomplete collection. This condition has already been established in the real setting by Fuchs, who used convex analysis. The proof given here …