Solve quadratically constrained overdetermined l1 minimization.

Solve min ||K * x - f||_1 s.t. ||y - x||_2 <= \epsilon where K has more rows than columns.

Description

=Solve quadratically constrained overdetermined l1 minimization:
  min ||K * x - f||_1 s.t. ||y - x||_2 <= \epsilon
using a primal interior point method (using a log barrier).

Sparse linear systems are solved using a specialized preconditioning scheme.

Use of Blendenpik and SpTriSolve is suggested (both are available through File Exchange).

Algorithm is described in Section 5 of:
"L1-sparse reconstruction of sharp point set surfaces"
http://www.cs.tau.ac.il/~haima/l1sparse-tog-final.pdf
also based (partially) on l1-Magic

• MATLAB release: MATLAB 7.4 (R2007a)