Stable Image Reconstruction Using Total Variation Minimization

Authors

Deanna Needell, Claremont McKenna CollegeFollow
Rachel Ward, University of Texas at Austin

Document Type

Article

Department

Mathematics (CMC)

Publication Date

3-13-2013

Abstract

This article presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization. In particular, we show that from O(s log(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in the null space of suitably incoherent matrices.

Rights Information

© 2013 Society for Industrial and Applied Mathematics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1137/120868281

Recommended Citation

Needell, D., Ward, R., "Stable Image Reconstruction Using Total Variation Minimization," SIAM J. Imaging Sci., 6(2), 1035–1058, 2013. doi: 10.1137/120868281