Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 6, Issue 2, Pages 1035-1058Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120868281
Keywords
compressed sensing; stability; restricted isometry property; Sobolev inequality; total variation minimization
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Funding
- Donald D. Harrington Faculty Fellowship
- Alfred P. Sloan Research Fellowship
- DOD-Navy grant [N00014-12-1-0743]
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This paper 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 a suitably incoherent matrix.
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