Stable image reconstruction using total variation minimization

Deanna Needell; Rachel Ward

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arXiv · 1202.6429

Stable image reconstruction using total variation minimization

Deanna Needell·Rachel Ward

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Abstract

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(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.

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Deanna Needell, Rachel Ward. 2012-02-29. Stable image reconstruction using total variation minimization. https://arxiv.org/abs/1202.6429

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