Stable image reconstruction using total variation minimization
This work addresses image recovery for applications like medical imaging or compressed sensing, offering incremental improvements in theoretical guarantees for existing methods.
The paper tackles the problem of robust image reconstruction from under-sampled noisy measurements by using total variation minimization, achieving near-optimal guarantees with reconstruction accuracy within the best s-term approximation of the gradient up to a logarithmic factor using O(slog(N)) measurements.
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.