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Robust video restoration by joint sparse and low rank matrix approximation. (English) Zbl 1234.68451

Summary: This paper presents a new patch-based video restoration scheme. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem. The resulting nuclear norm and \(\ell_1\) norm related minimization problem can also be efficiently solved by many recently developed numerical methods. The effectiveness of the proposed video restoration scheme is illustrated on two applications: video denoising in the presence of random-valued noise, and video in-painting for archived films. The numerical experiments indicate that the proposed video restoration method compares favorably against many existing algorithms.

MSC:

68U10 Computing methodologies for image processing
65J22 Numerical solution to inverse problems in abstract spaces
90C25 Convex programming
65K05 Numerical mathematical programming methods