Tensor error correction for corrupted values in visual data

Abstract

The multi-channel image or the video clip has the natural form of tensor. The values of the tensor can be corrupted due to noise in the acquisition process. We consider the problem of recovering a tensor L of visual data from its corrupted observations X = L + S, where the corrupted entries S are unknown and unbounded, but are assumed to be sparse. Our work is built on the recent studies about the recovery of corrupted low-rank matrix via trace norm minimization. We extend the matrix case to the tensor case by the definition of tensor trace norm in [6]. Furthermore, the problem of tensor is formulated as a convex optimization, which is much harder than its matrix form. Thus, we develop a high quality algorithm to efficiently solve the problem. Our experiments show potential applications of our method and indicate a robust and reliable solution.