Novel methods for multilinear data completion and de-noising based on tensor-SVD

TL;DR

This paper introduces novel tensor-SVD based methods for efficient multilinear data completion and de-noising, demonstrating superior performance in 3D and 4D video applications compared to existing techniques.

Contribution

The paper develops tensor nuclear norm penalized algorithms for video completion and robust PCA for de-noising, leveraging tensor-SVD for improved efficiency and accuracy.

Findings

Tensor-SVD enables more efficient video representation.

Proposed algorithms outperform existing methods in recovery accuracy.

Superior de-noising results for 3D video data with sparse corruptions.

Abstract

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].