Low-rank tensor completion method based on three-dimensional total variation and Tucker decomposition

Abstract

A low-rank tensor completion method based on three-dimensional total variation and Tucker decomposition comprises the following steps: reading a damaged video into MATLAB software, converting the damaged video into a three-dimensional tensor with the tensor size of X * Y * Z, optimizing a solved objective functional by using an augmented Lagrange formula, decomposing a mixed objective functional into a plurality of optimization sub-problems, introducing three auxiliary variables, dividing the three auxiliary variables into three independent parts, introducing a three-dimensional weighted difference operator into three-dimensional total variation constraint, retaining a multi-factor structure of the three-dimensional tensor, and describing a segmented smooth structure of a three-dimensional space domain of the tensor data; continuously iteratively updating the introduced three auxiliary variables and the tensor y needing to be repaired, and determined that the tensor completion is completed when the maximum number of iterations is reached or the relative error of the tensor y complemented for two consecutive times is smaller than a given parameter value epsilon. According to the method, multi-channel data can be effectively processed, the low-rank performance of the tensor is described, the proposed convex functional is efficiently solved, and the restoration of the high-loss-rate damaged video is completed.

Description

technical field [0001] The invention belongs to the technical field of digital image processing, and in particular relates to a low-rank tensor completion method based on three-dimensional full variation and Tucker decomposition, aiming at damaged videos. Background technique [0002] With the rapid development of data acquisition technology, a large number of multi-dimensional visual data are emerging, such as frequently used color images, videos, hyperspectral (HS) or multispectral (MS) images, magnetic resonance imaging (MRI) data, and electronic business data. In fact, these multi-dimensional visual data obtained from the application scene can be regarded as a tensor, and each channel, view or band is collectively called a component. For example, a color image (grayscale video sequence) can be viewed as a three-dimensional (3D) tensor due to its height, width, and color (temporal) channels. Among them, the scale and quantity of video data sets are increasing day by day,...

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Problems solved by technology

[0006] In the existing LRTV research, two-dimensional TV is usually used to constrain the tensor expansion matrix. However, a large number of studies have shown that directly expanding high-dimensional data into a two-dimensional matrix will inevitably lose the high-dimensional data. Spatial structure

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