Multi-Dimensional Visual Data Completion via Low-Rank Tensor Representation Under Coupled Transform.

Area of Science:

• Computer Vision
• Image Processing
• Applied Mathematics

Background:

• Tensor completion is crucial for recovering missing data in multi-dimensional arrays like images and videos.
• Representing the inherent low-rank structure of data is a key challenge in tensor completion.

Purpose of the Study:

• To propose a novel low-rank tensor representation for improved tensor completion.
• To develop an effective model and algorithm for recovering missing information in multi-dimensional visual data.

Main Methods:

• A novel low-rank tensor representation using coupled transforms: 2D framelet transform (spatial), 1D/2D Fourier transform (spectral/temporal), and Karhunen-Loéve transform (SVD).
• Formulation of a convex optimization problem for tensor completion based on the proposed representation.
• Development of the Alternating Directional Method of Multipliers (ADMM) algorithm to solve the optimization problem.

Main Results:

• The proposed coupled transform representation achieves better low tensor multi-rank approximation.
• Numerical experiments on color images, multispectral images, and videos demonstrate superior performance compared to state-of-the-art methods.
• The method shows significant improvements in both qualitative and quantitative aspects of data recovery.

Conclusions:

• The novel low-rank tensor representation and ADMM-based completion model offer a powerful approach for multi-dimensional visual data recovery.
• This method effectively exploits multi-scale spatial and spectral/temporal redundancies for enhanced completion accuracy.
• The proposed technique represents a significant advancement in the field of tensor completion for visual data.