Nonlinear Transformed Low-Rank Quaternion Tensor Total Variation for Multidimensional Color Image Completion

Area of Science:

• Computer Vision
• Image Processing
• Applied Mathematics

Background:

• Multidimensional color image completion is a significant challenge.
• Existing tensor methods often ignore intrinsic correlations between RGB channels.
• This limitation hinders holistic modeling and accurate image reconstruction.

Purpose of the Study:

• To develop a novel method for multidimensional color image completion.
• To preserve chromatic relationships by modeling RGB channels holistically.
• To improve the accuracy and compactness of low-rank image representations.

Main Methods:

• Representing RGB values as pure quaternions and organizing them into a quaternion tensor.
• Proposing a nonlinear transformation within the quaternion domain to capture data nonlinearities.
• Introducing novel regularization terms for global low-rankness and local smoothness.
• Optimizing the model using a nonlinear alternating direction method of multipliers (ADMM).

Main Results:

• The proposed quaternion tensor method significantly outperforms state-of-the-art techniques.
• The method effectively preserves chromatic relationships in color images.
• Nonlinear transformations enhance the exploitation of structural priors for better completion.

Conclusions:

• The novel quaternion tensor approach offers a superior solution for multidimensional color image completion.
• Holistic modeling of RGB channels through quaternions is crucial for preserving color information.
• The method demonstrates enhanced performance due to nonlinear modeling and effective regularization.