Quaternion-Based Dictionary Learning and Saturation-Value Total Variation Regularization for Color Image Restoration

Color image restoration is a critical task in imaging sciences. Most variational methods regard the color image as a Euclidean vector or the direct combination of three monochrome images and completely ignore the inherent color structures within channels. To better describe the relationship of color channels, we represent the color image as the so-called pure quaternion matrix. Note that the celebrated dictionary learning method has attracted considerable attention for image recovery in the past decade. Following this idea, we propose a novel quaternion-based color image recovery method. This model combines the advantages of dictionary learning and the total variation method for color image restoration. The new strategy used in the proposed model manages to handle the color image restoration problem in the quaternion space. Moreover, the new proposed model can be easily solved by the classical alternating direction method of multipliers (ADMM) algorithm. Numerical results demonstrate clearly that the performance of our proposed dictionary learning method is better than some state-of-the-art color image dictionary learning and total variation methods in terms of some criteria and visual quality.

I. Introduction

Color image restoration aims to recover a clean image from the degraded observation. In the processing of generating, transmission, and storage, the color image will be unavoidably degraded by noise and blur. As images are essential in various fields such as biomedical imaging, microscopy, astronomical imaging, and multimedia processing, it is critical to restoring the sharp image from the degraded observation.