Sparse Representation for Color Image Based on Geometric Algebra

Existing sparse representation models represent RGB channels separately without thinking about the relationship color channels, which lose some color structures inevitably. In this paper, we introduce a novel sparse representation model for color image based on geometric algebra (GA) theory and its corresponding dictionary learning algorithm, namely K-GASVD is proposed. The model represents the color image as a multivector with the spatial and spectral information in GA space, providing a kind of vectorial representation for the inherent color structures rather than a scalar representation via current sparse image models. The proposed sparse model is validated in the applications of color image denoising and reconstruction. The experimental results demonstrate that our sparse image model avoids the hue bias phenomenon successfully and retained the color structures completely. It shows its potential as a general and powerful tool in various applications of color image analysis.