Joint Sparse Representation Model for Multi-Channel Image Based on Reduced Geometric Algebra

IEEE Access

Wenming Cao¹  Miaomiao Shen²  Rui Wang² 

[1] College of Information Engineering, Shenzhen University, Shenzhen, China;Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, School of Communication and Information Engineering, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai, China;

关键词: Sparse representation;    reduced geometric algebra;    multi-channel image;    dictionary learning;   

DOI  :  10.1109/ACCESS.2018.2819691

来源: DOAJ

【 摘 要 】

Sparse representations have been extended to color image processing. However, existing sparse models treat each color image pixel either as a scalar which loses color structures or as a quaternion vector matrix with high computational complexity. In this paper, we propose a novel sparse representation model for color image that bears multiple channels based on geometric algebra. First, a novel theory of reduced geometric algebra (RGA) is provided, including commutative sparse basis and the geometric operations. Second, taking advantage of the RGA theory, the model represents color image with three-channel as a multivector with the spatial and spectral information in RGA space. Third, the dictionary learning algorithm is provided using the K-RGA-based singular value decomposition (K-RGASVD) (generalized K-means clustering for RGASVD) method. The comparison results demonstrate the proposed model can remove the data redundancy and reduce the computational complexity, and can meanwhile effectively preserve the inherent color structures. The result suggests its potential as a homogeneous and efficient tool in various applications of color image analysis.

【 授权许可】

Unknown