Multivector Sparse Representation for Multispectral Images Using Geometric Algebra

Multispectral images can provide more faithful representations for real scenes than the traditional images and improve the performance of image restoration tasks. In this paper, we propose a novel multivector sparse representation model for multispectral images using geometric algebra (GA), with the truth that GA is now well used in image processing and it gives a formidable way to represent multispectral images. The proposed model represents a multispectral image as a GA multivector by fully considering the spatial and spectral information, where a GA dictionary learning algorithm is presented using the K-GA-singular value decomposition (GASVD) (generalized K-means clustering for GASVD) method. Consequently, with the complete consideration of the relationship between spectral channels in multispectral images, artifacts and blurring effects can be successfully avoided. The experimental results demonstrate that the proposed sparse model surpasses the existing methods for multispectral images reconstruction and denoising tasks by capturing correlations between spectral channels thoroughly and shows its usefulness and effectiveness for multispectral images processing.