Abstract
The singular value decomposition (SVD) has been considered as one of the most powerful tools in numerical algebra and has witnessed great success in a wide range of image processing tasks, such as principal component analysis, linear discriminant analysis and sparse representation. However, the existing SVD algorithms cannot directly applied in octonion signals. In this paper, we propose a novel singular value decomposition algorithm for octonion signal, namely OSVD. Firstly, a new real representation according to the components of the original octonion signal is formed and the real SVD for the real matrix is performed. Then with several largest singular values and the corresponding vectors in both left and right unitary matrices selected, the octonion signal can be reconstructed successfully. It is demonstrated by the denoising experiments multispectral image with seven spectral channels that our proposed algorithm significantly outperforms existing state-of-the-art algorithms in both quantitative and visual performance.