Hypercomplex Sparse Representation And Its Application

At first, we propose a hypercomplex adaptive sparse dictionary learning method (QK-SVD) after formulizing hypercomplex sparse representation problem. The QK-SVD algorithm can learn a hypercomplex adaptive sparse representation dictionary from training data by catching both the important structural atoms and component correlation atoms. We use QK-SVD in color image denoising problem. With the help of hypercomplex, we can process the three components of R, G, B channels at the same time, without losing the relationship between each other. This ensures the integrity of color space. In the experiments, we show that QK-SVD has better performance on color image denoising issue than using K-SVD separately on each color channel.Considering the quick growth of computation complexity when signal's dimension rises, we propose a hypercomplex smooth Lo norm sparse representation (QSLo) algorithm. It is very suitable for hypercomplex sparse representation, due to its low computational complexity and little growth with higher signal's dimension. The QSLo can be effectively used in hypercomplex sparse component analysis (SCA). It gives good approximation of each dimensionality of hypercomplex sparse source. Also, in this paper, we extend our discussion to a noise setting and give a more robust smooth Lo algorithm (NSLo).Finally, this paper introduces an edge-weighted structural similarity index (EWSSIM) in image quality assessment field. After analyzing issues in structural similarity index (SSIM), we show the reasons why SSIM gives poor evaluations on blurring images and high Guassian white noise distorted images. With the help of edge structural information, the proposed index outperforms SSIM in blurred and Gaussian white noise distorted images and also gives a better coherent evaluation for all kinds of distortions in LIVE database. This paper proposes a method to evaluate color image quality by using hypercomplex adaptive sparse dictionary. The adaptive dictionary extracts important structure and texture information to evaluate distorted images. This method shows better results on blurring images.