Vector Sparse Representation of Color Image Using Quaternion Matrix Analysis based on Genetic Algorithm

Abstract - Vector sparse image models use color image pixel as a scalar vector, that represents color channels independently or concatenate color channels as an indefinite image. In this paper, we recommend a vector sparse representation model for color images using quaternion matrix scrutiny and Genetic algorithm for reduce distortion. The proposed system represents the color image as a quaternion matrix, where a quaternion-based dictionary learning algorithm is existing using the K-quaternion singular value decomposition system based on Genetic Algorithm. Genetic Algorithms (GAs) are adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetics. Sparse representations have been extended to deal with color images composed of three channels. It conducts the sparse origin selection in quaternion space, which uniformly transforms the channel image to an orthogonal color space. In this new color space, it is important that the inherent color structures can be entirely preserved during vector reconstruction. Additionally, the proposed sparse model is more efficient compare with the current sparse models for image restoration tasks due to poorer redundancy between the atoms of different color channels. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. By the use of Genetic algorithm, we remove the distortion from image.