Research On Color Image Encryption And Denoising Algorithms Using Quaternions

Color image processing usually adopts the approach of decomposing a color image into three channels. However, this approach fails to consider the holistic property of three channels and the inherent correlation between them. Therefore, based on the quaternion representation of color images and the algebra of quaternions, this dissertation focuses on the efficient application of the conventional tools for gray-scale images in color image encryption and color image denoising, dealing with color images in a holistic manner as well as considering the inherent correlation between the three channels. The main research works are as follows:(1) Multiple-parameter fractional quaternion Fourier transform (MPFrQFT) is defined to generalize multiple-parameter fractional Fourier transform (MPFrFT) for gray images to color images with little color information loss, Moreover, the proof of inverse transform and the effective discrete implementation of MPFrQFT are provided;(2) By combining with the double random phase encoding technology and the fractional quaternion transform, a color image encryption algorithm based on MPFrQFT is proposed. Experimental results and analysis demonstrate that, compared to the existing quaternion-based double random phase encoding encryption algorithms, the proposed MPFrQFT-based algorithm has larger key space and is more sensitive to the key transform orders though all of them perform well in statistical analysis test and robustness test;(3) Based on the holistic manner of color image processing using quaternion representation, and according to the different characteristics of the impulse noise and the Gaussian noise, an algorithm is proposed to remove mixed noise for color images denoising. This algorithm combines the algorithm based on quaternion directional vector order-statistics and the improved quaternion optimal weights non-local means filter. The proposed algorithm considers the inherent correlation among three channels and can reserve more texture details.