Research On Quaternion Orthogonal Transforms Of Color Images And Their Applications In Information Security

Unitary transforms have been extensively used in image analysis, and information security, etc. Generally speaking, there are two approaches that are often used for color images. The first one consists of transforming the color image into gray-scale one, which may lose some significant color information. The second one decomposes the color image into three channels, which does not consider the holistic property of three channels and the inherent correlation among them. Therefore, based on the algebra of quaternion and the quaternion representation of color images, two traditional unitary transforms for gray images have been generalized and applied to color image processing, especially in the application of image information security including digital watermarking and image encryption. The main contributions are as follows:(1) Modulated quaternion lapped transform (MQLT) and conjugate symmetric sequency-ordered quaternion hadamard transform (CS-SQHT) are respectively defined to generalize the conventional modulated complex lapped transform (MCLT) and the conventional conjugate symmetric sequency-ordered complex hadamard transform (CS-SCHT) for gray images. MQLT and CS-SQHT are suitable for the processing of color images.(2) The symmetric properties of the MQLT coefficients are analyzed after the establishment of the relationships between the MQLT coefficients and the MCLT coefficients of three channels. After that, combining with Arnold transform and multiple redundant embedding strategy, a robust blind dual color image watermarking algorithm is proposed based on MQLT and its symmetric property. In order to avoid a watermark energy loss, the MQLT coefficients are modified to embed watermarks according to their symmetric properties. The proposed algorithm fully utilizes the four-dimensional MQLT domain and embeds meaningful color watermarks into a color host image.(3) Combining with the block transform and the double random phase encoding technology, we propose a robust color image encryption algorithm based on the quaternion representation of color images and CS-SQHT. The proposed algorithm considers the holistic property of three channels of a color image and the inherent correlation among them.