Quaternion quantum image representation: new models

In quaternion algebra the color images are processed not by separating their color components, but these components are presented and processed together as one unit. In framework of the quaternion image representation, many effective methods of processing color images can be developed, including image enhancement in spatial and frequency domains. In this paper, we unite two approaches for processing color images, by proposing a quaternion representation in quantum imaging, which includes the color images in the RGB model together with the grayscale component or brightness. The concept of quaternion two-qubit is considered and applied for image representation in each quantum pixel. The colors at each pixel are processed as one unit in quaternion representation. Other new models for quaternion image representation are also described. It is shown that a quaternion image or four component image of 𝑁 × 𝑀 pixels, can be represented by (𝑟 + 𝑠 + 2) qubits, when 𝑁 = 2^𝑟 and 𝑀 = 2^𝑠, 𝑟, 𝑠 > 1. The number of qubits for representing the image can be reduced to (𝑟 + 𝑠), when using the quaternion 2-qubit concept.