Image processing using the quantum quaternion Fourier transform

Abstract

There is a growing interest in quantum image processing (QIP) that rose from the desire to exploit the properties of quantum computing to improve the performance of classical techniques and their applications. Since the introduction of a quaternion by Hamilton in 1843, quaternions had been used in a lot of applications. We show how the quantum states and quantum operators work in the field of quaternions and how we can use it to extend the quantum complex Fourier transform (QCFT) to the quantum quaternion Fourier transform (QQFT). We propose for the first time the novel algorithm for the QQFT. We explain the impossibility of the use of convolution in quantum image processing; we design filters in the quaternion Fourier spectrum and the space domain an edge detector and a quantum median filter.