Quaternionic phase and axis/colour retrieval

We demonstrate a quaternion-based phase and axis retrieval algorithm and a quaternionic realization of the Gerchberg–Saxton method, particularly suitable for RGB images. The RGB image is represented here as quaternion-valued image in polar form with the components quaternionic magnitude, axis and phase. We discuss their importance and relations in spatial and Fourier domain. We illustrate three versions of retrieval: the quaternionic phase only, the axis only and the joint phase and axis retrieval algorithm derived from the classical Gerchberg–Saxton algorithm. We discuss how the retrieval results are influenced by the choice of the Fourier axis of the quaternionic Fourier transform. Finally, we show that by including more constraints and prior knowledge, respectively, the retrieval can be improved.