2 - D Hexagonal Quaternion Fourier Transform in Color Image Processing

In this paper, we present a novel concept of the quaternion discrete Fourier transform on the two-dimensional hexagonal lattice, which we call the twodimensional hexagonal quaternion discrete Fourier transform (2-D HQDFT). The concept of the right-side 2D HQDFT is described and the left-side 2-D HQDFT is similarly con sidered. We analyze and present a new approach in processing the color images in the frequency domain, which is based on the tensor representation of color images. • In color tensor representation on the hexagonal lattice, three components of the image in the RGB space are described by one dimensional signal in the quaternion algebra. The representation is effective and allows us to process the color image by 1-D quaternion signals which can be processed separately. • The 2-D HQDFT can be calculated by a set of 1-D quaternion discrete Fourier transforms (QDFT) of the splitting-signals.  The tensor transform-based 2-D QDFT is simple to apply and design, which makes it very practical in color image processing in the frequency domain.