Quaternion Fourier Transform for Colour Images

The Fourier transforms plays a critical role in broad range of image processing applications, including enhancement, restoration, analysis and compression. For filtering of gray scale images 2D Fourier transform is an important tool which converts the image from spatial domain to frequency domain and then by applying filtering mask filtering is done. To filter color images, a new approach is implemented which uses hyper complex numbers (called as Quaternion) to represent color images and uses Quaternion Fourier transform for filtering. This transform allows color images to be transformed as whole, rather than as color separated components. This paper is concerned with frequency domain noise reduction of colour images using Quaternion Fourier transform. The approach is based on obtaining quaternion Fourier transform of colour image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion fourier transform, which explains the accuracy of this method. Keywords— Hypercomplex numbers, Quaternion Fourier Transform(QFT), Gaussian LPF and HPF.