Frequency Domain Filtering of Colour Images Using Quaternion Fourier Transforms

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The 2D Fourier Transform is an important image processing tool to decompose a grayscale image into its sine and cosine components. The output of the transformation represents the image in the frequency domain, given the input image in the spatial domain. Filtering in the frequency domain is a common image and signal processing technique. In this paper, the authors propose a new approach for filtering of colour images in the frequency domain using quaternion Fourier transform(also known as hyper-complex Fourier transform). This transform allows colour images to be transformed as a whole, rather than as colour separated components. Specifically, this paper deals with colour image smoothing and sharpening in the frequency domain by using quaternion Fourier transform.