Image Compression Using Fractional Fourier Transform

Abstract

The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing, and high-definition television (HDTV) has increased the need for effective and standardized image compression techniques. The purpose of image compression is to achieve a very low bit rate representation, while preserving a high visual quality of decompressed images. It has been recently noticed that the fractional Fourier transform (FRFT) can be used in the field of image processing. The significant feature of fractional Fourier domain image compression benefits from its extra degree of freedom that is provided by its fractional orders ‘a’. The fractional Fourier transform is a time-frequency distribution and an extension of the classical Fourier transform. The FRFT depends on a parameter ‘a’ can be interpreted as a rotation by an angle a=ap/2 in the time–frequency plane. An FRFT with a=p/2 corresponds to the classical Fourier Transform, and an FRFT with a=0 corresponds to identity operator. In the present study, the FRFT, which is generalization of Fourier transform, is used to compress the image with variation of its parameter ‘a’. It is found that by using FRFT, high visual quality decompressed image can be achieved for same amount of compression as that for Fourier transform. By adjusting ‘a’ to different values, FRFT can achieve low mean square error (MSE), better peak signal to noise ratio (PSNR), a high compression ratio (CR), while preserving good fidelity of decompressed image. By varying ‘a’, it can achieve high CR even for same cutoff. As cutoff increases, CR increases but image quality degrades since there is tradeoff between image quality and CR.