Image Compression Using Fractional Hartley Transform

Abstract

As use and reliance on computers continues to grow, so does the need for efficient ways of storing large amount of data. For example, someone with a web page or online catalog that uses dozens or hundreds of images will more than likely need to use some form of image compression to store those images. The purpose of image compression is to achieve a very low bit rate representation, while preserving a high visual quality of decompressed images. Basically there are two compression techniques, lossless and lossy. In lossy compression techniques various transforms are used. There are many transforms like Fourier transform, K-L transform, Haar transform, Hartley transform etc. In general the Fourier transform is difficult to apply because it depends on complex numbers. This problem can be avoided by using a similar transform known as the Hartley transform The Hartley transform maps real-valued sequences into real-valued frequency domain sequences. This work aims to implement the image compression using fractional Hartley transform (FRHT). The fractional Hartley transform is the generalization of Hartley transform that depends on a parameter ‘a’, which provides the additional degree of freedom. With variation of its parameter ‘a’. It is found that by using fractional Hartley transform, high visual quality decompressed image can be achieved for same amount of compression as compared to Hartley transform. By varying ‘a’ to different values, an optimum value of ‘a’ can be achieved with low root mean square error (RMSE), better peak signal to noise ratio (PSNR) i.e. better quality of decompressed image.