Image Compression using Fourier Transformation with Genetic Algorithm

Abstract

This paper introduce proposed algorithm consist of: (1) using Discreet Fourier Transformation (DFT) which convert an image into frequency domain image, then compress frequency domain image with Run-Length-Encoding (RLE), and Arithmetic Coding. (2) Apply Inverse Fourier Transformation (IDFT) to obtains an approximately original image, and then compared with original image to get the difference stored in a new matrix called (D(spatial) ). The matrix D(spatial) transformed to frequency domain by Discreet Cosine Transform (DCT) (D(frequency)). Finally applying weight vector (W= [0.5, 0.3, 0.2]) on the D(frequency), multiply "W" with each three coefficients from matrix D(frequency) to produce a new matrix (G), at last compress matrix G by arithmetic coding. (3) The decompression process start from arithmetic decoding to return frequency domain matrix (i.e. return DFT image), then apply Inverse DFT to get an image A, also from arithmetic decoding produced matrix G. The Genetic Algorithm used to produce minimized matrix D(frequency) by take each data from matrix G and using fitness function. Finally apply inverse DCT to generate matrix D(spatial), added with image A to produce a decompressed image. In this paper our approach, compared with JPEG technique, by using Peak Signal to Noise Ratio (PSNR).