Image Compression, Comparison between Discrete Cosine Transform and Fast Fourier Transform and the problems associated with DCT Imdad Ali Ismaili 1 , Sander Ali Khowaja 2 , Waseem Javed Soomro 3 1 Institute of Information and Communication Technology, University of Sindh, Jamshoro, Sindh, Pakistan 2 Institute of Information and Communication Technology, University of Sindh, Jamshoro, Sindh, Pakistan Abstract - The research article focuses on the Image Compression techniques such as. Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT). These techniques are chosen because of their vast use in image processing field, JPEG (Joint Photographic Experts Group) is one of the examples of compression technique which uses DCT. The Research compares the two compression techniques based on DCT and FFT and compare their results using MATLAB software, Graphical User Interface (GUI). These results are based on two compression techniques with different rates of compression i.e. Compression rates are 90%, 60%, 30% and 5%. The technique allows compressing any picture format to JPG format. The result shows that DCT is better technique than FFT; however the compression results are same as that of 30% compression to 5% compression reflecting not significant change in visual results excepting the file size varying to small fraction. The compression technique works fine with the images having little noise but the compression technique due to its lossy nature don’t work very well in medical images such as CT, X-ray etc. Keywords: Image Compression, JPEG, Discrete Cosine Transform, Fast Fourier Transform, Image Processing 1 Introduction As we can analyze that demand for multimedia data through the mobile network and conveniently accessing the concerned data through mobile services is growing day by day. In order to make the multimedia data usage efficient and insidious it is essential that the data representation and techniques for encoding the data at different platforms or in all applications should follow the same standard. In all multimedia data categories image data has got the highest preference because of its usage and lion’s share in terms of the bandwidth consumption for multimedia communication. Due to this it is very necessary as well as a challenge for the researchers to develop efficient methods for image compression for effective and efficient use of bandwidth. In spite of many disadvantages of analog representation of signals compared to digital counterpart, they need smaller number of bits for storage and transmission. For example, a low-resolution television quality color video of 36 frames/sec where each frame comprises of 800 x 600 pixels need more than 240 Mbps for storage, so the digitized color video for the duration of 1 hour will almost require 96 Gbps for storage. Similarly, the requirement for the HDTV will be much higher than the calculations mentioned above; this increases the bandwidth requirement of the channel which is very costly. This is the challenging part for the researchers to transmit theses digital signals through limited bandwidth communication channel, most of the times the way is found to overcome this obstacle but sometimes it is impossible to send these digital signals in its raw form. Though there has been a revolution in the increased capacity and decreased cost of storage over the past years but the requirement of data storage and data processing applications is growing explosively to out space this achievement.[8] 2 Fourier Theory Conversion of Time domain or spatial description i.e. pixel by pixel description of an image into frequency domain which applies to the entire image is called the Fourier Transform. The conversion of frequency domain to the real space description is called its inverse Fourier Transform. We can easily study the function as it is represented as the series of sum of Sines and Cosines but it has a disadvantage of very complex computation. [4] 3 Discrete Fourier Transform The Discrete Fourier Transform (DFT) is the study of Fourier analysis of finite-domain discrete time signals. The DFT is central to many kinds of signal processing, including the analysis of compression of video and sound information. DFT requires large number of multiplications and additions for the calculation. For example a 8-point DFT, there are 8 complex multiplications and 7 complex additions, that’s why DFT is computed efficiently using a Fast Fourier Transform (FFT) algorithm. [4] 4 Fast Fourier Transform To find the N-DFT of a given sequence, we only need to compute the N/2 complex coefficients, while the second N/2 complex coefficients can be achieved by manipulating the data from the first calculation. Hence N- point DFT requires N2 additions. But with Decimation in Time algorithms, it requires computing two times N/2-point DFT. Therefore, number of additions required is (1)