Reserved Discrete Cosine Transform Coefficients Effects on Image Compression

Abstract

Discrete Cosine Transform (DCT) is a special case of Discrete Fourier Transform (DFT) in which the sine component has been eliminated leaving only the cosine terms. DCT packing the energy into few numbers of transformed coefficients associated with low frequencies, the high frequency coefficients are discarded and replaced by zero coefficients. These coefficients may be discarded with little loss in energy and that will not effect that much on the image quality since the human eye doesn’t sense the high frequency components. The discarding process provides a trade-off between compression ratio and peak signal to noise ratio. Simulation programs were written using MATLAB with three images each of them of size (256×256) with 256 grayscale levels. Each line of these images is divided into blocks and each block is considered as a row vector of 128 pixels. 1D DCT is applied to convert each vector of pixels into a vector of 128 transformed coefficients. When the number of retained useful low frequency coefficient is 30% and less, the reconstructed images shows a noticeable degradation at all, in spite of increasing compression ratio. Two performance measurements have been employed, namely the objective and subjective.