Low dynamic range discrete cosine transform (LDR-DCT) for high-performance JPEG image compression

Abstract

In mathematical theory, the discrete cosine transform (DCT) is a lossless orthogonal transformation method which means it outputs exactly the same values of the input after the inverse transformation. However, this is impossible in today's technology due to the limited capacity of processors in which the maximum value that a number can take is 264 - 1 (20-digit number) in a 64-bit register. Since the DCT employs the floating values higher than this precision, there occurs a round-off error which causes a particular loss of information after the inverse transformation. For this reason, the dynamic range of the DCT coefficients should be reduced so that fewer precision digits are employed in the DCT calculations, thereby the round-off error and loss of information are minimized. In this study, conventional DCT equations are improved both in forward and inverse transformation for the sake of high-performance JPEG image compression. The proposed method reduces the dynamic range of the DCT coefficients and provides a low dynamic range DCT (LDR-DCT) by weighting the DCT coefficients with respect to the frequency level. The effectiveness of the proposed LDR-DCT method is experimented mainly by observing the inter-correlation between the compression ratio and the peak signal-to-noise ratio (PSNR) values which is defined as the compression performance (CP). An extensive experimental benchmarking study is done using the publicly available KODAK image dataset in both grayscale and RGB color spaces, separately. According to the experimental results, the average compression performance (CP) is increased up to about 26% in grayscale images and about 17% in RGB images when the quantization factors (21-121) are employed in the quantization process. Additionally, it is observed that there is an average increment in the compression performance (CP) up to about 8% in grayscale images and about 7% in RGB images when the standard IrfanView quantization tables (quality level of 40 to the quality level of 90) are applied. On the other hand, in the absence of quantization when either the quantization factor of 1 or the standard IrfanView quantization table with the quality level of 100 is applied, it is also observed that there is an average increment in the PSNR value up to about 15% in grayscale images and about 33% in RGB images with respect to the average PSNR values of 24 images in the KODAK image dataset. Therefore, though the proposed LDR-DCT method without quantization does not change the compression ratio, it improves the quality of the output obtained after the inverse transform dramatically. In other words, the conventional DCT method should be replaced by the proposed LDR-DCT method in certain areas where compression is not required. Besides, the study claims that the proposed LDR-DCT method can provide at least the same JPEG image quality as the conventional DCT method with much higher compression ratios if the quantization tables are redesigned accordingly.