A Comparison of Integer Cosine and Tchebichef Transforms for Image Compression Using Variable Quantization

Abstract

In the field of image and data compression, there are always new approaches being tried and tested to improve the quality of the reconstructed image and to reduce the computational complexity of the algorithm employed. However, there is no one perfect technique that can offer both maximum compression possible and best reconstruction quality, for any type of image. Depending on the level of compression desired and characteristics of the input image, a suitable choice must be made from the options available. For example in the field of video compression, the integer adaptation of discrete cosine transform (DCT) with fixed quantization is widely used in view of its ease of computation and adequate performance. There exist transforms like, discrete Tchebichef transform (DTT), which are suitable too, but are potentially unexploited. This work aims to bridge this gap and examine cases where DTT could be an alternative compression transform to DCT based on various image quality parameters. A multiplier-free fast implementation of integer DTT (ITT) of size 8 × 8 is also studied, for its low computational complexity. Due to the uneven spread of data across images, some areas might have intricate detail, whereas others might be rather plain. This prompts the use of a compression method that can be adapted according to the amount of detail. So, instead of fixed quantization this paper employs quantization that varies depending on the characteristics of the image block. This implementation is free from additional computational or transmission overhead. The image compression performance of ITT and ICT, using both variable and fixed quantization, is compared with a variety of images and the cases suitable for ITT-based image compression employing variable quantization are identified.