A case study on entropy-aware block-based linear transforms for lossless image compression

Data compression algorithms tend to reduce information entropy, which is crucial, especially in the case of images, as they are data intensive. In this regard, lossless image data compression is especially challenging. Many popular lossless compression methods incorporate predictions and various types of pixel transformations, in order to reduce the information entropy of an image. In this paper, a block optimisation programming framework <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> is introduced to support various experiments on raster images, divided into blocks of pixels. Eleven methods were implemented within <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> , including prediction methods, string transformation methods, and inverse distance weighting, as a representative of interpolation methods. Thirty-two different greyscale raster images with varying resolutions and contents were used in the experiments. It was shown that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> reduces information entropy better than the popular JPEG LS and CALIC predictors. The additional information associated with each block in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> is then evaluated. It was confirmed that, despite this additional cost, the estimated size in bytes is smaller in comparison to the sizes achieved by the JPEG LS and CALIC predictors.