A critique of some rough approximations of the DCT

摘要

Recently, rough approximations of the Discrete Cosine Transform (DCT) have been proposed that can be implemented as multiplier-less, low-area, and low-power circuits. Promoters of such algorithms considered simpler and simpler data-flow graphs, by using fewer and fewer additions and bit-shifts compared to finer approximations developed at the turn of the 20th and 21th centuries. However, they neglected to carefully check whether an approximation works like the original, and from another point of view, they ignore well-known essential results of the theory and practice of image transforms. This paper shows that one of such solutions is not as perfect as advertised, or even seems to be useless, suffering from inherent disadvantages of non-selective filters and non-smooth basis functions. We point out what is lacking in the published evaluations of the algorithm and analyse its properties, demonstrating that it behaves differently from the DCT and thus is suitable to neither image compression nor pattern recognition. In particular, we show that it poorly decorrelates samples of natural images, and unpleasant in-block artefacts appear in decoded pictures.