sc7@ukc.ac.uk (S.Chan) (06/21/91)
I have come across some early papers on using Hadamard Transform for image compression due to the smaller amount of computations required as compared to DFT and DCT. However the DCT has emerged as the popular choice. Can someone point out to me what are the demerits of the Hadamard transform in the application of image compression? References are welcome. Thanks. Chan Syin
edhall@rand.org (Ed Hall) (06/25/91)
In article <7832@harrier.ukc.ac.uk> sc7@ukc.ac.uk (S.Chan) writes: >I have come across some early papers on using Hadamard Transform for >image compression due to the smaller amount of computations required >as compared to DFT and DCT. However the DCT has emerged as the popular >choice. Can someone point out to me what are the demerits of the >Hadamard transform in the application of image compression? References >are welcome. Thanks. The Hadamard transform (perhaps better called the Walsh-Hadamard transform) has basis vectors in which all values are either 1 or -1. This makes it very easy to implement; no multiplication is necessary (except for final scaling--and a shift usually can take care of that). But its energy compression and decorrelation efficiencies are inferior to the discrete cosine transform (DCT). Given that DSP technology and fast DCT algoritms have reached the point where practical DCT coders can be implemented even at high data rates, interest in inferior transforms has slacked off. DCT compression is hardly the end of the line, though. Despite near- optimum performance in terms of compressing image blocks into few coefficients, there is a tendency toward "blockiness" in DCT systems as compression ratios are raised. (Such block-boundry artifacts are even more of a problem in Walsh-Hadamard systems.) Other transforms--wavelet transforms, for instance--tend not to have this problem, yielding a visually more pleasing result for a given degree of error. In addition, such systems often can lend themselves to progressive transmission--where detail is built up over the entire image over time--whereas DCT-based systems generally cannot. (Neither of these objections are absolute, and partial solutions exist.) To a certain extent, appropriate quantization and efficient coding of coefficients are more important than transform choice. A lot of recent research has been into these areas. -Ed Hall edhall@rand.org