Bulletin Spring‧Summer 1994

can in theory dial up and ask for amillion different programmes to be fetched and transmitted, each to the TV set that demands it. New consumer products such as high definition TV (HDTV) and video phones will also need to transmit a large volume of data. The information highway provided by optical fibres would thus see a traffic jam worse than that of our Cross Harbour Tunnel. Above Ground in Space The problem is compounded in the space programme. Many pictures of the pock-marked face of the Moon or the 'snow'-capped polar regions of Mars have been transmitted back to earth via radio waves by various spacecrafts. The Galileo spacecraft, for example, was launched by the US National Aeronautics and Space Administration (NASA) in October 1989 to probe the outer reaches of the solar system, and will soon reach Jupiter and transmit the first close-up pictures of that planet. But the high- performance antenna on Galileo has failed, and it is left with a spare low-performance antenna that transmits only 10 bits per second, hardly enough for many pictures. To make matters worse, the computer on board the Galileo was developed in those days when small PCs were only beginning to appear. It is therefore not powerful enough to handle complicated calculations required for image processing. Image Compression Is the Answer One answer to all these problems is image compression 一 any technique to store and transmit pictures using fewer bits of data. The Chinese University of Hong Kong, as a leading centre of research into information science and technology, has many on-going research projects in this area. One project that has borne fruit and received international recognition and acclaim is the work on integer cosine transform (ICT) by Dr. W.K. Cham, senior lecturer in the Department of Electronic Engineering. How Is It Done? Transform coding Transform coding, the technique involved in image compression, is hardly new. The idea is based on the work of 19th century French mathematician Fourier. Take an 'irregular' wave such as that in Fig.1a; think of it as a plot of greyness versus position. Fourier showed that it can be expressed as a sum of the 'regular' waves in Fig.1b; the latter are called cosines (and in fact also sines). All one has to do is to specify how much (i.e. the amplitude) of each cosine and sine to take and add up; the sum is called a Fourier series. Using such a theory, scientists developed cosine transfroms in 1974. They could use about 60,000 amplitudes to specify a typical TV picture (250,000 pixels) with good effect, a saving of a factor of 4. However, to convert a picture into the cosine amplitudes (i.e. forward transform), or vice versa (i.e. backwards transform), requires a lot of multiplications and additions. Futhermore, the amplitudes of the consines are not in integers. Most need to be represented in decimal numbers to be accurate. As a TV set displays 25 pictures every second, literally millions of multiplications may be involved in that second, an onerous task for the computer. Fig. la Fig. lb Integer cosine transforms (ICT) Dr. Cham's major contribution in this area is to simplify the calculations involved. First, he replaces real number multiplications by integer multiplications. As a finite number of shades of grey are sufficient to define a good picture, the greyness can be represented as integer rather than a continuous decimal number. So one only need to multiply (and add) integers rather than decimals, hence the name integer cosine transforms. Secondly, multiplication by 10 (or 100，1000, ...) is especially easy for humans, who count on ten fingers. Computers count on two fingers, and find it especially easy to multiply by 2 or 4. Dr. Cham showed, in a now-famous paper published in the lEE Proceedings in 1989, that one Research Projects 9