# WAVELETS – The Basis of digital image coding

WAVELETS – The basis of digital image coding

In information technology, signals, images and videos frequently are not directly represented in chronological order, but rather in a transformed sequence. A well-known example is the Fourier Transform, by which a signal is transformed into its Fourier spectrum. This spectrum shows how much of the bandwidth the signal consumes on a communications channel. Two-dimensional images are commonly transformed by a two-dimensional Cosine Transform. The transformed image displays the energy content, thus enabling image compressiontechniques to assign binary symbols (bits) only to those areas where thy are needed. this means the images use less storage capacity on a disk and can be transmitted faster via Internet..

During the last twelve years Professor Daubechies has worked on such a transformation, the “Wavelet Transform”, which can perform the task of image transformation in a much better way. Ingrid Daubechies not only carefully investigated the mathematical properties of these wavelet functions, but also further developed them in her paper of 1988 so that they allow perfect reconstruction using filter banks. Her work together with that of Mallat enabled the breakthrough of this transform technique for image and video recordings. The success of her fundamental work was underscored by the definition of a new image compression standard, called JPEG 2000. This new standard has been defined by an international group of experts and was finally released in December of 1999. therefore the wavelet based method will become the standard compression technique for image and video storage and for transmission through Internet and World Wide Web (WWW). When transformed using wavelets, the images need even fewer bits for their representation. Furthermore, the new technique avoid annoying artifacts during reconstruction and allows hierarchial image transmission. The latter feature means that a few packets are sufficient to obtain a crude picture; the following packets a re used for the enhandement of the image quality. This is an important feature for Internet transmission where packets can get lost on their way.

The wavelets investigated by Professor Daubechies are used in many other areas, such as time-frequency analysis, multi-carrier data transmission, radar, biomedicine and computer graphics.

Ingrid Daubechies is not only an innovative researcher, but also a good communicator in her papers and talks. Her award-winning book “Ten Lectures on Wavelets” contributed greatly to the popularization of the wavelet theory.

The Eduard Rhein Basic Award honors the fundamental research work of Professor Ingrid Daubechies, which shows in an exemplary way that theoretical research in basic mathematics can lead to very practical methods useful for a variety of applications in advanced information technology.

Prof. Dr. Joachim Hagenauer,

TU München