Book Review: Wavelet theory and its applications
Walter Schempp · Bulletin of the American Mathematical Society · 1994
At the end of the twentieth century, which sometimes is called the century of information processing, applied mathematics has become increasingly interested in the areas of signal analysis, high-resolution image processing, adaptive filter theory, and the implementation of neural network models for pattern recognition and associative memory.One of the problems of these rapidly evolving areas of high technology that has been receiving great attention is the efficient encoding and decoding of analog and digital information.Because the capacity of information transmission channels is always limited, a considerable amount of research has been spent on data compression techniques in recent years.Typical applications that benefit from data compression techniques are high-speed modems for computer communications and CD-ROMs scanned by wavelengthtunable laser diodes.High-technology applications like video, high-definition television (HDTV), and visualization in biomédical computing need fast algorithms for time compression and perfect reconstruction of univariate and multivariate signals.The technique of subband coding used in high-performance image processing for data compression purposes combined with the concept of quadrature mirror filter bank for signal reconstruction form important examples of high-tech math.Data compression techniques that are actually available allow the transmission of more than one hundred TV programs through a single low-loss wideband photonic fiber transmission channel.Due to a data-parallelprocessing minisupercomputer, the real-time display of holographic images has recently become a reality at the MIT Media Laboratory.Recent progress in computerized hoxel (holographic element) technology suggests that holographic TV for the display of three-dimensional images might be available within the next ten years.Holographic TV will provide even more impressive images than