New classes of hybrid Hadamard-wavelet transforms for signal-image processing

It is apparent that there is no future for telemedicine without signal compression. In fact the very idea of sending X-rays and other medical images and information electronically could not have been brought up without advances in compression technology over the past two decades. Leading compression standards, such as JPEG/MPEG and those based on Hadamard matrix, have been successfully implemented in numerous signal/image coding/decoding applications ranging from satellites to medical imaging. On the other hand, ever-increasing requirements in signal recognition and transmission, particularly related to telemedicine, have challenged the researchers to develop new compression techniques better suited for each practical situation. The wavelet technology emerged as one of the most promising tools in that direction. Both wavelet and Hadamard transform based algorithms provide excellent quality biomedical signal reconstruction at high compression ratios and can be implemented in real-time on existing microprocessors. The objective of this study is to construct hybrid Hadamard-wavelet transforms and to develop corresponding optimal zonal sampling methods with the use of such transforms. The designed hybrid transforms can be useful in various specific signal processing applications where combining properties of Hadamard and wavelet transforms may be of particular benefit.