Multiresolutional/fractal Compression of Still and Moving Pictures

The scope of the present dissertation is a deep lossy compression of still and moving grayscale pictures while maintaining their fidelity, with a specific goal of creating a working prototype of a software system for use in low bandwidth transmission of still satellite imagery and weather briefings with the best preservation of features considered important by the end user. Among the major results is a set of pyramidal compression algorithms with a loose wavelet basis specifically designed to reduce the entropy of the image representation as much as possible. Design principles are discussed and tradeoffs exposed. A number of examples of compressed and restored sample images are provided to demonstrate the quality of particular schemes. A modification of the wavelet transform is introduced that lets the user control the amount of distortion and compression for arbitrary specified image areas. A particular feature of this non-uniform compression scheme is a seamless and smooth incorporation of almost non-distorted information into broader context of large-scale features. Examples are provided. A regularized discrete derivative of an image is developed which effectively removes the local background and the fine-scale noise. Therefore, it may be used for localizing image patterns regardless of the lighting conditions, etc. A discovery of the property of self-similarity of the pyramidal image transform has opened up an entirely new approach to compression: zooming out from a (possibly shrunken) low-resolution image producing a sharp and crisp "natural looking" high-resolution view. It is demonstrated that the technique has features of preserving thinness of lines on expansion, translational invariance and providing a perfect high-resolution representation of the gradient fill. The multiresolutional transform algorithms and "smart" image magnification developed for still images have been generalized to deal with moving pictures as a three-dimensional, spatio-temporal frame sequence, which permits rapid compression, and has potential for use in video transmission in real time.