Wavelet and fractal processing and compression of nonstationary signals

作     者：Langi, Armein 

作者单位：University of Manitoba (Canada) 

学位级别：Ph.D.

导师姓名：Kinsner, W.

授予年度：1996年

摘      要：This thesis is concerned with new approaches to processing and compression of nonstationary signals using wavelets and multifractality, with applications to speech and images. Wavelets allow for simultaneous observations of time and frequency transients, while multifractality allows fractal dimension characterizations of signal singularities. A scheme is developed to separate stationary and nonstationary parts of speech signals using linear predictive coding (LPC) filters and LPC excitations, respectively, and to design (i) wavelet compact representation of the excitation to achieve 15.33 dB signal-to-noise ratio (SNR) at a 5.5 kbit per second (kbps) rate, and (ii) fractal characterization of 22 consonant excitations resulting in separable features. Wavelet representation is also suitable for image compression, where more than 90% truncation of wavelet coefficients still results in good perceptual quality. An optimum scalar quantization of such coefficients results in a peak SNR (PSNR) of 28.06 dB at a rate of 0.15 bit per pixel (bpp), outperforming the classical joint photographic expert group (JPEG) objectively and subjectively. Wavelet coefficients are also suitable for fast Rice entropy coders. In addition, wavelets and fractality lead to separation of signal from noise, and are used to obtain a 2:1 compression ratio of otherwise incompressible noise contaminated images. Wavelets and multifractality not only reveal that nonstationary parts are sufficient to represent natural images, with wavelet maxima detecting both the regular and singular transients, but also can be used to reconstruct such images. This has led to an edge preserving coding for aerial ortho images, achieving a quality of 27.89 dB PSNR, thus outperforming the edge quality of JPEG at 30 dB. Finally, a hierarchical neural network has been designed to extract nonstationary features and can classify 22 severe storm events accurately.