Multi-scale Analysis Research On Biomedical Signal And Image Processing

In biomedical signal processing, we have to detect signals in sophisticated condition, such as electrophysiologic signals and medical images, and it is difficult in general to characterize signals in such situation. Based on the inherent property of objects in the real world, i.e.they only exist as meaningful entities over certain range of scale, a multi-scale analysis of data has been developed in recent years for describing the structure of unknown real-world signals. Among the varieties of approaches, scale space theory and wavelet analysis provide us with a powerful tool to resolve these problems.Base on the multiresolution frame, in this dissertation, some new methods have been developed to detect biomedical signals in strong noise circumstances, such as the event related potentials (ERP) and x-ray image of bone, which can be summarized as the following 3 points: 1. A weighted algorithm of sparse decomposition is developed for recovery of signal in strong noisy circumstances. In this method, to find the real components in a complete dictionary, the target function was built with a weighted sum of the norm of residual errors and norm of sparse components. Using complete dictionary as the multiresolution wavelets, a feasible penalty is elaborately deduced according to two-scale relation of additive noise in wavelets dictionary. Analyzing the solving process of minimum problem, the difference of norm of signal components in the dictionary is proposed as the converging condition.through twice iterations. The method is confirmed by simulated data, and come up with good results when applied to single-channel ERP analysis.2. Different from the known quad-tree representation of image, a new triangle quad-tree structure is suggested to accomplish image decomposition, where a triangle-base is designed to eliminate the influence of the overlapping on triangle border. Therefore estimated mean of triangle region is globally unbiased. Simulationing test has proved the strong denoising ability of this structure. . 3. With Fourier Transform of edge response, a diagonal template for edge detection is constructed. This method effectively improves edge localization and reduces the influence of noises when a large scale template is adopted. Its effectiveness is confirmed by edge detection of bone.In this work, developed also is a simple and effective exponent restraint method of edge detection for an x-ray image of bone. Based on the exponent restraint, it is easy to apply histogram method to get bone image due to the difference of organic density. Combined with Canny method, this method can detect the edge of bone in a complex x-ray image.