A General Non-stationarity Measure And Applications To Biomedical Image And Signal Processing

Intensity variation is often used in signal or image processing algorithms afterbeing quantified by a measurement method. The method of measuring andquantifying the intensity variation is called a change measure. Change measure iscommonly used in the methods for signal change detection, image edge detection,edge-based segmentation model, and feature-preserving smoothing, etc. They arecollectively referred as change measure-based methods.In these methods, change measure plays such an important role that theirperformances are greatly affected by the measuring result of intensity variation. Inthe processing of biomedical images or signals, the existing change measures mayprovide inaccurate information on changes due to the high noise level or the strongrandomness, which leads to the degradation of the performance of the change-measure based methods.In this context, our research perspective is to study a robust change measureand propose several processing methods based on it. These methods should berobust to noise, and could reduce undesirable phenomena which often present in theresults obtained by other change measure-based methods.Moreover, prompted by new medical imaging techniques, many multi-valuedimage processing methods are proposed, which require corresponding changemeasures. How to robustly measure variations in tensor-valued data becomes a newproblem in image processing.Non-Stationarity Measure (NSM) is a rubust change measure with a goodnoise-immunity ability. It can reflect and quantify changes in an image or a signalthrough measuring its degree of non-stationarity. In this work, the NSM method isimproved and extended, several image and signal processing approches based onthe NSM are proposed and applied to deal with various medical images with highnoise levels and signals showing strong randomness. Additionally, the extendedNSM can measure changes in the vector-and tensor-valued data. The specificresearch contents are as follows:Firstly, the NSM is comprehensively improved and extended. The notion ofgeneral parameter stationarity is introduced. Based on the notion, the NSM iselaborated and explained using more appropriate notions and a general formulationof the NSM is given. Then, the construction process of the NSM operators isgeneralized. The outputs of the NSM operators in several typical cases are studied.The advantage of the NSM operator in terms of noise immunity is theoreticallyproved. And the selection of critical parameters is discussed. Finally, the NSM operator is extended to deal with N dimensional data and to measure changes in thevector-and tensor-valued data, thus becoming a general and robust changemesurement method.Secondly, aiming at the problem of false alarms and misdetections in thechange detection of strong random signals and the problem of false edges in theedge detection of highly noisy signals, a NSM-based change detection method anda NSM-based edge detection method are respectively proposed and applied todetect changes in the heart rate signal and the EEG signal, and to detect edges inthe cardiac diffusion weighted (DW) images. Experimental results show that theNSM-based detection methods can provide more accurate positions of changepoints and edges, and can effectively reduce false detections which often present inthe results of other change measure-based methods.Thirdly, aiming at the problem of false contours and leakages in thesegmentation of highly noisy images, a NSM-based geometric active contour(NSM-GAC) model is proposed and applied to segment the carotid ultrasoundimages. The model makes use of the NSM instead of the gradient magnitude toprovide edge information for driving the motion of the zero level set toward desiredlocations. The segmentation results of highly noisy synthetic images, simulated andreal carotid ultrasound images show that the NSM-GAC model can obtain betterresults with less iterations and computation time, and can reduce false contours andleakages.Last and more important, focusing on the difficult compromise between thesmoothness of homogeneous regions and the preservation of desirable features inthe smoothing of low SNR images, a new feature-preserving smoothing approachNonstationarity adaptive filtering (NAF) is proposed. It estimates the intensity of apixel by averaging intensities in its adaptive homogeneous neighborhood. The latteris determined according to five constraints and the NSM map. The proposedapproach is applied to smooth the2-D and3-D cardiac DW images. Experimentalresults show that the proposed method can achieve a better compromise betweensmoothing homogeneous regions and preserving of desirable features such asboundaries, thus leading to homogeneously consistent tensor fields andconsequently more coherent fibers.