Sub-octave wavelet representations and applications for medical image processing

This dissertation describes sub-octave wavelet representations and presents applications for medical image processing, including de-noising the feature enhancement. A sub-octave wavelet representation is a generalization of a traditional octave dyadic wavelet representation. In comparison to this transform, by finer divisions of each octave into sub-octave components, we demonstrate a superior ability to capture transient activities in a signal or image. In addition, sub-octave wavelet representations allow us to characterize band-limited features more efficiently. De-Noising and enhancement are accomplished through techniques of minimizing noise energy and nonlinear processing of sub-octave coefficients to improve low contrast features. We identify a class of sub-octave wavelets that can be implemented through band-splitting techniques using FIR filters corresponding to a mother dyadic wavelet. The methodology of sub-octave based nonlinear processing with noise suppression is applied to enhance features significant to medical diagnosis of dense radiographs.;In our preliminary studies we investigated several de-noising and enhancement algorithms. De-Noising under an orthonormal wavelet transform was shown to cause artifacts, including pseudo-Gibbs phenomena. To avoid the problem, we adopt a dyadic wavelet transform for de-noising and enhancement. The advantage is that less pseudo-Gibbs phenomena was shown in our experimental results. We developed algorithms for reducing additive and multiplicative noise. The algorithm for speckle reduction and contrast enhancement was applied to echocardiographic images. Within a framework of multiscale wavelet analysis, we applied wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features. In addition, nonlinear processing of feature energy was carried out to improve contrast within local structures and along object boundaries.;A study using a database of clinical echocardiographic images suggests that such de-noising and enhancement may improve the overall consistency and reliability of myocardial borders as defined by expert observers. Comparative studies on quantitative measurements of experimental results between our algorithms and other methods are presented. In addition, we applied wavelet representations under dyadic or sub-octave wavelet transforms to other medical image processing problems, such as border identification and mass segmentation.