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Biomedical Signal and Image Processing Ph.d. Thesis Synopsis Introduction

The main goal of the thesis is to show the de-noising algorithms based upon the discrete wavelet transform (DWT) that can be applied successfully to enhance noisy multidimensional magnetic resonance (MR) data sets i.e two-dimensional (2-D) image slices and three-dimensional (3-D) image volumes. Noise removal or de-noising is an important task in image processing used to recover a signal that has been corrupted by noise. Random noise that is present in MR images is generated by electronic components in the instrumentation. The thesis present both 2-D image decomposition, thresholding and reconstruction and the 3-D de-noising of MR image volumes using the DWT as a new approach which can be used in the processing of biomedical images. A novel use of the complex wavelet transform for the study and application in the de-noising of MR images is presented in the main part of the thesis. Segmentation of image textures using a watershed transform and a wavelet based feature extraction for classification of image textures by a competitive neural network will be shown. Further topic of interest to be presented in the thesis is the visualization of 2-D MR slices and 3-D image volumes using some MATLAB functions. This makes it possible to visualize images without the need of special glasses especially for 3-D image volumes or using special expensive software programs which will need some bit of expertise. The application of the proposed algorithms is mainly in the area of magnetic resonance imaging (MRI) as an imaging technique used primarily in medical field to produce high quality images of the soft tissues of the human body. An insight to the visualization of MRI data sets i.e. 2-D image slices or 3-D image volumes is of paramount importance to the medical doctors. The thesis presents the theory of the fundamental mathematical tools (discrete Fourier transform (DFT) and DWT) that are used for the analysis and processing of biomedical images. DWT plays an increasingly important role in the de-noising of MR images. 3-D digital image processing, and in particular 3-D DWT, is a rapidly developing research area with applications in many scientific fields such as biomedicine, seismology, remote sensing, material science, etc. The 3-D DWT algorithms are implemented as an extension of the existing 2-D algorithms. The performance of the de-noising algorithms are quantitatively assessed using different criteria namely the mean square error (MSE), peak signal-to-noise ratio (PSNR) and the visual appearance. The results are discussed in accordance to the type of noise and wavelets implemented. The properties of wavelets make them special 1 in that they have a good time and frequency localization which make them ideal for the processing of non-stationary signals like the biomedical signals (EEG, ECG,..) and images (MR). The traditional Fourier transform only provides the spectral information of a signal and thus it is not suitable for the analysis of non-stationary signals. A novel complex wavelet transform (CWT) which was introduced by Dr. Nick Kingsbury of Cambridge University is analyzed and implemented in the main part of the thesis. The description of the dual tree implementation of CWT is followed by its analysis and discussions devoted to its advantages over the classical wavelet transform. This enhanced transform is then applied to MRI data analysis. Experimental results show that complex wavelet de-noising algorithm can powerfully enhance the PSNR in noisy MRI data sets. The further part of the thesis devoted to the description of basic principles of a watershed transform for segmentation of MR images. After its verification for simulated textures it is used for segmentation of a human knee MR image. The anatomical regions of the knee which includes the muscle, bone and tissue can be easily distinguished by this algorithm. Segmentation is an important field in medical applications and can be used for disease diagnosis e.g. detecting brain tumor cells. Texture analysis of artificial textures based on image wavelet decomposition is considered as a pre-processing method for the classification of the textures. The wavelet features are obtained by using the mean or the standard deviations of the wavelet coefficients. For the classification of the textures these feature vectors form the inputs to a competitive neural network. The work also presents own algorithms for class boundaries evaluation. Texture analysis is used in a variety of applications, including remote sensing, satellite imaging, medical image processing, etc. Finally, I conclude and give suggestions for future research work. The thesis also gives a review of the de-noising and visualization of biomedical images on the web using the Matlab Web Server (MWS).