Wavelet Shrinkage Based Image Denoising using Soft Computing

Noise reduction is an open problem and has received considerable attention in the literature for several decades. Over the last two decades, wavelet based methods have been applied to the problem of noise reduction and have been shown to outperform the traditional Wiener filter, Median filter, and modified Lee filter in terms of root mean squared error (MSE), peak signal noise ratio (PSNR) and other evaluation methods. In this research, two approaches for the development of high performance algorithms for de-noising are proposed, both based on soft computing tools, such as fuzzy logic, neural networks, and genetic algorithms. First, an improved additive noise reduction method for digital grey scale nature images, which uses an interval type-2 fuzzy logic system to shrink wavelet coefficients, is proposed. This method is an extension of a recently published approach for additive noise reduction using a type-1 fuzzy logic system based wavelet shrinkage. Unlike the type-1 fuzzy logic system based wavelet shrinkage method, the proposed approach employs a thresholding filter to adjust the wavelet coefficients according to the linguistic uncertainty in neighborhood values, inter-scale dependencies and intra-scale correlations of wavelet coefficients at different resolutions by exploiting the interval type-2 fuzzy set theory. Experimental results show that the proposed approach can efficiently and rapidly remove additive noise from digital grey scale images. Objective analysis and visual observations show that the proposed approach outperforms current fuzzy non-wavelet methods and fuzzy wavelet based methods, and is comparable with some recent but more complex wavelet methods, such as Hidden Markov Model based additive noise de-noising method. The main differences between the proposed approach and other wavelet shrinkage based approaches and the main improvements of the proposed approach are also illustrated in this thesis. Second, another improved method of additive noise reduction is also proposed. The method is based on fusing the results of different filters using a Fuzzy Neural Network (FNN). The proposed method combines the advantages of these filters and has outstanding ability of smoothing out additive noise while preserving details of an image (e.g. edges and lines) effectively. A Genetic Algorithm (GA) is applied to choose the optimal parameters of the FNN. The experimental results show that the proposed method is powerful for removing noise from natural images, and the MSE of this approach is less, and the PSNR of is higher, than that of any individual filters which are used for fusion. Finally, the two proposed approaches are compared with each other from different point of views, such as objective analysis in terms of mean squared error(MSE), peak signal to noise ratio (PSNR), image quality index (IQI) based on quality assessment of distorted images, and Information Theoretic Criterion (ITC) based on a human vision model, computational cost, universality, and human observation. The results show that the proposed FNN based algorithm optimized by GA has the best performance among all testing approaches. Important considerations for these proposed approaches and future work are discussed

Curvelet-Based Texture Classification in Computerized Critical Gleason Grading of Prostate Cancer Histological Images

Classical multi-resolution image processing using wavelets provides an efficient analysis of image characteristics represented in terms of pixel-based singularities such as connected edge pixels of objects and texture elements given by the pixel intensity statistics. Curvelet transform is a recently developed approach based on curved singularities that provides a more sparse representation for a variety of directional multi-resolution image processing tasks such as denoising and texture analysis. The objective of this research is to develop a multi-class classifier for the automated classification of Gleason patterns of prostate cancer histological images with the utilization of curvelet-based texture analysis. This problem of computer-aided recognition of four pattern classes between Gleason Score 6 (primary Gleason grade 3 plus secondary Gleason grade 3) and Gleason Score 8 (both primary and secondary grades 4) is of critical importance affecting treatment decision and patients’ quality of life. Multiple spatial sampling within each histological image is examined through the curvelet transform, the significant curvelet coefficient at each location of an image patch is obtained by maximization with respect to all curvelet orientations at a given location which represents the apparent curved-based singularity such as a short edge segment in the image structure. This sparser representation reduces greatly the redundancy in the original set of curvelet coefficients. The statistical textural features are extracted from these curvelet coefficients at multiple scales. We have designed a 2-level 4-class classification scheme, attempting to mimic the human expert’s decision process. It consists of two Gaussian kernel support vector machines, one support vector machine in each level and each is incorporated with a voting mechanism from classifications of multiple windowed patches in an image to reach the final decision for the image. At level 1, the support vector machine with voting is trained to ascertain the classification of Gleason grade 3 and grade 4, thus Gleason score 6 and score 8, by unanimous votes to one of the two classes, while the mixture voting inside the margin between decision boundaries will be assigned to the third class for consideration at level 2. The support vector machine in level 2 with supplemental features is trained to classify an image patch to Gleason grade 3+4 or 4+3 and the majority decision from multiple patches to consolidate the two-class discrimination of the image within Gleason score 7, or else, assign to an Indecision category. The developed tree classifier with voting from sampled image patches is distinct from the traditional voting by multiple machines. With a database of TMA prostate histological images from Urology/Pathology Laboratory of the Johns Hopkins Medical Center, the classifier using curvelet-based statistical texture features for recognition of 4-class critical Gleason scores was successfully trained and tested achieving a remarkable performance with 97.91% overall 4-class validation accuracy and 95.83% testing accuracy. This lends to an expectation of more testing and further improvement toward a plausible practical implementation

Studying Large Multi-Protein Complexes Using Single Molecule Localization Microscopy

Biology would not be where it is today without fluorescence microscopy. It is arguably one of the most commonly used tools in the biologists toolbox and it has helped scientists study the localization of cellular proteins and other small things for decades, but it is not without its limitations. Due to the diffraction limit, conventional fluorescence microscopy is limited to micrometer-range structures. Science has long relied upon electron microscopy and X-ray crystallography to study phenomena that occur below this limit. However, many of lifes processes occur between these two spatial domains. Super-resolution microscopy, the next stage of evolution of fluorescence microscopy, has the potential to bridge this gap between micro and nano. It combines superior resolutions of down to a few nanometers with the ability to view objects in their natural environments. It is the ideal tool for studying the large, multi-protein complexes that carry out most of lifes functions, but are too complex and fragile to put on an electron microscope or into a synchrotron. A form of super-resolution microscopy called SMLM Microscopy shows especially high promise in this regard. With its ability to detect individual molecules, it combines the high resolution needed for structural studies with the quantitative readout required for obtaining data on the stoichiometry of multi-protein complexes. This thesis describes new tools which expand the toolbox of SMLM with the specific aim of studying multi-protein complexes. First, the development of a novel fluorescent tagging system that is a mix of genetic tagging and immuno-staining. The system, termed BC2, consists of a short, genetically encodable peptide that is targeted by a nanobody (BC2 nanobody). The system brings several advantages. The small tag is not disruptive to the protein it is attached to and the small nanobody can get into tight spaces, making it an excellent tag for dense multi-protein structures. Next, several new variants of some commonly used green-to-red fluorescent proteins. The novel variants, which can be converted with a combination of blue and infrared light are especially useful for live-cell imaging. The developed fluorescent proteins can also be combined with photo-activatable fluorescent proteins to enable imaging of several targets with the same color protein. Finally, an application of the latter technique to study the multi-protein kinetochore complex and gain first glimpses into its spatial organization and the stoichiometry of its subunits

Persistent Homology in Multivariate Data Visualization

Technological advances of recent years have changed the way research is done. When describing complex phenomena, it is now possible to measure and model a myriad of different aspects pertaining to them. This increasing number of variables, however, poses significant challenges for the visual analysis and interpretation of such multivariate data. Yet, the effective visualization of structures in multivariate data is of paramount importance for building models, forming hypotheses, and understanding intrinsic properties of the underlying phenomena. This thesis provides novel visualization techniques that advance the field of multivariate visual data analysis by helping represent and comprehend the structure of high-dimensional data. In contrast to approaches that focus on visualizing multivariate data directly or by means of their geometrical features, the methods developed in this thesis focus on their topological properties. More precisely, these methods provide structural descriptions that are driven by persistent homology, a technique from the emerging field of computational topology. Such descriptions are developed in two separate parts of this thesis. The first part deals with the qualitative visualization of topological features in multivariate data. It presents novel visualization methods that directly depict topological information, thus permitting the comparison of structural features in a qualitative manner. The techniques described in this part serve as low-dimensional representations that make the otherwise high-dimensional topological features accessible. We show how to integrate them into data analysis workflows based on clustering in order to obtain more information about the underlying data. The efficacy of such combined workflows is demonstrated by analysing complex multivariate data sets from cultural heritage and political science, for example, whose structures are hidden to common visualization techniques. The second part of this thesis is concerned with the quantitative visualization of topological features. It describes novel methods that measure different aspects of multivariate data in order to provide quantifiable information about them. Here, the topological characteristics serve as a feature descriptor. Using these descriptors, the visualization techniques in this part focus on augmenting and improving existing data analysis processes. Among others, they deal with the visualization of high-dimensional regression models, the visualization of errors in embeddings of multivariate data, as well as the assessment and visualization of the results of different clustering algorithms. All the methods presented in this thesis are evaluated and analysed on different data sets in order to show their robustness. This thesis demonstrates that the combination of geometrical and topological methods may support, complement, and surpass existing approaches for multivariate visual data analysis