Correspondence between Multiwavelet Shrinkage/Multiple Wavelet Frame Shrinkage and Nonlinear Diffusion

There are numerous methodologies for signal and image denoising. Wavelet, wavelet frame shrinkage, and nonlinear diffusion are effective ways for signal and image denoising. Also, multiwavelet transforms and multiple wavelet frame transforms have been used for signal and image denoising. Multiwavelets have important property that they can possess the orthogonality, short support, good performance at the boundaries, and symmetry simultaneously. The advantage of multiwavelet transform for signal and image denoising was illustrated by Bui et al. in 1998. They showed that the evaluation of thresholding on a multiwavelet basis has produced good results. Further, Strela et al. have showed that the decimated multiwavelet denoising provides superior results than decimated conventional (scalar) wavelet denoising. Mrazek, Weickert, and Steidl in 2003 examined the association between one-dimensional nonlinear diffusion and undecimated Haar wavelet shrinkage. They proved that nonlinear diffusion could be presented by using wavelet shrinkage. High-order nonlinear diffusion in terms of one-dimensional frame shrinkage and two-dimensional frame shrinkage were presented in 2012 by Jiang, and in 2013 by Dong, Jiang, and Shen, respectively. They obtained that the correspondence between both approaches leads to a different form of diffusion equation that mixes benefits from both approaches. The objective of this dissertation is to study the correspondence between one-dimensional multiwavelet shrinkage and high-order nonlinear diffusion, and to study high-order nonlinear diffusion in terms of one-dimensional multiple frame shrinkage also well. Further, this dissertation formulates nonlinear diffusion in terms of 2D multiwavelet shrinkage and 2D multiple wavelet frame shrinkage. From the experiment results, it can be inferred that nonlinear diffusion in terms of multiwavelet shrinkage/multiple frame shrinkage gives better results than a scalar case. On the whole, this dissertation expands nonlinear diffusion in terms of wavelet shrinkage and nonlinear diffusion in terms of frame shrinkage from the scalar wavelets and frames to the multiwavelets and multiple frames

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

Time-varying nonlinear causality detection using regularized orthogonal least squares and multi-wavelets with applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modelling framework, and is applied to real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modelling approach employs a nonlinear autoregressive with external input (NARX) model, whose parameters are approximated by a set of multiwavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experiment results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface (BCI) systems

Dynamic reliability analysis using the extended support vector regression (X-SVR)

© 2019 Elsevier Ltd For engineering applications, the dynamic system responses can be significantly affected by uncertainties in the system parameters including material and geometric properties as well as by uncertainties in the excitations. The reliability of dynamic systems is widely evaluated based on the first-passage theory. To improve the computational efficiency, surrogate models are widely used to approximate the relationship between the system inputs and outputs. In this paper, a new machine learning based metamodel, namely the extended support vector regression (X-SVR), is proposed for the reliability analysis of dynamic systems via utilizing the first-passage theory. Furthermore, the capability of X-SVR is enhanced by a new kernel function developed from the vectorized Gegenbauer polynomial, especially for solving complex engineering problems. Through the proposed approach, the relationship between the extremum of the dynamic responses and the input uncertain parameters is approximated by training the X-SVR model such that the probability of failure can be efficiently predicted without using other computational tools for numerical analysis, such as the finite element analysis (FEM). The feasibility and performance of the proposed surrogate model in dynamic reliability analysis is investigated by comparing it with the conventional ε-insensitive support vector regression (ε-SVR) with Gaussian kernel and Monte Carlo simulation (MSC). Four numerical examples are adopted to evidently demonstrate the practicability and efficiency of the proposed X-SVR method

Wavelet Methods and Inverse Problems

Archaeological investigations are designed to acquire information without damaging the archaeological site. Magnetometry is one of the important techniques for producing a surface grid of readings, which can be used to infer underground features. The inversion of this data, to give a fitted model, is an inverse problem. This type of problem can be ill-posed or ill-conditioned, making the estimation of model parameters less stable or even impossible. More precisely, the relationship between archaeological data and parameters is expressed by a likelihood. It is not possible to use the standard regression estimate obtained through the likelihood, which means that no maximum likelihood estimate exists. Instead, various constraints can be added through a prior distribution with an estimate produced using the posterior distribution. Current approaches incorporate prior information describing smoothness, which is not always appropriate. The biggest challenge is that the reconstruction of an archaeological site as a single layer requires various physical features such as depth and extent to be assumed. By applying a smoothing prior in the analysis of stratigraphy data, however, these features are not easily estimated. Wavelet analysis has proved to be highly efficient at eliciting information from noisy data. Additionally, complicated signals can be explained by interpreting only a small number of wavelet coefficients. It is possible that a modelling approach, which attempts to describe an underlying function in terms of a multi-level wavelet representation will be an improvement on standard techniques. Further, a new method proposed uses an elastic-net based distribution as the prior. Two methods are used to solve the problem, one is based on one-stage estimation and the other is based on two stages. The one-stage considers two approaches a single prior for all wavelet resolution levels and a level-dependent prior, with separate priors at each resolution level. In a simulation study and a real data analysis, all these techniques are compared to several existing methods. It is shown that the methodology using a single prior provides good reconstruction, comparable even to several established wavelet methods that use mixture priors

30th International Conference on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2017)

Proceedings of COMADEM 201