Machine Learning And Image Processing For Noise Removal And Robust Edge Detection In The Presence Of Mixed Noise

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level

Sequential Monte Carlo pricing of American-style options under stochastic volatility models

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001) 113-147], and the other solving the same problem using a "brute force" gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating the posterior distribution of the market price of volatility risk for each of the three equities.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS286 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms

Dynamic Epitope Expression from Static Cytometry Data: Principles and Reproducibility

Background: An imprecise quantitative sense for the oscillating levels of proteins and their modifications, interactions, and translocations as a function of the cell cycle is fundamentally important for a cartoon/narrative understanding for how the cell cycle works. Mathematical modeling of the same cartoon/narrative models would be greatly enhanced by an openended methodology providing precise quantification of many proteins and their modifications, etc. Here we present methodology that fulfills these features. Methodology: Multiparametric flow cytometry was performed on Molt4 cells to measure cyclins A2 and B1, phospho-S10histone H3, DNA content, and light scatter (cell size). The resulting 5 dimensional data were analyzed as a series of bivariate plots to isolate the data as segments of an N-dimensional ‘‘worm’ ’ through the data space. Sequential, unidirectional regions of the data were used to assemble expression profiles for each parameter as a function of cell frequency. Results: Analysis of synthesized data in which the true values where known validated the approach. Triplicate experiments demonstrated exceptional reproducibility. Comparison of three triplicate experiments stained by two methods (single cyclin or dual cyclin measurements with common DNA and phospho-histone H3 measurements) supported the feasibility of combining an unlimited number of epitopes through this methodology. The sequential degradations of cyclin A2 followed by cyclin B1 followed by de-phosphorylation of histone H3 were precisely mapped. Finally, a two phase expression rat

Wavelet Signatures and Diagnostics for the Assessment of ICU Agitation-Sedation Protocols

The use of quantitative modelling to enhance understanding of the agitation-sedation (A-S) system and the provision of an A-S simulation platform are key tools in this area of patient critical care. A suite of wavelet techniques and metrics based on the discrete wavelet transform (DWT) are developed in this chapter which are shown to successfully establish the validity of deterministic agitation-sedation (A-S) models against empirical (recorded) dynamic A-S infusion profiles. The DWT approach is shown to provide robust performance metrics of A-S control and also yield excellent visual assessment tools. This approach is generalisable to any study which investigates the similarity or closeness of bivariate time series of, say, a large number of units (patients, households etc) and of disparate lengths and of possibly extremely long length. This work demonstrates the value of the DWT for assessing ICU agitation-sedation deterministic models, and suggests new wavelet based diagnostics by which to assess the A-S models