Space-Varying Coefficient Models for Diffusion Tensor Imaging using 3d Wavelets

In this paper, the space-varying coefficients model on the basis of B-splines (Heim et al., (2006)) is adapted to wavelet basis functions and re-examined using artificial and real data. For an introduction to diffusion tensor imaging refer to Heim et al. (2005, Chap. 2). First, wavelet theory is introduced and explained by means of 1d and 2d examples (Sections 1.1 { 1.3). Section 1.4 is dedicated to the most common thresholding techniques that serve as regularization concepts for wavelet based models. Prior to application of the 3d wavelet decomposition to the space-varying coe cient elds, the SVCM needs to be rewritten. The necessary steps are outlined in Section 2 together with the incorporation of the positive de niteness constraint using log-Cholesky parametrization. Section 3 provides a simulation study as well as a comparison with the results obtained through B-splines and standard kernel application. Finally, a real data example is presented and discussed. The theoretical parts are based on books of Gen cay et al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise

Parameter optimization for local polynomial approximation based intersection confidence interval filter using genetic algorithm: an application for brain MRI image de-noising

Magnetic resonance imaging (MRI) is extensively exploited for more accuratepathological changes as well as diagnosis. Conversely, MRI suffers from variousshortcomings such as ambient noise from the environment, acquisition noise from theequipment, the presence of background tissue, breathing motion, body fat, etc.Consequently, noise reduction is critical as diverse types of the generated noise limit the efficiency of the medical image diagnosis. Local polynomial approximation basedintersection confidence interval (LPA-ICI) filter is one of the effective de-noising filters.This filter requires an adjustment of the ICI parameters for efficient window size selection.From the wide range of ICI parametric values, finding out the best set of tunes values is itselfan optimization problem. The present study proposed a novel technique for parameteroptimization of LPA-ICI filter using genetic algorithm (GA) for brain MR imagesde-noising. The experimental results proved that the proposed method outperforms theLPA-ICI method for de-noising in terms of various performance metrics for different noisevariance levels. Obtained results reports that the ICI parameter values depend on the noisevariance and the concerned under test image

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Techniques for enhancing digital images

The images obtain from either research studies or optical instruments are often corrupted with noise. Image denoising involves the manipulation of image data to produce a visually high quality image. This thesis reviews the existing denoising algorithms and the filtering approaches available for enhancing images and/or data transmission. Spatial-domain and Transform-domain digital image filtering algorithms have been used in the past to suppress different noise models. The different noise models can be either additive or multiplicative. Selection of the denoising algorithm is application dependent. It is necessary to have knowledge about the noise present in the image so as to select the appropriated denoising algorithm. Noise models may include Gaussian noise, Salt and Pepper noise, Speckle noise and Brownian noise. The Wavelet Transform is similar to the Fourier transform with a completely different merit function. The main difference between Wavelet transform and Fourier transform is that, in the Wavelet Transform, Wavelets are localized in both time and frequency. In the standard Fourier Transform, Wavelets are only localized in frequency. Wavelet analysis consists of breaking up the signal into shifted and scales versions of the original (or mother) Wavelet. The Wiener Filter (mean squared estimation error) finds implementations as a LMS filter (least mean squares), RLS filter (recursive least squares), or Kalman filter. Quantitative measure (metrics) of the comparison of the denoising algorithms is provided by calculating the Peak Signal to Noise Ratio (PSNR), the Mean Square Error (MSE) value and the Mean Absolute Error (MAE) evaluation factors. A combination of metrics including the PSNR, MSE, and MAE are often required to clearly assess the model performance

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world

Statistical Diffusion Tensor Imaging

Magnetic resonance diffusion tensor imaging (DTI) allows to infere the ultrastructure of living tissue. In brain mapping, neural fiber trajectories can be identified by exploiting the anisotropy of diffusion processes. Manifold statistical methods may be linked into the comprehensive processing chain that is spanned between DTI raw images and the reliable visualization of fibers. In this work, a space varying coefficients model (SVCM) using penalized B-splines was developed to integrate diffusion tensor estimation, regularization and interpolation into a unified framework. The implementation challenges originating in multiple 3d space varying coefficient surfaces and the large dimensions of realistic datasets were met by incorporating matrix sparsity and efficient model approximation. Superiority of B-spline based SVCM to the standard approach was demonstrable from simulation studies in terms of the precision and accuracy of the individual tensor elements. The integration with a probabilistic fiber tractography algorithm and application on real brain data revealed that the unified approach is at least equivalent to the serial application of voxelwise estimation, smoothing and interpolation. From the error analysis using boxplots and visual inspection the conclusion was drawn that both the standard approach and the B-spline based SVCM may suffer from low local adaptivity. Therefore, wavelet basis functions were employed for filtering diffusion tensor fields. While excellent local smoothing was indeed achieved by combining voxelwise tensor estimation with wavelet filtering, no immediate improvement was gained for fiber tracking. However, the thresholding strategy needs to be refined and the proposed model of an incorporation of wavelets into an SVCM needs to be implemented to finally assess their utility for DTI data processing. In summary, an SVCM with specific consideration of the demands of human brain DTI data was developed and implemented, eventually representing a unified postprocessing framework. This represents an experimental and statistical platform to further improve the reliability of tractography

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

Big Data Analytics and Information Science for Business and Biomedical Applications II

The analysis of big data in biomedical, business and financial research has drawn much attention from researchers worldwide. This collection of articles aims to provide a platform for an in-depth discussion of novel statistical methods developed for the analysis of Big Data in these areas. Both applied and theoretical contributions to these areas are showcased