Regularized Field Map Estimation in MRI

In fast magnetic resonance (MR) imaging with long readout times, such as echo-planar imaging (EPI) and spiral scans, it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring. Such corrections require an accurate field map, a map of the off-resonance frequency at each voxel. Standard field map estimation methods yield noisy field maps, particularly in image regions with low spin density. This paper describes regularized methods for field map estimation from two or more MR scans having different echo times. These methods exploit the fact that field maps are generally smooth functions. The methods use algorithms that decrease monotonically a regularized least-squares cost function, even though the problem is highly nonlinear. Results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85871/1/Fessler22.pd

Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise

Impulse noise is a most common noise which affects the image quality during acquisition or transmission, reception or storage and retrieval process. Impulse noise comes under two categories: (1) fixed-valued impulse noise, also known as salt-and-pepper noise (SPN) due to its appearance, where the noise value may be either the minimum or maximum value of the dynamic gray-scale range of image and (2) random-valued impulse noise (RVIN), where the noisy pixel value is bounded by the range of the dynamic gray-scale of the image. In literature, many efficient filters are proposed to suppress the impulse noise. But their performance is not good under moderate and high noise conditions. Hence, there is sufficient scope to explore and develop efficient filters for suppressing the impulse noise at high noise densities. In the present research work, efforts are made to propose efficient filters that suppress the impulse noise and preserve the edges and fine details of an image in wide range of noise densities. It is clear from the literature that detection followed by filtering achieves better performance than filtering without detection. Hence, the proposed filters in this thesis are based on detection followed by filtering techniques. The filters which are proposed to suppress the SPN in this thesis are: Adaptive Noise Detection and Suppression (ANDS) Filter Robust Estimator based Impulse-Noise Reduction (REIR) Algorithm Impulse Denoising Using Improved Progressive Switching Median Filter (IDPSM) Impulse-Noise Removal by Impulse Classification (IRIC) A Novel Adaptive Switching Filter-I (ASF-I) for Suppression of High Density SPN A Novel Adaptive Switching Filter-II (ASF-II) for Suppression of High Density SPN Impulse Denoising Using Iterative Adaptive Switching Filter (IASF) In the first method, ANDS, neighborhood difference is employed for pixel classification. Controlled by binary image, the noise is filtered by estimating the value of a pixel with an adaptive switching based median filter applied exclusively to neighborhood pixels that are labeled noise-free. The proposed filter performs better in retaining edges and fine details of an image at low-to-medium densities of fixed-valued impulse noise.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities

Machine learning in portfolio management

Financial markets are difficult learning environments. The data generation process is time-varying, returns exhibit heavy tails and signal-to-noise ratio tends to be low. These contribute to the challenge of applying sophisticated, high capacity learning models in financial markets. Driven by recent advances of deep learning in other fields, we focus on applying deep learning in a portfolio management context. This thesis contains three distinct but related contributions to literature. First, we consider the problem of neural network training in a time-varying context. This results in a neural network that can adapt to a data generation process that changes over time. Second, we consider the problem of learning in noisy environments. We propose to regularise the neural network using a supervised autoencoder and show that this improves the generalisation performance of the neural network. Third, we consider the problem of quantifying forecast uncertainty in time-series with volatility clustering. We propose a unified framework for the quantification of forecast uncertainty that results in uncertainty estimates that closely match actual realised forecast errors in cryptocurrencies and U.S. stocks

Internal Defect Detection in Hardwood Logs With Fast Magnetic Resonance Imaging.

Identification of defects such as knots in logs before the cutting operation would allow lumber mills to maximize the value of lumber from each log. This dissertation presented images obtained from scanning an oak log with magnetic resonance imaging (MRI). The unique characteristics of MRI images of hardwood logs were noted and were used to derive a quick algorithm to isolate defects. Defect regions had some pixels that varied considerably in intensity from their neighborhood, providing a seed for initiating the defect region. There was an overlap between the pixel gray level of the defects and clear wood. Therefore, traditional thresholding techniques did not cleanly separate these regions. In this study, region-growing methods were used to extract the defects. The algorithm grew the defect region seed until the border-pixel gray levels approached the average level of the neighborhood. The region-growing methods obtained more accurate defect regions than thresholding methods because of the simultaneous consideration of gray level and adjacency information. Two methods of MRI imaging were considered: spin-echo and echo-planar. Spin-echo imaging provided clear, detailed images but required about 20 seconds of acquisition time, which was too slow to be used in a production environment. Echo-planar images could be acquired in about 1/2 second, which was fast enough for production, but the images were fuzzy and noisy. The dissertation presented an algorithm that found the defect regions in spin-echo images. Region-growing methods use a number of parameters and the best parameters were unique for each image. However, common image statistics could be used to predict the proper parameters. The dissertation also presented an algorithm that found most of the defect regions in echo-planar images. Enhancing the echo-planar images using common general-purpose image-enhancement techniques failed because the lack of discrimination allowed the process to smooth image structures as well as noise. By taking advantage of the structure of a tree, smoothing between MRI frames accomplished the goal of smoothing along homogeneous areas and not across image structures. This z-axis smoothing enhanced the echo-planar image visually and reduced the number of false alarm defect regions

Using Complex-Orthogonal Transformations to Diagonalize a Complex Symmetric Matrix

In this paper, we propose the use of complex-orthogonal transformations for finding the eigenvalues of a complex symmetric matrix. Using these special transformations can significantly reduce computational costs because the tridiagonal structure of a complex symmetric matrix is maintained. Keywords: Complex symmetric matrix, eigenvalue decomposition, complex-orthogonal transformation, tridiagonal matrix. 1. INTRODUCTION In many applications, such as directions of arrival, nuclear magnetic resonance, image restoration, system identification, speech processing, coding theory, and so on, the signals are modeled by linear combinations of a set of exponentials: s k = r X i=1 a i z k i ; (1:1) where a i are complex coefficients and z i are complex exponentials. The problem of the exponential decomposition is as follows. Given a finite sequence of signals: s = fs 0 ; s 1 ; :::; s n g; find the smallest integer r, and sets of r coefficients fa i g and r exponentials fz i g so that (1..