Matching Items (9)

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Incorporating the Sparsity of Edges into the Fourier Reconstruction of Piecewise Smooth Functions

Description

In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce

In applications such as Magnetic Resonance Imaging (MRI), data are acquired as Fourier samples. Since the underlying images are only piecewise smooth, standard recon- struction techniques will yield the Gibbs phenomenon, which can lead to misdiagnosis. Although filtering will reduce the oscillations at jump locations, it can often have the adverse effect of blurring at these critical junctures, which can also lead to misdiagno- sis. Incorporating prior information into reconstruction methods can help reconstruct a sharper solution. For example, compressed sensing (CS) algorithms exploit the expected sparsity of some features of the image. In this thesis, we develop a method to exploit the sparsity in the edges of the underlying image. We design a convex optimization problem that exploits this sparsity to provide an approximation of the underlying image. Our method successfully reduces the Gibbs phenomenon with only minimal "blurring" at the discontinuities. In addition, we see a high rate of convergence in smooth regions.

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2014-05

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A Novel Computing Platform for Accelerated Magnetic Resonance Spectroscopic Cancer Imaging

Description

Compressed sensing magnetic resonance spectroscopic imaging (MRSI) is a noninvasive and in vivo potential diagnostic technique for cancer imaging. This technique undersamples the distribution of specific cancer biomarkers within an MR image as well as changes in the temporal dimension

Compressed sensing magnetic resonance spectroscopic imaging (MRSI) is a noninvasive and in vivo potential diagnostic technique for cancer imaging. This technique undersamples the distribution of specific cancer biomarkers within an MR image as well as changes in the temporal dimension and subsequently reconstructs the missing data. This technique has been shown to retain a high level of fidelity even with an acceleration factor of 5. Currently there exist several different scanner types that each have their separate analytical methods in MATLAB. A graphical user interface (GUI) was created to facilitate a single computing platform for these different scanner types in order to improve the ease and efficiency with which researchers and clinicians interact with this technique. A GUI was successfully created for both prospective and retrospective MRSI data analysis. This GUI retained the original high fidelity of the reconstruction technique and gave the user the ability to load data, load reference images, display intensity maps, display spectra mosaics, generate a mask, display the mask, display kspace and save the corresponding spectra, reconstruction, and mask files. Parallelization of the reconstruction algorithm was explored but implementation was ultimately unsuccessful. Future work could consist of integrating this parallelization method, adding intensity overlay functionality and improving aesthetics.

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2016-05

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Optimization of complex thermal-fluid processes

Description

First, in a large-scale structure, a 3-D CFD model was built to simulate flow and temperature distributions. The flow patterns and temperature distributions are characterized and validated through spot measurements. The detailed understanding of them then allows for optimization of

First, in a large-scale structure, a 3-D CFD model was built to simulate flow and temperature distributions. The flow patterns and temperature distributions are characterized and validated through spot measurements. The detailed understanding of them then allows for optimization of the HVAC configuration because identification of the problematic flow patterns and temperature mis-distributions leads to some corrective measures. Second, an appropriate form of the viscous dissipation term in the integral form of the conservation equation was considered, and the effects of momentum terms on the computed drop size in pressure-atomized sprays were examined. The Sauter mean diameter (SMD) calculated in this manner agrees well with experimental data of the drop velocities and sizes. Using the suggested equation with the revised treatment of liquid momentum setup, injection parameters can be directly input to the system of equations. Thus, this approach is capable of incorporating the effects of injection parameters for further considerations of the drop and velocity distributions under a wide range of spray geometry and injection conditions. Lastly, groundwater level estimation was investigated using compressed sensing (CS). To satisfy a general property of CS, a random measurement matrix was used, the groundwater network was constructed, and finally the l-1 optimization was run. Through several validation tests, correct estimation of groundwater level by CS was shown. Using this setup, decreasing trends in groundwater level in the southwestern US was shown. The suggested method is effective in that the total measurements of registered wells can be reduced down by approximately 42 %, sparse data can be visualized and a possible approach for groundwater management during extreme weather changes, e.g. in California, was demonstrated.

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2015

Model agnostic extreme sub-pixel visual measurement and optimal characterization

Description

It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3%

It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.

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2012

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Non-linear system identification using compressed sensing

Description

This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity

This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.

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2011

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Compressed sensing accelerated magnetic resonance spectroscopic imaging

Description

Magnetic resonance spectroscopic imaging (MRSI) is a valuable technique for assessing the in vivo spatial profiles of metabolites like N-acetylaspartate (NAA), creatine, choline, and lactate. Changes in metabolite concentrations can help identify tissue heterogeneity, providing prognostic and diagnostic information to

Magnetic resonance spectroscopic imaging (MRSI) is a valuable technique for assessing the in vivo spatial profiles of metabolites like N-acetylaspartate (NAA), creatine, choline, and lactate. Changes in metabolite concentrations can help identify tissue heterogeneity, providing prognostic and diagnostic information to the clinician. The increased uptake of glucose by solid tumors as compared to normal tissues and its conversion to lactate can be exploited for tumor diagnostics, anti-cancer therapy, and in the detection of metastasis. Lactate levels in cancer cells are suggestive of altered metabolism, tumor recurrence, and poor outcome. A dedicated technique like MRSI could contribute to an improved assessment of metabolic abnormalities in the clinical setting, and introduce the possibility of employing non-invasive lactate imaging as a powerful prognostic marker.

However, the long acquisition time in MRSI is a deterrent to its inclusion in clinical protocols due to associated costs, patient discomfort (especially in pediatric patients under anesthesia), and higher susceptibility to motion artifacts. Acceleration strategies like compressed sensing (CS) permit faithful reconstructions even when the k-space is undersampled well below the Nyquist limit. CS is apt for MRSI as spectroscopic data are inherently sparse in multiple dimensions of space and frequency in an appropriate transform domain, for e.g. the wavelet domain. The objective of this research was three-fold: firstly on the preclinical front, to prospectively speed-up spectrally-edited MRSI using CS for rapid mapping of lactate and capture associated changes in response to therapy. Secondly, to retrospectively evaluate CS-MRSI in pediatric patients scanned for various brain-related concerns. Thirdly, to implement prospective CS-MRSI acquisitions on a clinical magnetic resonance imaging (MRI) scanner for fast spectroscopic imaging studies. Both phantom and in vivo results demonstrated a reduction in the scan time by up to 80%, with the accelerated CS-MRSI reconstructions maintaining high spectral fidelity and statistically insignificant errors as compared to the fully sampled reference dataset. Optimization of CS parameters involved identifying an optimal sampling mask for CS-MRSI at each acceleration factor. It is envisioned that time-efficient MRSI realized with optimized CS acceleration would facilitate the clinical acceptance of routine MRSI exams for a quantitative mapping of important biomarkers.

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2016

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Towards Clinical Development and Implementation of Fast MR Spectroscopic Imaging Techniques

Description

Magnetic resonance spectroscopic imaging (MRSI) is a non-invasive technique that offers a unique ability to provide the spatial distribution of relevant biochemical compounds (metabolites). The ‘spectrum’ of information provided by MRSI is used as biomarkers for the differential diagnosis of

Magnetic resonance spectroscopic imaging (MRSI) is a non-invasive technique that offers a unique ability to provide the spatial distribution of relevant biochemical compounds (metabolites). The ‘spectrum’ of information provided by MRSI is used as biomarkers for the differential diagnosis of several diseases such as cancer or neurological disorders. Treatment responsive brain tumors can appear similar to non-responsive tumors on conventional anatomical MR images, earlier in the therapy, leading to a poor prognosis for many patients. Biomarkers such as lactate are particularly of interest in the oncological studies of solid tumors to determine their energy metabolism, blood flow, and hypoxia. Despite the capability of nearly all clinical MRI scanners to perform MRSI only limited integration of MRSI into routine clinical studies has occurred to date. The major challenges affecting its true potential are the inherently long acquisition time, low signal-to-noise (SNR) of the signals, overlapping of spectral lines, or the presence of artifacts. The goal of this dissertation work is to facilitate MRSI in routine clinical studies without affecting the current patient throughput.
In this work, the Compressed Sensing (CS) strategy was used to accelerate conventional Point RESolved Spectroscopy (PRESS) MRSI by sampling well below the Shannon-Nyquist limit. Two undersampling strategies, namely the pseudo-random variable density and a novel a priori method was developed and implemented on a clinical scanner. Prospectively undersampled MRSI data was acquired from patients with various brain-related concerns. Spatial-spectral post-processing and CS reconstruction pipeline was developed for multi-channel undersampled data. The fidelity of the CS-MRSI method was determined by comparing the CS reconstructed data to the fully sampled data. Statistical results showed that the a priori approach maintained high spectral fidelity compared to the fully sampled reference for an 80% reduction in scan time. Next, an improvement to the CS-MRSI reconstruction was achieved by incorporating coil sensitivity maps as support in the iterative process. Further, a CS-MRSI-based fast lactate spectroscopic imaging method was developed and implemented to achieve complete water and fat suppression for accurate spatial localization and quantification of lactate in tumors. In vitro phantoms were developed, and the sequence was tested to determine the efficacy of CS-MRSI for low SNR signals, the efficacy of the CS acceleration was determined with statistical analysis.

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Date Created
2021

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Image reconstruction, classification, and tracking for compressed sensing imaging and video

Description

Compressed sensing (CS) is a novel approach to collecting and analyzing data of all types. By exploiting prior knowledge of the compressibility of many naturally-occurring signals, specially designed sensors can dramatically undersample the data of interest and still achieve

Compressed sensing (CS) is a novel approach to collecting and analyzing data of all types. By exploiting prior knowledge of the compressibility of many naturally-occurring signals, specially designed sensors can dramatically undersample the data of interest and still achieve high performance. However, the generated data are pseudorandomly mixed and must be processed before use. In this work, a model of a single-pixel compressive video camera is used to explore the problems of performing inference based on these undersampled measurements. Three broad types of inference from CS measurements are considered: recovery of video frames, target tracking, and object classification/detection. Potential applications include automated surveillance, autonomous navigation, and medical imaging and diagnosis.

Recovery of CS video frames is far more complex than still images, which are known to be (approximately) sparse in a linear basis such as the discrete cosine transform. By combining sparsity of individual frames with an optical flow-based model of inter-frame dependence, the perceptual quality and peak signal to noise ratio (PSNR) of reconstructed frames is improved. The efficacy of this approach is demonstrated for the cases of \textit{a priori} known image motion and unknown but constant image-wide motion.

Although video sequences can be reconstructed from CS measurements, the process is computationally costly. In autonomous systems, this reconstruction step is unnecessary if higher-level conclusions can be drawn directly from the CS data. A tracking algorithm is described and evaluated which can hold target vehicles at very high levels of compression where reconstruction of video frames fails. The algorithm performs tracking by detection using a particle filter with likelihood given by a maximum average correlation height (MACH) target template model.

Motivated by possible improvements over the MACH filter-based likelihood estimation of the tracking algorithm, the application of deep learning models to detection and classification of compressively sensed images is explored. In tests, a Deep Boltzmann Machine trained on CS measurements outperforms a naive reconstruct-first approach.

Taken together, progress in these three areas of CS inference has the potential to lower system cost and improve performance, opening up new applications of CS video cameras.

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Date Created
2016

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High-order sparsity exploiting methods with applications in imaging and PDEs

Description

High-order methods are known for their accuracy and computational performance when applied to solving partial differential equations and have widespread use

in representing images compactly. Nonetheless, high-order methods have difficulty representing functions containing discontinuities or functions having slow spectral decay

High-order methods are known for their accuracy and computational performance when applied to solving partial differential equations and have widespread use

in representing images compactly. Nonetheless, high-order methods have difficulty representing functions containing discontinuities or functions having slow spectral decay in the chosen basis. Certain sensing techniques such as MRI and SAR provide data in terms of Fourier coefficients, and thus prescribe a natural high-order basis. The field of compressed sensing has introduced a set of techniques based on $\ell^1$ regularization that promote sparsity and facilitate working with functions having discontinuities. In this dissertation, high-order methods and $\ell^1$ regularization are used to address three problems: reconstructing piecewise smooth functions from sparse and and noisy Fourier data, recovering edge locations in piecewise smooth functions from sparse and noisy Fourier data, and reducing time-stepping constraints when numerically solving certain time-dependent hyperbolic partial differential equations.

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Date Created
2016