Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the sampling rate. Then, the signal can be perfectly reconstructed from its samples. Increasing evidence shows that the requirements imposed by Shannon's sampling theorem are too conservative for many naturally-occurring signals, which can be accurately characterized by sparse representations that require lower sampling rates closer to the signal's intrinsic information rates. Finite rate of innovation (FRI) is a new theory that allows to extract underlying sparse signal representations while operating at a reduced sampling rate. The goal of this PhD work is to advance reconstruction techniques for sparse signal representations from both theoretical and practical points of view. Specifically, the FRI framework is extended to deal with applications that involve temporal and spatial localization of events, including inverse source problems from radiating fields. We propose a novel reconstruction method using a model-fitting approach that is based on minimizing the fitting error subject to an underlying annihilation system given by the Prony's method. First, we showed that this is related to the problem known as structured low-rank matrix approximation as in structured total least squares problem. Then, we proposed to solve our problem under three different constraints using the iterative quadratic maximum likelihood algorithm. Our analysis and simulation results indicate that the proposed algorithms improve the robustness of the results with respect to common FRI reconstruction schemes. We have further developed the model-fitting approach to analyze spontaneous brain activity as measured by functional magnetic resonance imaging (fMRI). For this, we considered the noisy fMRI time course for every voxel as a convolution between an underlying activity inducing signal (i.e., a stream of Diracs) and the hemodynamic response function (HRF). We then validated this method using experimental fMRI data acquired during an event-related study. The results showed for the first time evidence for the practical usage of FRI for fMRI data analysis. We also addressed the problem of retrieving a sparse source distribution from the boundary measurements of a radiating field. First, based on Green's theorem, we proposed a sensing principle that allows to relate the boundary measurements to the source distribution. We focused on characterizing these sensing functions with particular attention for those that can be derived from holomorphic functions as they allow to control spatial decay of the sensing functions. With this selection, we developed an FRI-inspired non-iterative reconstruction algorithm. Finally, we developed an extension to the sensing principle (termed eigensensing) where we choose the spatial eigenfunctions of the Laplace operator as the sensing functions. With this extension, we showed that eigensensing principle allows to extract partial Fourier measurements of the source functions from boundary measurements. We considered photoacoustic tomography as a potential application of these theoretical developments

Modulation of BOLD and Arterial Spin Labeling (ASL-CBF) Response in Patients with Transient Visual Impairment after Posterior Circulation Stroke*

Background and Purpose:: Blood oxygenation level-dependent (BOLD) signal and arterial spin labeling cerebral blood flow (ASL-CBF) changes, as detected by functional magnetic resonance imaging (fMRI) are closely related to neural activity. The aim of this case series study was to investigate modulations of the BOLD and ASL-CBF response in the primary visual cortex after posterior circulation stroke with transient visual impairment. Methods:: BOLD activity, resting CBF and task-related ASL-CBF response have been investigated 24-48 h after onset of transient visual symptoms in two patients who were treated conservatively, two patients who received thrombolysis after posterior circulation stroke, and five healthy controls with checkerboard stimulation and visual evoked potentials (VEPs). Results:: After normalization of transient visual symptoms the BOLD response and VEPs showed no hemispheric differences between patients and controls. The relative blood flow in the posterior cerebral arteries and the relative ASL-CBF response to checkerboard stimulation were reduced in three patients, compared to controls. In one patient who received intraarterial thrombolytic therapy, improvement of the relative CBF and ASL-CBF responses was observed, indicating early reperfusion. Conclusion:: In this case series of four patients, different CBF responses to conservative and thrombolytic therapy were observed, and early reperfusion after intraarterial thrombolysis was detected. Functional imaging, which makes use of the ASL-CBF technique, is feasible to measure early poststroke vascular changes, which are hardly detectable with BOLD-fMR

DICOM for EIT

With EIT starting to be used in routine clinical practice [1], it important that the clinically relevant information is portable between hospital data management systems. DICOM formats are widely used clinically and cover many imaging modalities, though not specifically EIT. We describe how existing DICOM specifications, can be repurposed as an interim solution, and basis from which a consensus EIT DICOM ‘Supplement’ (an extension to the standard) can be writte

Estimation of thorax shape for forward modelling in lungs EIT

The thorax models for pre-term babies are developed based on the CT scans from new-borns and their effect on image reconstruction is evaluated in comparison with other available models

Rapid generation of subject-specific thorax forward models

For real-time monitoring of lung function using accurate patient geometry, shape information needs to be acquired and a forward model generated rapidly. This paper shows that warping a cylindrical model to an acquired shape results in meshes of acceptable mesh quality, in terms of stretch and aspect ratio

Torso shape detection to improve lung monitoring

Two methodologies are proposed to detect the patient-specific boundary of the chest, aiming to produce a more accurate forward model for EIT analysis. Thus, a passive resistive and an inertial prototypes were prepared to characterize and reconstruct the shape of multiple phantoms. Preliminary results show how the passive device generates a minimum scatter between the reconstructed image and the actual shap

Nanoparticle electrical impedance tomography

We have developed a new approach to imaging with electrical impedance tomography (EIT) using gold nanoparticles (AuNPs) to enhance impedance changes at targeted tissue sites. This is achieved using radio frequency (RF) to heat nanoparticles while applying EIT imaging. The initial results using 5-nm citrate coated AuNPs show that heating can enhance the impedance in a solution containing AuNPs due to the application of an RF field at 2.60 GHz

The Boston University Photonics Center annual report 2014-2015

This repository item contains an annual report that summarizes activities of the Boston University Photonics Center in the 2014-2015 academic year. The report provides quantitative and descriptive information regarding photonics programs in education, interdisciplinary research, business innovation, and technology development. The Boston University Photonics Center (BUPC) is an interdisciplinary hub for education, research, scholarship, innovation, and technology development associated with practical uses of light.This has been a good year for the Photonics Center. In the following pages, you will see that the center’s faculty received prodigious honors and awards, generated more than 100 notable scholarly publications in the leading journals in our field, and attracted $18.6M in new research grants/contracts. Faculty and staff also expanded their efforts in education and training, and were awarded two new National Science Foundation– sponsored sites for Research Experiences for Undergraduates and for Teachers. As a community, we hosted a compelling series of distinguished invited speakers, and emphasized the theme of Advanced Materials by Design for the 21st Century at our annual symposium. We continued to support the National Photonics Initiative, and are a part of a New York–based consortium that won the competition for a new photonics- themed node in the National Network of Manufacturing Institutes. Highlights of our research achievements for the year include an ambitious new DoD-sponsored grant for Multi-Scale Multi-Disciplinary Modeling of Electronic Materials led by Professor Enrico Bellotti, continued support of our NIH-sponsored Center for Innovation in Point of Care Technologies for the Future of Cancer Care led by Professor Catherine Klapperich, a new award for Personalized Chemotherapy Through Rapid Monitoring with Wearable Optics led by Assistant Professor Darren Roblyer, and a new award from DARPA to conduct research on Calligraphy to Build Tunable Optical Metamaterials led by Professor Dave Bishop. We were also honored to receive an award from the Massachusetts Life Sciences Center to develop a biophotonics laboratory in our Business Innovation Center