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

Morphometric analysis of the thoracic cage in adults: Anatomical considerations in relation to neurosurgical thoracoscopic procedures

Study Design: Direct measurements of the adult human intercostal spaces and depths of thoracoscopically accessible anatomical structures from common entrance points on the posterior axillary line for thoracoscopic tools. Objectives: To determine morphometry of the adult human chest wall and thoracic cavity that can be utilized during thoracoscopic procedures and in thoracoscopic tool design. Background Data: Although certain entrance points through the intercostal spaces are recommended for thoracoscopy, no anatomical data have been tabulated in the literature quantifying distances from these entrance points or investigating variability among subjects. Materials and Methods: Direct measurements of the intercostal spacings of 10 unembalmed cadavers were obtained. Distances between the 1st-10th rib at the posterior axillary line and the caput of the corresponding ribs and the junction of the lateral edge of the aorta and the intervertebral disc were measured. Results: Intercostal spacings gradually increased from rostral to caudal and were maximum at T10-11 (mean 15.2 mm). Distance from the posterior axillary line to the caputs of the corresponding ribs was greatest at the 7th rib (mean 11.4 cm). Distance from the posterior axillary line to the junction points of the corresponding intervertebral discs and aorta was greatest at the 7th rib level (mean 12.6 cm). Conclusion: These data provide a quantitative anatomical basis that can be used to help limit neural and vascular complications during thoracoscopy, improve thoracoscopic techniques, design new thoracoscopic equipment, and compare to the anatomy of the animals used for thoracoscopic training

Genetic characterization of Turkish cattle breeds by microsatellite markers: Usefulness for parentage testing Türkiye yerli si{dotless}ǧi{dotless}r irklari{dotless}ni{dotless}n mikrosatellit belirteçler ile genetik karakterizasyonu: Kimliklendirme çali{dotless}şmalari{dotless}nda kullani{dotless}labilirliǧi

Objective of this study was to evaluate microsatellite markers in paternity testing of native cattle breeds in Turkey. Blood samples were collected from Anatolian Black (n=51), Anatolian Grey (n=54), South Anatolian Red (n=51), Native Southern Anatolian Yellow (n=51), East Anatolian Red (n=45) and Zavot (n = 19) cattle. From the blood samples DNA was isolated by using a standard phenol/chloroform method. A total of 20 microsatellite loci were selected from a FAO/ISAG-suggested list. Polymerase chain reaction products were separated by capillary electrophoresis and marker genotypes were determined by fragment analysis. In statistical analyses, allel numbers, observed (Ho) and expected (He) heterozygosities, deviation from Hardy-Weinberg Equilibrium and probability of exclusion (PE) at each microsatellite locus were calculated. A total of 269 different alleles were observed and the mean allele was identified as 13.45. Mean Ho and He values were observed as 0.619-0.852 and 0.669-0.877, respectively. The results indicated that the microsatellite test panel including the most informative 7 loci had total PE value of >0.9999 in each populations and can thereby be used for parentage testing studies of native cattle breeds in Turkey

In vitro biomechanical analysis of a new lumbar low-profile locking screw-plate construct versus a standard top-loading cantilevered pedicle screw-rod construct: Technical report

Objective: A standard top-loading lumbar pedicle screw-rod system is compared with a pedicle screw-plate system with smaller-diameter screws, more medial entry, and lower profile to assess the relative stability, strength, and resistance to fatigue of the 2 systems. Methods: Seven human cadaveric specimens were studied with each surgical construct. Nondestructive, nonconstraining pure moments were applied to specimens to induce flexion, extension, lateral bending, and axial rotation while recording L5-S1 motion optoelectronically. After initial tests, specimens were fatigued for 10 000 cycles and retested to assess early postoperative loosening. Specimens were then loaded to failure in hyperextension. Results: The standard screw-rod construct reduced range of motion to a mean of 20% of normal, whereas the screw-plate construct reduced range of motion to 13% of normal. Differences between systems were not significant in any loading mode (P \u3e 0.06). The 14% loosening of the screw-rod system with fatigue was not significantly different from the 10% loosening observed with the screw-plate system (P \u3e 0.15). Mean failure loads of 30 Nm for screw-rod and 37 Nm for screw-plate were also not significantly different (P = 0.38). Conclusion: Posterior fixation at L5-S1 using the low-profile screw-plate system offers stability, resistance to fatigue, and resistance to failure equivalent to fixation using a standard cantilevered pedicle screw-rod system. Copyright © 2010 by the Congress of Neurological Surgeons