High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two novel greedy approaches to solving this problem. The first estimates the non-zero covariates of the overall inverse covariance matrix using a series of global forward and backward greedy steps. The second estimates the neighborhood of each node in the graph separately, again using greedy forward and backward steps, and combines the intermediate neighborhoods to form an overall estimate. The principal contribution of this paper is a rigorous analysis of the sparsistency, or consistency in recovering the sparsity pattern of the inverse covariance matrix. Surprisingly, we show that both the local and global greedy methods learn the full structure of the model with high probability given just $O(d\log(p))$ samples, which is a \emph{significant} improvement over state of the art $\ell_1$-regularized Gaussian MLE (Graphical Lasso) that requires $O(d^2\log(p))$ samples. Moreover, the restricted eigenvalue and smoothness conditions imposed by our greedy methods are much weaker than the strong irrepresentable conditions required by the $\ell_1$-regularization based methods. We corroborate our results with extensive simulations and examples, comparing our local and global greedy methods to the $\ell_1$-regularized Gaussian MLE as well as the Neighborhood Greedy method to that of nodewise $\ell_1$-regularized linear regression (Neighborhood Lasso).Comment: Accepted to AI STAT 2012 for Oral Presentatio

Quasi-Exact Helical Cone Beam Reconstruction for Micro CT

A cone beam micro-CT system is set up to collect truncated helical cone beam data. This system includes a micro-focal X-ray source, a precision computer-controlled X-Y-Z-theta stage, and an image-intensifier coupled to a large format CCD detector. The helical scanning mode is implemented by rotating and translating the stage while keeping X-ray source and detector stationary. A chunk of bone and a mouse leg are scanned and quasi-exact reconstruction is performed using the approach proposed in J. Hu et al. (2001). This approach introduced the original idea of accessory paths with upper and lower virtual detectors having infinite axial extent. It has a filtered backprojection structure which is desirable in practice and possesses the advantages of being simple to implement and computationally efficient compared to other quasi-exact helical cone beam algorithms for the long object problem

Quantification of Pulmonary Arterial Wall Distensibility Using Parameters Extracted from Volumetric Micro-CT Images

Stiffening, or loss of distensibility, of arterial vessel walls is among the manifestations of a number of vascular diseases including pulmonary arterial hypertension. We are attempting to quantify the mechanical properties of vessel walls of the pulmonary arterial tree using parameters derived from high-resolution volumetric x-ray CT images of rat lungs. The pulmonary arterial trees of the excised lungs are filled with a contrast agent. The lungs are imaged with arterial pressures spanning the physiological range. Vessel segment diameters are measured from the inlet to the periphery, and distensibilities calculated from diameters as a function of pressure. The method shows promise as an adjunct to other morphometric techniques such as histology and corrosion casting. It possesses the advantages of being nondestructive, characterizing the vascular structures while the lungs are imaged rapidly and in a near-physiological state, and providing the ability to associate mechanical properties with vessel location in the intact tree hierarchy

A Possible Approach for Addressing Neglected Human Factors Issues of Systems Engineering

The increasing complexity of safety-critical applications has led to the introduction of decision support tools in the transportation and process industries. Automation has also been introduced to support operator intervention in safety-critical applications. These innovations help reduce overall operator workload, and filter application data to maximize the finite cognitive and perceptual resources of system operators. However, these benefits do not come without a cost. Increased computational support for the end-users of safety-critical applications leads to increased reliance on engineers to monitor and maintain automated systems and decision support tools. This paper argues that by focussing on the end-users of complex applications, previous research has tended to neglect the demands that are being placed on systems engineers. The argument is illustrated through discussing three recent accidents. The paper concludes by presenting a possible strategy for building and using highly automated systems based on increased attention by management and regulators, improvements in competency and training for technical staff, sustained support for engineering team resource management, and the development of incident reporting systems for infrastructure failures. This paper represents preliminary work, about which we seek comments and suggestions

SPECT Imaging of Pulmonary Blood Flow in a Rat

Small animal imaging is experiencing rapid development due to its importance in providing high-throughput phenotypic data for functional genomics studies. We have developed a single photon emission computed tomography (SPECT) system to image the pulmonary perfusion distribution in the rat. A standard gamma camera, equipped with a pinhole collimator, was used to acquire SPECT projection images at 40 sec/view of the rat thorax following injection of Tc99m labeled albumin that accumulated in the rat\u27s lungs. A voxel-driven, ordered-subset expectation maximization reconstruction was implemented. Following SPECT imaging, the rat was imaged using micro-CT with Feldkamp conebeam reconstruction. The two reconstructed image volumes were fused to provide a structure/function image of the rat thorax. Reconstruction accuracy and performance were evaluated using numerical simulations and actual imaging of an experimental phantom consisting of Tc99m filled chambers with known diameters and count rates. Full-width half-maximum diameter measurement errors decreased with increasing chamber diameter, ranging from \u3c 6% down to 0.1%. Errors in the ratio of count rate estimates between tubes were also diameter dependent but still relatively small. This preliminary study suggests that SPECT will be useful for imaging and quantifying the pulmonary blood flow distribution and the distribution of Tc99m labeled ligands in the lungs of small laboratory animals

The Identification of Extreme Asymptotic Giant Branch Stars and Red Supergiants in M33 by 24 {\mu}m Variability

We present the first detection of 24 {\mu}m variability in 24 sources in the Local Group galaxy M33. These results are based on 4 epochs of MIPS observations, which are irregularly spaced over ~750 days. We find that these sources are constrained exclusively to the Holmberg radius of the galaxy, which increases their chances of being members of M33. We have constructed spectral energy distributions (SEDs) ranging from the optical to the sub-mm to investigate the nature of these objects. We find that 23 of our objects are most likely heavily self-obscured, evolved stars; while the remaining source is the Giant HII region, NGC 604. We believe that the observed variability is the intrinsic variability of the central star reprocessed through their circumstellar dust shells. Radiative transfer modeling was carried out to determine their likely chemical composition, luminosity, and dust production rate (DPR). As a sample, our modeling has determined an average luminosity of (3.8 $\pm$ 0.9) x 10$^4$ L$_\odot$ and a total DPR of (2.3 $\pm$ 0.1) x 10$^{-5}$ M$_\odot$ yr$^{-1}$. Most of the sources, given the high DPRs and short wavelength obscuration, are likely "extreme" AGB (XAGB) stars. Five of the sources are found to have luminosities above the classical AGB limit (M$_{\rm bol}$ 54,000 L$_\odot$), which classifies them as probably red supergiants (RSGs). Almost all of the sources are classified as oxygen rich. As also seen in the LMC, a significant fraction of the dust in M33 is produced by a handful of XAGB and RSG stars.Comment: 36 pages, 14 figures, 4 tables, Accepted for publication in A