Reconstruction of Lamb wave dispersion curves by sparse representation with continuity constraints.

Ultrasonic Lamb waves are a widely used research tool for nondestructive structural health monitoring. They travel long distances with little attenuation, enabling the interrogation of large areas. To analyze Lamb wave propagation data, it is often important to know precisely how they propagate. Yet, since wave propagation is influenced by many factors, including material properties, temperature, and other varying conditions, acquiring this knowledge is a significant challenge. In prior work, this information has been recovered by reconstructing Lamb wave dispersion curves with sparse wavenumber analysis. While effective, sparse wavenumber analysis requires a large number of sensors and is sensitive to noise in the data. In this paper, it extended and significantly improved by constraining the reconstructed dispersion curves to be continuous across frequencies. To enforce this constraint, it is included explicitly in a sparse optimization formulation, and by including in the reconstruction an edge detection step to remove outliers, and by using variational Bayesian Gaussian mixture models to predict missing values. The method is validated with simulation and experimental data. Significant improved performance is demonstrated over the original sparse wavenumber analysis approach in reconstructing the dispersion curves, in synthesizing noise-removed signals, in reducing the number of measurements, and in localizing damage.

Geodesic distance on a Grassmannian for monitoring the progression of Alzheimer's disease.

We propose a geodesic distance on a Grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi, amygdalas, and lateral ventricles in healthy control (HC), mild cognitive impairment (MCI), and Alzheimer's disease (AD). Longitudinal magnetic resonance imaging (MRI) scans of 754 subjects (3092 scans in total) were used in this study. Longitudinally, the geodesic distance was found to be proportional to the elapsed time separating the two scans in question. Cross-sectionally, utilizing a linear mixed-effects statistical model, we found that each structure's annualized rate of change in the geodesic distance followed the order of AD>MCI>HC, with statistical significance being reached in every case. In addition, for each of the six structures of interest, within the same time interval (e.g., from baseline to the 6th month), we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the ADAS-cog increase and the MMSE decrease. Furthermore, as the disease progresses over time, this linkage between the inter-shape geodesic distance and the cognitive decline becomes considerably stronger and more significant.

Data-driven and calibration-free Lamb wave source localization with sparse sensor arrays.

Most Lamb wave localization techniques require that we know the wave's velocity characteristics; yet, in many practical scenarios, velocity estimates can be challenging to acquire, are unavailable, or are unreliable because of the complexity of Lamb waves. As a result, there is a significant need for new methods that can reduce a system's reliance on a priori velocity information. This paper addresses this challenge through two novel source localization methods designed for sparse sensor arrays in isotropic media. Both methods exploit the fundamental sparse structure of a Lamb wave's frequency-wavenumber representation. The first method uses sparse recovery techniques to extract velocities from calibration data. The second method uses kurtosis and the support earth mover's distance to measure the sparseness of a Lamb wave's approximate frequency-wavenumber representation. These measures are then used to locate acoustic sources with no prior calibration data. We experimentally study each method with a collection of acoustic emission data measured from a 1.22 m by 1.22 m isotropic aluminum plate. We show that both methods can achieve less than 1 cm localization error and have less systematic error than traditional time-of-arrival localization methods.

Dispersion curve recovery with orthogonal matching pursuit.

Dispersion curves characterize many propagation mediums. When known, many methods use these curves to analyze waves. Yet, in many scenarios, their exact values are unknown due to material and environmental uncertainty. This paper presents a fast implementation of sparse wavenumber analysis, a method for recovering dispersion curves from data. This approach, based on orthogonal matching pursuit, is compared with a prior implementation, based on basis pursuit denoising. In the results, orthogonal matching pursuit provides two to three orders of magnitude improvement in speed and a small average reduction in prediction capability. The analysis is demonstrated across multiple scenarios and parameters.

Data-driven matched field processing for Lamb wave structural health monitoring.

Matched field processing is a model-based framework for localizing targets in complex propagation environments. In underwater acoustics, it has been extensively studied for improving localization performance in multimodal and multipath media. For guided wave structural health monitoring problems, matched field processing has not been widely applied but is an attractive option for damage localization due to equally complex propagation environments. Although effective, matched field processing is often challenging to implement because it requires accurate models of the propagation environment, and the optimization methods used to generate these models are often unreliable and computationally expensive. To address these obstacles, this paper introduces data-driven matched field processing, a framework to build models of multimodal propagation environments directly from measured data, and then use these models for localization. This paper presents the data-driven framework, analyzes its behavior under unmodeled multipath interference, and demonstrates its localization performance by distinguishing two nearby scatterers from experimental measurements of an aluminum plate. Compared with delay-based models that are commonly used in structural health monitoring, the data-driven matched field processing framework is shown to successfully localize two nearby scatterers with significantly smaller localization errors and finer resolutions.

An efficient method to detect periodic behavior in botnet traffic by analyzing control plane traffic.

Botnets are large networks of bots (compromised machines) that are under the control of a small number of bot masters. They pose a significant threat to Internet's communications and applications. A botnet relies on command and control (C2) communications channels traffic between its members for its attack execution. C2 traffic occurs prior to any attack; hence, the detection of botnet's C2 traffic enables the detection of members of the botnet before any real harm happens. We analyze C2 traffic and find that it exhibits a periodic behavior. This is due to the pre-programmed behavior of bots that check for updates to download them every T seconds. We exploit this periodic behavior to detect C2 traffic. The detection involves evaluating the periodogram of the monitored traffic. Then applying Walker's large sample test to the periodogram's maximum ordinate in order to determine if it is due to a periodic component or not. If the periodogram of the monitored traffic contains a periodic component, then it is highly likely that it is due to a bot's C2 traffic. The test looks only at aggregate control plane traffic behavior, which makes it more scalable than techniques that involve deep packet inspection (DPI) or tracking the communication flows of different hosts. We apply the test to two types of botnet, tinyP2P and IRC that are generated by SLINGbot. We verify the periodic behavior of their C2 traffic and compare it to the results we get on real traffic that is obtained from a secured enterprise network. We further study the characteristics of the test in the presence of injected HTTP background traffic and the effect of the duty cycle on the periodic behavior.

Sparse recovery of the multimodal and dispersive characteristics of Lamb waves.

Guided waves in plates, known as Lamb waves, are characterized by complex, multimodal, and frequency dispersive wave propagation, which distort signals and make their analysis difficult. Estimating these multimodal and dispersive characteristics from experimental data becomes a difficult, underdetermined inverse problem. To accurately and robustly recover these multimodal and dispersive properties, this paper presents a methodology referred to as sparse wavenumber analysis based on sparse recovery methods. By utilizing a general model for Lamb waves, waves propagating in a plate structure, and robust l1 optimization strategies, sparse wavenumber analysis accurately recovers the Lamb wave's frequency-wavenumber representation with a limited number of surface mounted transducers. This is demonstrated with both simulated and experimental data in the presence of multipath reflections. With accurate frequency-wavenumber representations, sparse wavenumber synthesis is then used to accurately remove multipath interference in each measurement and predict the responses between arbitrary points on a plate.

Scale transform signal processing for optimal ultrasonic temperature compensation.

In structural health monitoring, temperature compensation is an important step to reduce systemic errors and avoid false-positive results. Several methods have been developed to accomplish temperature compensation in guided wave systems, but these techniques are often limited in computational speed. In this paper, we present a new methodology for optimal, stretch-based temperature compensation that operates on signals in the stretch factor and scale-transform domains. Using these tools, we demonstrate three algorithms for temperature compensation that show improved computational speed relative to other optimal methods. We test the performance of these algorithms using experimental guided wave data.

Automatic detection of regional heart rejection in USPIO-enhanced MRI.

Contrast-enhanced magnetic resonance imaging (MRI) is useful to study the infiltration of cells in vivo. This research adopts ultrasmall superparamagnetic iron oxide (USPIO) particles as contrast agents. USPIO particles administered intravenously can be endocytosed by circulating immune cells, in particular, macrophages. Hence, macrophages are labeled with USPIO particles. When a transplanted heart undergoes rejection, immune cells will infiltrate the allograft. Imaged by T(2)(*)-weighted MRI, USPIO-labeled macrophages display dark pixel intensities. Detecting these labeled cells in the image facilitates the identification of acute heart rejection. This paper develops a classifier to detect the presence of USPIO-labeled macrophages in the myocardium in the framework of spectral graph theory. First, we describe a USPIO-enhanced heart image with a graph. Classification becomes equivalent to partitioning the graph into two disjoint subgraphs. We use the Cheeger constant of the graph as an objective functional to derive the classifier. We represent the classifier as a linear combination of basis functions given from the spectral analysis of the graph Laplacian. Minimization of the Cheeger constant based functional leads to the optimal classifier. Experimental results and comparisons with other methods suggest the feasibility of our approach to study the rejection of hearts imaged by USPIO-enhanced MRI.

Immune cells detection of the in vivo rejecting heart in USPIO-enhanced magnetic resonance imaging.

Contrast-enhanced magnetic resonance imaging (MRI) is useful to study the infiltration of immune cells, in particular macrophages. Contrast agents, for example ultra-small superparamagnetic iron oxide (USPIO) particles, administered intravenously into the blood stream will be engulfed by macrophages circulating in the circulation system. When a transplanted heart rejects, macrophages and other immune cells will infiltrate the rejecting tissue. Imaged by T*2 weighted MRI, USPIO-labeled macrophages will display dark pixel intensities. Detecting the presence of USPIO particles in the images facilitates the study of heart rejection. We cast the problem of detecting the presence of USPIO-labeled myocardium in the framework of spectral graph theory, and treat our decision function as a level set function on the image. The pixels with positive level set values correspond to the presence of immune cells, and negative to the absence. When the image is modeled by a graph, the spectral analysis of the graph Laplacian provides a basis to represent the level set function. We develop from the Cheeger constant of the graph an objective functional of the level set function. The minimization of the objective leads to the optimal level set function. Experimental results suggest the feasibility of our approach in the study of rejecting hearts.

Affine-permutation invariance of 2-D shapes.

Shapes provide a rich set of clues on the identity and topological properties of an object. In many imaging environments, however, the same object appears to have different shapes due to distortions such as translation, rotation, reflection, scaling, or skewing. Further, the order by which the object's feature points are scanned changes, i.e., the order of the pixels may be permuted. Relating two-dimensional shapes of the same object distorted by different affine and permutation transformations is a challenge. We introduce a shape invariant that we refer to as the intrinsic shape of an object and describe an algorithm, BLAISER, to recover it. The intrinsic shape is invariant to affine-permutation distortions. It is a uniquely defined representative of the equivalence class of all affine-permutation distortions of the same object. BLAISER computes the intrinsic shape from any arbitrarily affine-permutation distorted image of the object, without prior knowledge regarding the distortions or the undistorted shape of the object. The critical step of BLAISER is the determination of the shape orientation and we provide a detailed discussion on this topic. The operations of BLAISER are based on low-order moments of the input shape and, thus, robust to error and noise. Examples illustrate the performance of the algorithm.

Figure-ground segmentation from occlusion.

Layered video representations are increasingly popular; see [2] for a recent review. Segmentation of moving objects is a key step for automating such representations. Current motion segmentation methods either fail to segment moving objects in low-textured regions or are computationally very expensive. This paper presents a computationally simple algorithm that segments moving objects, even in low-texture/low-contrast scenes. Our method infers the moving object templates directly from the image intensity values, rather than computing the motion field as an intermediate step. Our model takes into account the rigidity of the moving object and the occlusion of the background by the moving object. We formulate the segmentation problem as the minimization of a penalized likelihood cost function and present an algorithm to estimate all the unknown parameters: the motions, the template of the moving object, and the intensity levels of the object and of the background pixels. The cost function combines a maximum likelihood estimation term with a term that penalizes large templates. The minimization algorithm performs two alternate steps for which we derive closed-form solutions. Relaxation improves the convergence even when low texture makes it very challenging to segment the moving object from the background. Experiments demonstrate the good performance of our method.

STACS: new active contour scheme for cardiac MR image segmentation.

The paper presents a novel stochastic active contour scheme (STACS) for automatic image segmentation designed to overcome some of the unique challenges in cardiac MR images such as problems with low contrast, papillary muscles, and turbulent blood flow. STACS minimizes an energy functional that combines stochastic region-based and edge-based information with shape priors of the heart and local properties of the contour. The minimization algorithm solves, by the level set method, the Euler-Lagrange equation that describes the contour evolution. STACS includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional. Three particularly attractive features of STACS are: 1) ability to segment images with low texture contrast by modeling stochastically the image textures; 2) robustness to initial contour and noise because of the utilization of both edge and region-based information; 3) ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors. Application of STACS to a set of 48 real cardiac MR images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures (the left and right ventricles and the epicardium.) We compare STACS' automatically generated contours with manually-traced contours, or the "gold standard," using both area and edge similarity measures. This assessment demonstrates very good and consistent segmentation performance of STACS.

Improving spatiotemporal resolution of USPIO-enhanced dynamic imaging of rat kidneys.

This paper addresses the problem of enhancing spatiotemporal resolution of ultra-small superparamagnetic iron oxide (USPIO)-enhanced dynamic MRI of rat kidneys. To alleviate the limited resolution problem of conventional full-scan Fourier imaging methods, we use a generalized series-based imaging scheme to reduce coverage of kappa-space. Experimental results demonstrate that the generalized series imaging method with basis functions constructed using two references (pre- and post-contrast) can reduce the number of phase encodings measured during the dynamic contrast wash-in process by a factor of 4 with a negligible or minimal loss of image quality. The method is expected to make 3D studies possible using USPIO-enhanced dynamic imaging of rat kidneys, and prove valuable for early detection of renal rejection after kidney transplantation.

In vivo detection of acute rat renal allograft rejection by MRI with USPIO particles.

BACKGROUND: Magnetic resonance imaging (MRI) for non-invasively detecting renal rejection was developed by monitoring the accumulation of macrophages labeled with dextran-coated ultrasmall superparamagnetic iron oxide (USPIO) particles at the rat renal allografts during acute rejection. METHODS: Five groups of male rats with DA-->BN renal allografts and one group with BN-->BN renal isografts were investigated by MRI before, immediately after, and 24 hr after intravenous infusion with different doses of USPIO particles. All infusions were done on post-operative day 4. MRI experiments were carried out in a 4.7-Tesla instrument using a gradient echo sequence. RESULTS: MR signal intensity (MRSI) of the cortex was found to decrease with higher dosages of USPIO particles. In the absence of USPIO infusion, a decrease in MRSI was seen in the medulla region, presumably due to hemorrhage associated with renal graft rejection, while no significant change was observed in the cortex. The optimal dose of USPIO particles for visualizing rejection-associated changes in our rat kidney model appears to be 6 mg Fe/kg body weight. Iron staining results correlated with the MRSI data, indicating that the signal reduction in the MR images was due to the presence of iron. Immunohistochemical results indicated that USPIO particles were mostly taken up by infiltrating macrophages in the rejecting grafts. CONCLUSIONS: Our results suggest that MRI with intravenous administration of dextran-coated USPIO particles appears to be a valuable and promising tool that can be used as a non-invasive and sensitive method to detect graft rejection in renal transplantation.