Birsen Yazici

An adaptive statistical time-frequency method for detection of broken bars and bearing faults in motors using stator current

It is well known that motor current is a nonstationary signal, the properties of which vary with respect to the time-varying normal operating conditions of the motor. As a result, Fourier analysis makes it difficult to recognize fault conditions from the normal operating conditions of the motor. Time-frequency analysis, on the other hand, unambiguously represents the motor current which makes signal properties related to fault detection more evident in the transform domain. In this paper, the authors present an adaptive, statistical, time-frequency method for the detection of broken bars and bearing faults. Due to the time-varying normal operating conditions of the motor and the effect of motor geometry on the current, they employ a training-based approach in which the algorithm is trained to recognize the normal operating modes of the motor before the actual testing starts. During the training stage, features which are relevant to fault detection are estimated using the torque and mechanical speed estimation. These features are then statistically analyzed and segmented into normal operating modes of the motor. For each mode, a representative and a threshold are computed and stored in a database to be used as a baseline during the testing stage. In the testing stage, the distance of the test features to the mode representatives are computed and compared with the thresholds. If it is larger than all the thresholds, the measurement is tagged as a potential fault signal. In the postprocessing stage, the testing is repeated for multiple measurements to improve the accuracy of the detection. The experimental results from their study suggest that the proposed method provides a powerful and a general approach to the motor-current-based fault detection.

Diffuse optical tomography with a priori anatomical information.

Diffuse optical tomography (DOT) poses a typical ill-posed inverse problem with a limited number of measurements and inherently low spatial resolution. In this paper, we propose a hierarchical Bayesian approach to improve spatial resolution and quantitative accuracy by using a priori information provided by a secondary high resolution anatomical imaging modality, such as magnetic resonance (MR) or x-ray. In such a dual imaging approach, while the correlation between optical and anatomical images may be high, it is not perfect. For example, a tumour may be present in the optical image, but may not be discernable in the anatomical image. The proposed hierarchical Bayesian approach allows incorporation of partial a priori knowledge about the noise and unknown optical image models, thereby capturing the function-anatomy correlation effectively. We present a computationally efficient iterative algorithm to simultaneously estimate the optical image and the unknown a priori model parameters. Extensive numerical simulations demonstrate that the proposed method avoids undesirable bias towards anatomical prior information and leads to significantly improved spatial resolution and quantitative accuracy.

Pharmacokinetic-rate images of indocyanine green for breast tumors using near-infrared optical methods

In this paper, we develop a method of forming pharmacokinetic-rate images of indocyanine green (ICG) and apply our method to in vivo data obtained from three patients with breast tumors. To form pharmacokinetic-rate images, we first obtain a sequence of ICG concentration images using the differential diffuse optical tomography technique. We next employ a two-compartment model composed of plasma, and extracellular-extravascular space (EES), and estimate the pharmacokinetic rates and concentrations in each compartment using the extended Kalman filtering framework. The pharmacokinetic-rate images of the three patient show that the rates from the tumor region and outside the tumor region are statistically different. Additionally, the ICG concentrations in plasma, and the EES compartments are higher around the tumor region agreeing with the hypothesis that around the tumor region ICG may act as a diffusible extravascular flow in compromised capillary of cancer vessels. Our study indicates that the pharmacokinetic-rate images may provide superior information than single set of pharmacokinetic rates estimated from the entire breast tissue for breast cancer diagnosis.

Synthetic-aperture inversion in the presence of noise and clutter

This paper presents an analytic method for synthetic-aperture inversion when the measurements are corrupted with noise and clutter. We use microlocal analysis in a statistical setting to develop filtered-backprojection-type reconstruction methods. The inversion method is applicable in non-ideal scenarios, such as those involving arbitrary source trajectories or variable antenna beam patterns. We show that the backprojection preserves the location and orientation of the singularities of the first- and second-order statistics of the target scene. We derive backprojection filters with respect to different statistical criteria. In particular, if we use a criterion based on first-order statistics, the resulting image can be interpreted as approximately unbiased. Alternatively, if we use a criterion based on second-order statistics to design the backprojection filter, such as a minimum-mean-square error criterion, the strength of the singularities due to noise and clutter is suppressed in the resulting image. Although we have developed our approach specifically for synthetic-aperture radar application, the method is also applicable to other inversion problems in which microlocal techniques are relevant, such as geophysics and x-ray tomography.

A class of second-order stationary self-similar processes for 1/f phenomena

We propose a class of statistically self-similar processes and outline an alternative mathematical framework for the modeling and analysis of 1/f phenomena. The foundation of the proposed class is based on the extensions of the basic concepts of classical time series analysis, in particular, on the notion of stationarity. We consider a class of stochastic processes whose second-order structure is invariant with respect to time scales, i.e., E[X(t)X(/spl lambda/t)]=t/sup 2H//spl lambda//sup H/R(/spl lambda/), t>0 for some -x<H</spl infin/. For H=0, we refer to these processes as wide sense scale stationary. We show that any self-similar process can be generated from scale stationary processes. We establish a relationship between linear scale-invariant system theory and the proposed class that leads to a concrete analysis framework. We introduce new concepts, such as periodicity, autocorrelation, and spectral density functions, by which practical signal processing schemes can be developed. We give several examples of scale stationary processes including Gaussian, non-Gaussian, covariance, and generative models, as well as fractional Brownian motion as a special case. In particular, we introduce a class of finite parameter self-similar models that are similar in spirit to the ordinary ARMA models by which an arbitrary self-similar process can be approximated. Results from our study suggest that the proposed self-similar processes and the mathematical formulation provide an intuitive, general, and mathematically simple approach to 1/f signal processing.

Synthetic Aperture Hitchhiker Imaging

We introduce a novel synthetic-aperture imaging method for radar systems that relies on sources of opportunity. We consider receivers that fly along arbitrary, but known, flight trajectories and develop a spatio-temporal correlation-based filtered-backprojection-type image reconstruction method. The method involves first correlating the measurements from two different receiver locations. This leads to a forward model where the radiance of the target scene is projected onto the intersection of certain hyperboloids with the surface topography. We next use microlocal techniques to develop a filtered-backprojection-type inversion method to recover the scene radiance. The method is applicable to both stationary and mobile, and cooperative and noncooperative sources of opportunity. Additionally, it is applicable to nonideal imaging scenarios such as those involving arbitrary flight trajectories, and has the desirable property of preserving the visible edges of the scene radiance. We present an analysis of the computational complexity of the image reconstruction method and demonstrate its performance in numerical simulations for single and multiple transmitters of opportunity.

Doppler synthetic aperture hitchhiker imaging

In this paper we consider passive airborne receivers that use backscattered signals from sources of opportunity transmitting single-frequency or ultra-narrowband waveforms. Because of its combined passive synthetic aperture and the single-frequency nature of the transmitted waveforms, we refer to the system under consideration as Doppler synthetic aperture hitchhiker (DSAH). We present a novel image formation method for DSAH. Our method first correlates the windowed signal obtained from one receiver with the windowed, filtered, scaled and translated version of the received signal from another receiver. This processing removes the transmitter-related variables from the phase of the Fourier integral operator that maps the radiance of the scene to the correlated signal. Next, we use microlocal analysis to reconstruct the scene radiance by the weighted backprojection of the correlated signal. The image reconstruction method is applicable to both cooperative and non-cooperative sources of opportunity using one or more airborne receivers. It has the desirable property of preserving the visible edges of the scene radiance. Additionally, it is an analytic reconstruction technique that can be made computationally efficient. We present numerical simulations to demonstrate the performance of the image reconstruction method and to verify the theoretical results.

Multistatic Synthetic Aperture Radar Image Formation

In this paper, we consider a multistatic synthetic aperture radar (SAR) imaging scenario where a swarm of airborne antennas, some of which are transmitting, receiving or both, are traversing arbitrary flight trajectories and transmitting arbitrary waveforms without any form of multiplexing. The received signal at each receiving antenna may be interfered by the scattered signal due to multiple transmitters and additive thermal noise at the receiver. In this scenario, standard bistatic SAR image reconstruction algorithms result in artifacts in reconstructed images due to these interferences. In this paper, we use microlocal analysis in a statistical setting to develop a filtered-backprojection (FBP) type analytic image formation method that suppresses artifacts due to interference while preserving the location and orientation of edges of the scene in the reconstructed image. Our FBP-type algorithm exploits the second-order statistics of the target and noise to suppress the artifacts due to interference in a mean-square sense. We present numerical simulations to demonstrate the performance of our multistatic SAR image formation algorithm with the FBP-type bistatic SAR image reconstruction algorithm. While we mainly focus on radar applications, our image formation method is also applicable to other problems arising in fields such as acoustic, geophysical and medical imaging.

Doppler-Hitchhiker: A Novel Passive Synthetic Aperture Radar Using Ultranarrowband Sources of Opportunity

In this paper, we present a novel synthetic aperture radar imaging modality that uses ultranarrowband sources of opportunity and passive airborne receivers to form an image of the ground. Due to its combined passive synthetic aperture and high Doppler resolution of the transmitted waveforms, we refer to this modality as the Doppler Synthetic Aperture Hitchhiker or Doppler-hitchhiker for short. Our imaging method first correlates the windowed signal obtained from one receiver with the scaled and translated version of the received signal in another window from the same or another receiver. We show that this correlation processing removes the transmitter-related variables from the phase of the resulting operator that maps the radiance of the scene to the correlated signals. We define a concept of passive Doppler scale factor using the radial velocities of the receivers. Next, we show that the scaled, translated, and correlated signal is the projection of the scene radiance onto the contours that are formed by the intersection of the surfaces of constant passive Doppler scale factor and ground topography. We use microlocal analysis to design a generalized filtered-backprojection operator to reconstruct the scene radiance from its projections. Our analysis shows that the resolution of the reconstructed images improves with the increased time duration and center frequency of the transmitted ultranarrowband signals. Our reconstruction method is analytic and therefore can be made computationally efficient. Furthermore, it easily accommodates arbitrary flight trajectories, nonflat topography, and system-related parameters. We present numerical simulations to demonstrate the performance of our imaging method.

Extended Kalman Filtering for the Modeling and Analysis of ICG Pharmacokinetics in Cancerous Tumors Using NIR Optical Methods

Compartmental modeling of indocyanine green (ICG) pharmacokinetics, as measured by near infrared (NIR) techniques, has the potential to provide diagnostic information for tumor differentiation. In this paper, we present three different compartmental models to model the pharmacokinetics of ICG in cancerous tumors. We introduce a systematic and robust approach to model and analyze ICG pharmacokinetics based on the extended Kalman filtering (EKF) framework. The proposed EKF framework effectively models multiple-compartment and multiple-measurement systems in the presence of measurement noise and uncertainties in model dynamics. It provides simultaneous estimation of pharmacokinetic parameters and ICG concentrations in each compartment. Moreover, the recursive nature of the Kalman filter estimator potentially allows real-time monitoring of time varying pharmacokinetic rates and concentration changes in different compartments. Additionally, we introduce an information theoretic criteria for the best compartmental model order selection, and residual analysis for the statistical validation of the estimates. We tested our approach using the ICG concentration data acquired from four Fischer rats carrying adenocarcinoma tumor cells. Our study indicates that, in addition to the pharmacokinetic rates, the EKF model may provide parameters that may be useful for tumor differentiation