Taufiquar Khan

Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data.

We present a carefully designed phantom experimental study aimed to provide solid evidence that both absorption and scattering images of heterogeneous scattering media can be reconstructed independently from dc data. We also study the important absorption-scattering cross-talk issue. In this regard, we develop a simple normalizing scheme that is incorporated into our nonlinear finite-element-based reconstruction algorithm. Our results from the controlled phantom experiments show that the cross talk of an absorption object appearing in scattering images can be eliminated and that the cross talk of a scattering object appearing in absorption images can be reduced considerably. In addition, these carefully designed phantom experiments clearly suggest that both absorption and scattering images can be simultaneously recovered and quantitatively separated in highly scattering media by use of dc measurements. Finally, we discuss our results in light of recent theoretical findings on nonuniqueness for dc image reconstruction.

A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices

Traditionally, the diffusion approximation is derived for a medium with a spatially constant refractive index (Ishimaru 1978 Wave Propagation and Scattering in Random Media vol 1 (New York: Academic)). In this paper, we derive a new diffusion approximation to the radiative transfer equation for a medium with a spatially varying refractive index.

Inverse problem in refractive index based optical tomography

In optical tomography, conventionally the diffusion approximation to the radiative transport equation (RTE) with a constant refractive index is used to image highly scattering or turbid media. Diffusion optical tomography with a constant refractive index is rather difficult due to the exponential instability of the inverse problem. Therefore, it is beneficial to find a simple yet stable model that adequately describes the physics of radiative transport, for example, refractive index based optical tomography. In this paper, we formulate a refractive index based optical tomography inverse problem based on the diffusion approximation to the RTE with a spatially varying refractive index. We establish formally the theoretical framework for both the forward and the inverse problem. We simulate both the forward and the inverse problem using the finite-element method. We reconstruct the refractive index parameter in our model for the inverse problem. Our simulations indicate that refractive index based optical tomography shows promise at least for the reconstruction of refractive index inclusions with circular geometry.

Function spaces and optimal currents in impedance tomography

Abstract The main objective of this paper is to compare – analytically as well as numerically – different approaches for obtaining optimal input currents in impedance tomography. Following the approaches described in, e.g. [Cheney and Isaacson, IEEE Trans. Biomed. Eng. 39: 852–860, 1992, Isaacson, IEEE Trans. Med. Imag. 5: 91–95, 1986, Ito and Kunisch, SIAM J. Contr. Optim. 33: 643–666., 1995, Knowles, An optimal current functional for electrical impedance tomography, 2004], we aim at constructing input currents j, which contain the most information about the difference between the unknown physical conductivity σ* and a given approximation σ 0. The differences can be measured by different discrepancy functionals and the optimal input currents which maximize these functionals depend on the function spaces chosen for defining j and on the norm for measuring the discrepancy. Moreover, the definition of the appropriately weighted Sobolev spaces depends on σ and this subsequently influences the iteration for maximizing the functionals. Numerical experiments illustrate features of the optimal input currents obtained for several combinations of function spaces. The reconstructions with these optimal currents are compared with those with standard input currents (sinusoid and dipole). The differences between the optimal currents obtained by different function space settings are significant. Two newly developed optimal currents can yield qualitatively better reconstructions.

Convergence and application of a modified iteratively regularized Gauss?Newton algorithm

Theoretical convergence results for an iteratively regularized Gauss?Newton (IRGN) algorithm with a Tikhonov regularization term using a seminorm generated by a linear operator are established. The convergence theorem uses an a posteriori stopping rule and a modified source condition, without any restriction on the nonlinearity of the operator. The theoretical results are illustrated by simulations for a one-dimensional version of the exponentially ill-posed optical tomography inverse problem for the diffusion (D) and absorption (?) coefficient spatial distributions. The modified Tikhonov regularization performs the mapping of the minimization variables, which are the coefficients of the spline expansions for D and ?, to physical space. This incorporates the inherently differing scales of these variables in the minimization, and also suggests relative weighting of the regularization terms with respect to each parameter space. The presented modification of the IRGN allows greater flexibility for implementations of IRGN solutions of ill-posed inverse problems in which differing scales in physical space hinder standard IRGN inversions.

Classification trees for complex synchrophasor data

Abstract Classification and regression trees (CART) has been used for various applications in power systems. In most of these applications, phasor data obtained from phasor measurement units are used for building the decision tree. However, the splits in CART are based on a single attribute or a combination of variables chosen by CART itself rather than the user. But as phasor measurement unit data are complex numbers, both the attributes—real and imaginary—should be considered simultaneously for making critical decisions. For example, changing the reference bus in situations where the split is only on the real or imaginary part of a complex voltage (or current) measurement can cause the performance of the tree to degrade significantly. An algorithm is proposed in this article to allow splits on complex synchrophasor data. The methodology is implemented on two systems: a detailed model of the California Power System, where it is used for developing an adaptive protection scheme, and the IEEE 118-bus system, where it is used to classify dynamic events based on trajectories of voltage measurements obtained from phasor measurement units. MATLAB® (The MathWorks, Natick, Massachusetts, USA) implementation of classification and regression trees (classregtree.m) has been used for performing both analyses.

On uniqueness in refractive index optical tomography

In optical tomography, conventionally a constant refractive index assumption is used. The uniqueness and non-uniqueness of the inverse problem for the diffusion approximation to the radiative transport equation has been studied in the past. In this letter, we report the uniqueness and non-uniqueness of the optical tomography inverse problem based on a spatially varying refractive index. We establish criteria for uniqueness applying the well-known results of Sylvester and Uhlmann (1987 Ann. Math. 125 153–69) which has been applied by Arridge and Lionheart (1998 Opt. Lett. 23 882–4) for the constant refractive index case. Our result suggests that if either n, D, or μa/D is assumed to be known, all parameters (n, D, μa) can be uniquely determined from the Dirichlet-to-Neumann map.

1D inverse problem in diffusion based optical tomography using iteratively regularized Gauss-Newton algorithm

In this paper, we investigate an one-dimensional inverse problem in diffusion based optical tomography using iteratively regularized Gauss-Newton (IRGN) algorithm for ill-posed nonlinear problems. We devise a stable reconstruction algorithm for the inverse problem using iterative regularization with Armijo-Goldstein-Wolf (AGW) type line search strategy. We demonstrate the efficacy of the IRGN combined with AGW by reconstructing the scattering parameter relevant to the inverse problem in optical tomography.

Integrated Savitzky-Golay Filter from Inverse Taylor Series Approach

The purpose of this paper is to use the Inverse Taylor series approach on the Savitzky-Golay (S-G) filter to derive an Integrated S-G filter which acts as a low-pass filter for noise while simultaneously directly estimating values of signal x(t) and its first k ---1 derivatives. It is similar in structure to a Finite Impulse Response (FIR) filter, and its coefficients are calcuated using the method of least squares. Initial tests indicate that this filter has significantly greater attenuation of frequencies above the cutoff frequency than the S-G filter does.

Evaluation of Driver Car-Following Behavior Models for Cooperative Adaptive Cruise Control Systems

A cooperative adaptive cruise control (CACC) system targeted to obtain a high level of user acceptance must replicate the driving experience in each CACC vehicle without compromising the occupant’s comfort. “User acceptance” can be defined as the safety and comfort of the occupant in the CACC vehicle in terms of acceptable vehicle dynamics (i.e., the maximum acceleration or deceleration) and string stability (i.e., the fluctuations in the vehicle’s position, speed, and acceleration). The primary objective of this study was to develop an evaluation framework for the application of a driver car-following behavior model in CACC system design to ensure user acceptance in terms of vehicle dynamics and string stability. The authors adopted two widely used driver car-following behavior models, (a) the optimum velocity model (OVM) and (b) the intelligent driver model (IDM), to prove the efficacy of the evaluation framework developed in this research for CACC system design. A platoon of six vehicles was simulated for three traffic flow states (uniform speed, speed with constant acceleration, and speed with constant deceleration) with different acceleration and deceleration rates. The maximum acceleration or deceleration and the sum of the squares of the errors of the follower vehicle speed were measured to evaluate user acceptance in terms of vehicle dynamics and string stability. Analysis of the simulation results revealed that the OVM performed better at modeling a CACC system than did the IDM in terms of acceptable vehicle dynamics and string stability.