Naren Naik

A Nonlinear Iterative Reconstruction and Analysis Approach to Shape-Based Approximate Electromagnetic Tomography

A nonlinear Helmholtz-equation-modeled electromagnetic tomographic reconstruction problem is solved for the object boundary and inhomogeneity parameters in a damped Tikhonov-regularized Gauss-Newton (DTRGN) solution framework. In this paper, the object is represented in a suitable global basis, whereas the boundary is expressed as the zero level set of a signed-distance function. For an explicit parameterized boundary-representation-based reconstruction scheme, analytical Jacobian and Hessian calculations are made to express the changes in scattered field values w.r.t. changes in the inhomogeneity parameters and the control points in a spline representation of the object boundary, via the use of a level-set representation of the object. Even though, in this paper, a homogeneous dielectric is considered and a spline representation has been used to represent the boundary, the formulation can be used for a general global basis representation of the inhomogeneity as well as arbitrary parameterizations of the boundary, and is generalizable to three dimensions. Reconstruction results are presented for test cases of landminelike dielectric objects embedded in the ground under noisy data conditions. To confirm convergence and, at times, to know which of the obtained iterates are closer to the actual unknown solution, using a perturbation theory framework, a local (Hessian-based) convergence analysis is applied to the DTRGN scheme for the reconstruction, yielding estimates of convergence rates in the residual and parameter spaces.

An implicit radial basis function based reconstruction approach to electromagnetic shape tomography

In a reconstruction problem for subsurface tomography (modeled by the Helmholtz equation), we formulate a novel reconstruction scheme for shape and electromagnetic parameters from scattered field d ...

Fully Nonlinear

In fluorescence optical tomography, many works in the literature focus on the linear reconstruction problem to obtain the fluorescent yield or the linearized reconstruction problem to obtain the absorption coefficient. The nonlinear reconstruction problem, to reconstruct the fluorophore absorption coefficient, is of interest in imaging studies as it presents the possibility of better reconstructions owing to a more appropriate model. Accurate and computationally efficient forward models are also critical in the reconstruction process. The

{SP}_{3}

{\text{SP}}_{N}

Approximation Based Fluorescence Optical Tomography

approximation to the radiative transfer equation (RTE) is gaining importance for tomographic reconstructions owing to its computational advantages over the full RTE while being more accurate and applicable than the commonly used diffusion approximation. This paper presents Gauss–Newton-based fully nonlinear reconstruction for the

An SP3-approximation based fully non-linear reconstruction scheme for fluorescence optical tomography

{\text{SP}}_{3}

Radial-basis-function level-set-based regularized Gauss-Newton-filter reconstruction scheme for dynamic shape tomography

approximated fluorescence optical tomography problem with respect to shape as well as the conventional finite-element method-based representations. The contribution of this paper is the Frechet derivative calculations for this problem and demonstration of reconstructions in both representations. For the shape reconstructions, radial-basis-function represented level-set-based shape representations are used. We present reconstructions for tumor-mimicking test objects in scattering and absorption dominant settings, respectively, for moderately noisy data sets in order to demonstrate the viability of the formulation. Comparisons are presented between the nonlinear and linearized reconstruction schemes in an element wise setting to illustrate the benefits of using the former especially for absorption dominant media.

A constant gain Kalman filter approach to track maneuvering targets

We present a novel fully non-linear reconstruction scheme for fluorescence optical tomography with light propagation model as the SP3 approximation to the radiative transfer equation. We evaluate an adjoint based Frechet derivative, and present preliminary reconstruction results.

Shape based pharmacokinetic fluorescence optical tomography

The dynamic reconstruction problem in tomographic imaging is encountered in several applications, such as species determination, the study of blood flow through arteries/veins, motion compensation in medical imaging, and process tomography. The reconstruction method of choice is the Kalman filter and its variants, which, however, are faced by issues of filter tuning. In addition, since the time-propagation models of physical parameters are typically very complex, most of the time, a random walk model is considered. For geometric deformations, affine models are typically used. In our work, with the objectives of minimizing tuning issues and reconstructing time-varying geometrically deforming features of interest with affine in addition to pointwise-normal scaling motions, a novel level-set-based reconstruction scheme for ray tomography is proposed for shape and electromagnetic parameters using a regularized Gauss-Newton-filter-based scheme. We use an implicit Hermite-interpolation-based radial basis function representation of the zero level set corresponding to the boundary curve. Another important contribution of the paper is an evaluation of the shape-related Frechet derivatives that does not need to evaluate the pointwise Jacobian (the ray-path matrix in our ray-tomography problem). Numerical results validating the formulation are presented for a straight ray-based tomographic reconstruction. To the best of our knowledge, this paper presents the first tomographic reconstruction results in these settings.

Joint optimization of SINR and power allocation to relays in cluster-based wireless sensor networks

Tracking of maneuvering targets is an important area of research with applications in both the military and civilian domains. One of the most fundamental and widely used approaches to target tracking is the Kalman filter. In presence of unknown noise statistics there are difficulties in the Kalman filter yielding acceptable results. In the Kalman filter operation for state variable models with near constant noise and system parameters, it is well known that after the initial transient the gain tends to a steady state value. Hence working directly with Kalman gains it is possible to obtain good tracking results dispensing with the use of the usual covariances. The present work applies an innovations based cost function minimization approach to the target tracking problem of maneuvering targets, in order to obtain the constant Kalman gain. Our numerical studies show that the constant gain Kalman filter gives good performance compared to the standard Kalman filter. This is a significant finding in that the constant gain Kalman filter circumvents or in other words trades the gains with the filter statistics which are more difficult to obtain. The problems associated with using a Kalman filter for tracking a maneuvering target with unknown system and measurement noise statistics can be circumvented by using the constant gain approach which seeks to work only with the gains instead of the state and measurement noise covariances. The approach is applied to a variety of standard maneuvering target models.