Venkateswaran P. Krishnan

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.

Synthetic aperture radar imaging exploiting multiple scattering

In this paper, we consider an imaging scenario, where a bi-static synthetic aperture radar (SAR) system is used in a multiple scattering environment. We consider a ray-theoretic approximation to the Green function to model a multiple scattering environment. This allows us to incorporate the multiple paths followed by the transmitted signal, thereby providing different views of the object to be imaged. However, the received signal from the multiple paths and additive thermal noise may interfere and produce artifacts when standard backprojection-based reconstruction algorithms are used. We use microlocal analysis in a statistical setting to develop a novel filtered-backprojection type image reconstruction method that not only exploits the multi-paths leading to enhancement of the reconstructed image but also suppresses the artifacts due to interference. We assume a priori knowledge of the second-order statistics of the target and noise to suppress the artifacts due to interference in a mean-square error sense. We present numerical simulations to demonstrate the performance of our image reconstruction method. While the focus of this paper is on radar applications, our image formation method is also applicable to other problems arising in fields such as acoustic, geophysical and medical imaging.

On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform

Abstract We generalize the inversion formulas obtained by Pestov–Uhlmann for the geodesic ray transform of functions and vector fields on 2-dimensional manifolds with boundary of constant curvature. Our formulas hold for simple 2-dimensional manifolds whose curvatures are close to a constant.

Microlocal Analysis of Elliptical Radon Transforms with Foci on a Line

In this paper, we take a microlocal approach to the study of an integral geometric problem involving integrals of a function on the plane over two-dimensional sets of ellipses on the plane. We focus on two cases: (a) the family of ellipses where one focus is fixed at the origin and the other moves along the x-axis, and (b) the family of ellipses having a common offset geometry.

An Efficient Numerical Algorithm for the Inversion of an Integral Transform Arising in Ultrasound Imaging

We present an efficient and novel numerical algorithm for inversion of transforms arising in imaging modalities such as ultrasound imaging, thermoacoustic and photoacoustic tomography, intravascular imaging, non-destructive testing, and radar imaging with circular acquisition geometry. Our algorithm is based on recently discovered explicit inversion formulas for circular and elliptical Radon transforms with radially partial data derived by Ambartsoumian, Gouia-Zarrad, Lewis and by Ambartsoumian and Krishnan. These inversion formulas hold when the support of the function lies on the inside (relevant in ultrasound imaging, thermoacoustic and photoacoustic tomography, non-destructive testing), outside (relevant in intravascular imaging), both inside and outside (relevant in radar imaging) of the acquisition circle. Given the importance of such inversion formulas in several new and emerging imaging modalities, an efficient numerical inversion algorithm is of tremendous topical interest. The novelty of our non-iterative numerical inversion approach is that the entire scheme can be pre-processed and used repeatedly in image reconstruction, leading to a very fast algorithm. Several numerical simulations are presented showing the robustness of our algorithm.

SAR imaging exploiting multi-path

We present a new filtered-backprojection (FBP) type image reconstruction method for synthetic aperture radar (SAR) that exploits multi-path in the presence of a perfectly reflecting wall. The new method is designed to take advantage of multiple scattering and incorporates the multiple scattered waves in the image reconstruction process enhancing the reconstructed image. We present numerical simulation to demonstrate the performance of the new method. While the focus of this paper is on radar applications, our image formation method is also applicable to other problems arising in fields such as acoustic, geophysical and medical imaging.

Determination of lower order perturbations of the polyharmonic operator from partial boundary data

We consider a perturbed polyharmonic operator of order defined on a bounded simply connected domain with smooth connected boundary of the form: where and stands for the greatest integer function. In the biharmonic case, such operators arise in the study of certain elasticity and buckling problems. We study an inverse problem involving and show that all the coefficients , and can be recovered from partial Dirichlet-to-Neumann (D-N) data on the boundary.

Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials

Abstract In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half the boundary, respectively. For the case of measurements on the whole boundary, the stability estimates are of ln-type and for the case of measurements on slightly more than half of the boundary, we derive estimates that are of ln ⁡ ln -type.

Singular FIOs in SAR Imaging, II: Transmitter and Receiver at Different Speeds

In this article, we consider two bistatic cases arising in synthetic aperture radar imaging: when the transmitter and receiver are both moving with different speeds along a single line parallel to the ground in the same direction or in the opposite directions. In both cases, we classify the forward operator

A fully non-linear optimization approach to acousto-electric tomography

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