Venkateswaran P. Krishnan

Gaik Ambartsoumian, Rim Gouia-Zarrad, Venkateswaran P. Krishnan et al.

We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of radially incomplete data, we show that the spherical Radon transform can be uniquely inverted recovering the image function in spherical shells. Our result is valid when the support of the image function is inside the data acquisition sphere, outside that sphere, as well as on both sides of the sphere. Furthermore, in addition to the uniqueness result our method of proof provides reconstruction formulas for all those cases. We present a robust computational algorithm based on our inversion formula and demonstrate its accuracy and efficiency on several numerical examples.

Alphin J Thottupattu, Jayanthi Sivaswamy, Venkateswaran P. Krishnan

Normative aging trends of the brain can serve as an important reference in the assessment of neurological structural disorders. Such models are typically developed from longitudinal brain image data -- follow-up data of the same subject over different time points. In practice, obtaining such longitudinal data is difficult. We propose a method to develop an aging model for a given population, in the absence of longitudinal data, by using images from different subjects at different time points, the so-called cross-sectional data. We define an aging model as a diffeomorphic deformation on a structural template derived from the data and propose a method that develops topology preserving aging model close to natural aging. The proposed model is successfully validated on two public cross-sectional datasets which provide templates constructed from different sets of subjects at different age points.

Alphin J. Thottupattu, Jayanthi Sivaswamy, Venkateswaran P. Krishnan

Anatomical variabilities seen in longitudinal data or inter-subject data is usually described by the underlying deformation, captured by non-rigid registration of these images. Stationary Velocity Field (SVF) based non-rigid registration algorithms are widely used for registration. SVF based methods form a metric-free framework which captures a finite dimensional submanifold of deformations embedded in the infinite dimensional smooth manifold of diffeomorphisms. However, these methods cover only a limited degree of deformations. In this paper, we address this limitation and define an approximate metric space for the manifold of diffeomorphisms $\mathcal{G}$. We propose a method to break down the large deformation into finite compositions of small deformations. This results in a broken geodesic path on $\mathcal{G}$ and its length now forms an approximate registration metric. We illustrate the method using a simple, intensity-based, log-demon implementation. Validation results of the proposed method show that it can capture large and complex deformations while producing qualitatively better results than the state-of-the-art methods. The results also demonstrate that the proposed registration metric is a good indicator of the degree of deformation.