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.