Estimating view parameters from random projections for Tomography using spherical MDS

This work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is non-iterative and computationally efficient.The effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method.Our study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available on https://engineering.purdue.edu/PRECISE/SMDS webcite.This work studies the problem of 2D tomography with unknown view angles and discusses the potential applications of our work. We give the background of our work, reviews of the existing methods and a brief introduction of our proposed method in the following subsections.The computed tomography has been successfully applied to various fields over the past decades, for example, medical imaging, synthetic aperture radar (SAR) and Cryo-electron microscopy (cryoEM) for structuring viruses [1-4]. The traditional tomography is defined as a process of recovering the object from the measurements that are line integrals of that object at some set of known orientations (view angles). However