X-ray computed tomography (CT) is one of the most widely used imaging modalities for diagnostic tasks in the clinical application. As X-ray dosage given to the patient has potential to induce undesirable clinical consequences, there is a need for reduction in dosage while maintaining good quality in reconstruction. The present work attempts to address low-dose tomography via an optimization method. In particular, we formulate the reconstruction problem in the form of a matrix system involving a binary matrix. We then recover the image deploying the ideas from the emerging field of compressed sensing (CS). Further, we study empirically the radial and angular sampling parameters that result in a binary matrix possessing sparse recovery parameters. The experimental results show that the performance of the proposed binary matrix with reconstruction using TV minimization by Augmented Lagrangian and ALternating direction ALgorithms (TVAL3) gives comparably better results than Wavelet based Orthogonal Matching Pursuit (WOMP) and the Least Squares solution.