This paper proposes an new optimization framework for tomographic reconstruction of 3D volumes when only a limited number of projection views are available. The problem has several important clinical applications spanning coronary angiographic imaging, breast tomosynthesis and dental imaging. We first show that the limited view reconstruction problem can be formulated as a "constrained" version of the metric labeling problem. This lays the groundwork for a linear programming framework that brings together metric labeling classification and classical algebraic tomographic reconstruction (ART) in a unified model. If the imaged volume is known to be comprised of a finite set of attenuation coefficients, given a regular limited view reconstruction as an input, we can view it as a "denoising" task - where voxels must be reassigned subject to maximally maintaining consistency with the input reconstruction and the objective of ART simultaneously. The approach can reliably reconstruct volumes with several multiple contrast objects as well as the simpler binary contrast case which can be solved near-optimally in practice. We present evaluations on cone bean computed tomography, it can also be readily extended to other tomographic modalities as a viable approach for limited-view tomographic reconstruction.

We propose an optimization algorithm to solve the brachytherapy seed localization problem in prostate brachytherapy. Our algorithm is based on novel geometric approaches to exploit the special structure of the problem and relies on a number of key observations which help us formulate the optimization problem as a minimization integer program (IP). Our IP model precisely defines the feasibility polyhedron for this problem using a polynomial number of half-spaces; the solution to its corresponding linear program is rounded to yield an integral solution to our task of determining correspondences between seeds in multiple projection images. The algorithm is efficient in theory as well as in practice and performs well on simulation data (approximately 98% accuracy) and real X-ray images (approximately 95% accuracy). We present in detail the underlying ideas and an extensive set of performance evaluations based on our implementation.