A Novel Convex Relaxation for Non-binary Discrete Tomography
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations.
KeywordsLinear Programming Relaxation Convex Relaxation Bundle Method High Order Factor Restricted Isometry Property
- 1.IBM ILOG CPLEX Optimizer. http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/
- 10.Keiper, S., Kutyniok, G., Lee, D.G., Pfander, G.E.: Compressed sensing for finite-valued signals. ArXiv e-prints, September 2016Google Scholar
- 15.Sontag, D., Globerson, A., Jaakkola, T.: Introduction to dual decomposition for inference. In: Optimization for Machine Learning. MIT Press (2011)Google Scholar
- 16.Tarlow, D., Swersky, K., Zemel, R.S., Adams, R.P., Frey, B.J.: Fast exact inference for recursive cardinality models. In: UAI (2012)Google Scholar
- 17.Weber, S., Schnörr, C., Hornegger, J.: A linear programming relaxation for binary tomography with smoothness priors. In: IWCIA (2003)Google Scholar