Concurrent propagation for solving ill-posed problems of global discrete optimisation

Classical frameworks for global 1D discrete optimisation: dynamic programming (DP) and belief propagation (BP) - presume well-posed problems with unique solutions. Ill-posed problems, being the most common in applied pattern recognition and computer vision, are regularised to restore well-posedness. However, typical heuristic regularisation does not guarantee that a set of multiple equivalent solutions is reduced to a single solution. An alternative concurrent propagation (CP) proposed in this paper extends the DP to allow for determining whether the problem is well- or ill-posed and storing implicitly in the latter case the entire set of solutions (e.g. for its structural analysis to improve regularisation). The CP, DP, and BP have similar computational complexity.