A stochastically evolving non-local search and solutions to inverse problems with sparse data. (October 2016) - Venugopal, Mamatha; Vasu, Ram Mohan; Roy, Debasish
Abstract: Building on a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed using change of measures on the states that evolve as diffusion processes and splitting of the state-space along the lines of a Bayesian game. To begin with, the efficacy of the optimizer, when contrasted with one of the most efficient existing schemes, is assessed against a family of Np -hard benchmark problems. Then, using both simulated and experimental data, potentialities of the new proposal are further explored in the context of an inverse problem of significance in photoacoustic imaging, wherein the superior reconstruction features of a global search vis-à-vis the commonly adopted local or quasi-local schemes are brought into relief. Highlights: A game theoretic perspective to global stochastic search, based on state space splitting, is suggested. Using change of measures, the search renders the posterior distribution unimodal around the global optimum. The search can perform single- and multi-objective optimization with similar efficacy. The scheme is adapted to solve inverse problems with sparse data, yielding reconstructions with superior resolution.