A deterministic-statistical approach to reconstruct moving sources using sparse partial data
Yanfang Liu, Yukun Guo, Jiguang Sun
Abstract
Abstract We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The well-posedness of the posterior measure is analyzed in the sense of the Hellinger distance. Both steps are based on the same physical model and use the same set of measured data. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples.
Topics & Concepts
Hellinger distanceMathematicsBayesian probabilityMeasure (data warehouse)AlgorithmSet (abstract data type)Inversion (geology)Prior informationInverse problemData setSampling (signal processing)Pattern recognition (psychology)Artificial intelligencePosterior probabilityNoisy dataFinite setPrior probabilityBayesian inferenceMathematical optimizationInversePartial derivativeNumerical methods in inverse problemsMicrowave Imaging and Scattering AnalysisMedical Imaging Techniques and Applications