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Personalized noninvasive imaging of subject-specific cardiac electrical activity can guide and improve preventive diagnosis and treatment of cardiac arrhythmia. Compared to body surface potential (BSP) recordings and electrophysiological information reconstructed on heart surfaces, volumetric myocardial transmembrane potential (TMP) dynamics is of greater clinical importance in exhibiting arrhythmic details and arrythmogenic substrates inside the myocardium. This paper presents a physiological-model-constrained statistical framework to reconstruct volumetric TMP dynamics inside the 3-D myocardium from noninvasive BSP recordings. General knowledge of volumetric TMP activity is incorporated through the modeling of cardiac electrophysiological system, and is used to constrain TMP reconstruction. This physiological system is reformulated into a stochastic state-space representation to take into account model and data uncertainties, and nonlinear data assimilation is developed to estimate volumetric myocardial TMP dynamics from personal BSP data. Robustness of the presented framework to practical model and data errors is evaluated. Comparison of epicardial potential reconstructions with classical regularization-based approaches is performed on computational phantom regarding right bundle branch blocks. Further, phantom experiments on intramural focal activities and an initial real-data study on postmyocardial infarction demonstrate the potential of the framework in reconstructing local arrhythmic details and identifying arrhythmogenic substrates inside the myocardium.