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An accelerated model-based information theoretic approach is presented to perform the task of Magnetic Resonance (MR) thermal image reconstruction from a limited number of observed samples on k-space. The key idea of the proposed approach is to utilize information theoretic techniques to optimally detect samples of k-space that are information rich with respect to a model of the thermal data acquisition. These highly informative k-space samples are then used to refine the mathematical model and reconstruct the image. The information theoretic reconstruction is demonstrated retrospectively in data acquired during MR guided Laser Induced Thermal Therapy (MRgLITT) procedures. The approach demonstrates that locations of high-information content with respect to a model based reconstruction of MR thermometry may be quantitatively identified. The predicted locations of high-information content are sorted and retrospectively extracted from the fully sampled k-space measurements data set. The effect of interactively increasing the predicted number of data points used in the subsampled reconstruction is quantified using the L2-norm of the distance between the subsampled and fully sampled reconstruction. Performance of the proposed approach is also compared with clinically available subsampling techniques (rectilinear subsampling and variable-density Poisson disk undersampling). It is shown that the proposed subsampling scheme results in accurate reconstructions using small fraction of k-space points and suggest that the reconstruction technique may be useful in improving the efficiency of the thermometry data temporal resolution., Comment: 29 pages, 25 figures