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A texture interpolation technique based on the locally piecewise auto-regressive (PAR) model and the non-local (NL) training procedure is investigated in this work. The proposed PAR/NL scheme selects model parameters adaptively based on local image properties with an objective to improve the interpolation performance of nonadaptive models, e.g., the bicubic algorithm. To determine model parameters for stochastic texture, we use the non-local (NL) learning algorithm to update and refine these local model parameters under the assumption that the PAR model parameters are self-regular. As compared to previous interpolation algorithms, the proposed PAR/NL scheme boosts texture details, and eliminates blurring artifacts perceptually. Experimental results are given to demonstrate the performance of the proposed technique.