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In this paper we propose a novel iterative algorithm for wavelet-based image denoising following a Maximum a Posteriori (MAP) approach. The wavelet shrinkage problem is modeled according to the Bayesian paradigm, providing a strong and extremely flexible framework for solving general image denoising problems. To approximate the MAP estimator, we propose GSAShrink, a modified version of a known combinatorial optimization algorithm based on non-cooperative game theory (Game Strategy Approach, or GSA). In order to modify the original algorithm to our purposes, we generalize GSA by introducing some additional control parameters and steps to reflect the nature of wavelet shrinkage applications. To test and evaluate the proposed method, experiments using several wavelet basis on noisy images are proposed. Additionally to better visual quality, the obtained results produce quantitative metrics (MSE, PSNR, ISNR and UIQ) that show significant improvements in comparison to traditional wavelet denoising approaches known as soft and hard thresholding, indicating the effectiveness of the proposed algorithm.