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The goal of this letter is to study convergence conditions for a previously presented iterative wavelet denoising method and to shed light on its relationship with outlier rejection. This method involves a user-defined parameter, which must fulfill certain conditions in order to ensure denoising. Using generalized Gaussian modeling for the wavelet coefficients distribution, we obtain a lower bound for this parameter, and the resulting threshold, both adapted to the shape of the distribution. The properties of this threshold are examined, and the proposed method is compared with other classical rejection methods.