In this paper, we discuss the image denoising model which DeVore et al. had established, in which both distance and
smoothness can be measured by the objective function, and analysis the model for wavelet image denoising in the Besov
spaces with <i>p</i> = <i>q</i>. In addition, we give the exact thresholds for the model, and prove that for 0 < <i>p</i> <1 the effect of
noise removal using our methods is in between hard wavelet shrinkage and soft wavelet shrinkage. For the case
0 < <i>p</i> < 1 and 1 ≤ <i>p</i> ≤ ∞, which refers to the problems on the convergence of the iteration of the equations and on the
complexity of computation, we give the simplified algorithms. Comparing the threshold given by this paper with Lorenz
threshold, we conclude that the former is more meticulous than the latter for the model.