A novel Bayesian nonparametric estimator in the wavelet domain is presented. In this approach, a prior model is imposed on the wavelet coefficients designed to capture the sparseness of the wavelet expansion. Seeking probability models for the marginal densities of the wavelet coefficients, the new family of Bessel K forms (BKF) densities are shown to fit very well to the observed histograms. Exploiting this prior, we designed a Bayesian nonlinear denoiser and we derived a closed form for its expression. We then compared it to other priors that have been introduced in the literature, such as the generalized Gaussian density (GGD) or the α-stable models, where no analytical form is available for the corresponding Bayesian denoisers. Specifically, the BKF model turns out to be a good compromise between these two extreme cases (hyperbolic tails for the α-stable and exponential tails for the GGD). Moreover, we demonstrate a high degree of match between observed and estimated prior densities using the BKF model. Finally, a comparative study is carried out to show the effectiveness of our denoiser which clearly outperforms the classical shrinkage or thresholding wavelet-based techniques.