The BKF Bayesian wavelet estimator

Bayesian approach for wavelet estimation has been a popular topic. The recent papers by Boubchir and Fadili [A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior, Pattern Recognition Lett. 27 (September 2006) 1370–1382, Analytical form for a Bayesian wavelet estimator of images using the Bessel KK form densities, IEEE Trans. Image Process. 14 (February 2005) 231–240] derived a Bayesian wavelet estimator when the prior for wavelet coefficients is assumed to take the Bessel K form (BKF). Actually, only an approximate formula for the wavelet estimator was derived because it was claimed that the exact analytical form of the BKF prior model was difficult to deal with. In this note, we derive the corresponding expression in its exact form and provide computer programs. The expression involves some well-known special functions.