LMMSE and MAP estimators for reduction of multiplicative noise in the nonsubsampled contourlet domain

In this paper, two algorithms for multiplicative noise reduction, using the undecimated separable wavelet transform, are extended to the nonsubsampled contourlet (NSCT) domain. Such algorithms use either a maximum a posteriori (MAP) or a linear minimum mean square error (LMMSE) filtering approach, and involve the estimation of the moments of the NSCT coefficients up to the fourth order. The MAP filter relies on the conjecture that the NSCT coefficients follow a generalized Gaussian distribution (GGD), whose parameters locally vary. The extension of the denoising algorithms to the NSCT domain is not trivial, because several issues, related to the nonseparable implementation of the NSCT and the estimation of the moments, are to be considered to obtain viable solutions. Simulation results show that the MAP filter always outperforms the LMMSE one, confirming that the nonstationary GGD model is suitable for describing NSCT coefficients. Both denoising algorithms benefit from the multidirectional domain. However, the improvements on the LMMSE filter are greater than those on the MAP filter, showing that denoising in the NSCT domain is less effective when the nonstationary MAP estimator is used.