Video denoising in three-dimensional complex wavelet domain using a doubly stochastic modelling

This study presents a new video denoising method in the three-dimensional (3D) discrete complex wavelet transform (DCWT) domain. The authors assume that the coefficients have zero mean and Gaussian local distributions given the unknown variances. In practice, the locally estimated variances (LEVs) are not accurate and are simply maximum-likelihood estimates from the conditional Gaussian distribution. To take into account the inaccuracies of LEVs and motivated by experiments, the authors assume that the LEVs have gamma distributions. This is equivalent to the unconditional heavy-tailed local Bessel K-form prior densities given LEVs. This model is able to more accurately model the intrascale dependency between adjacent wavelet coefficients. The authors employ both maximum a posteriori and minimum mean-squared error MMSE estimators of the unconditional distributions, to reduce the noise in the 3D DCWT domain. The authors examine their spatially adaptive algorithm for reduction of various types of noise including additive white Gaussian noise, non-stationary noise, Poisson noise and speckle noise. The proposed method results in an impressive video enhancement without any explicit use of motion estimation. This is because, the 3D DCWT is a motion selective transform and isolates the motions and directions in its sub-bands.