Image/video denoising based on a mixture of Laplace distributions with local parameters in multidimensional complex wavelet domain

Noise reduction in the wavelet domain can be expressed as an estimation problem in a Bayesian framework. So, the proposed distribution for the noise-free wavelet coefficients plays a key role in the performance of wavelet-based image/video denoising. This paper presents a new image/video denoising algorithm based on the modeling of wavelet coefficients in each subband with a mixture of Laplace probability density functions (pdfs) that uses local parameters for the mixture model. The mixture model is able to capture the heavy-tailed nature of wavelet coefficients and the local parameters model the intrascale dependency between the coefficients. Therefore, this relatively new pdf potentially can fit better the statistical properties of the wavelet coefficients than several other existing models. Within this framework, we describe a novel method for image/video denoising based on designing a maximum a posteriori (MAP) estimator, which relies on the mixture distributions for each wavelet coefficient in each subband. We employ two different versions of expectation maximization (EM) algorithm to find the parameters of mixture model and compare our new method with other image denoising techniques that are based on (1) non mixture pdfs that are not local, (2) non mixture pdfs with local variances, (3) mixture pdfs without local parameters and (4) methods that consider both heavy-tailed and locality properties. The simulation results show that our proposed technique is among the best reported in the literature both visually and in terms of peak signal-to-noise ratio (PSNR). In addition, we use the proposed algorithm for video denoising in multidimensional complex wavelet domain. Because 3-D complex wavelet transform provides a motion-based multiscale decomposition for video, we can see that our algorithm for video denoising, has very good performance without explicitly using motion estimation.