Video denoising based on a bivariate cauchy distribution in 3-D complex wavelet domain

This paper presents a new video denoising algorithm based on the modeling of wavelet coefficients in each subband with a bivariate Cauchy probability density function (pdf). This bivariate pdf takes into account the statistical dependency of wavelet coefficients in adjacent scales. Within this framework, we describe a novel method for video denoising based on designing a maximum a posteriori (MAP) estimator employing a bivariate Cauchy random variable. Because separate 3-D transforms, such as ordinary 3-D wavelet transforms, have visual artifacts that degrade their performance in applications, we implement our algorithm in 3-D complex wavelet transform. This non-separable and oriented transform provides a motion-based multiscale decomposition for video that separates in its subbands motion along different directions. In addition, we use our denoising algorithm in 2-D complex wavelet domain, where the 2-D transform is applied to each frame individually. Despite the simplicity of our method in its implementation, our denoising results achieves better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR).