A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shift-Invariant image denoising using mixture of laplace distributions in wavelet-domain
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
IEEE Transactions on Signal Processing
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Wavelet thresholding via MDL for natural images
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Adaptive wavelet thresholding for image denoising and compression
IEEE Transactions on Image Processing
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image denoising in steerable pyramid domain based on a local Laplace prior
Pattern Recognition
Face recognition using dual-tree complex wavelet features
IEEE Transactions on Image Processing
Image denoising with anisotropic bivariate shrinkage
Signal Processing
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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.