High-Dimensional Mixture Models for Unsupervised Image Denoising (HDMI)

Abstract

This work addresses the problem of patch-based image denoising through the unsupervised learning of a probabilistic high-dimensional mixture models on the noisy patches. The model, named hereafter HDMI, proposes a full modeling of the process that is supposed to have generated the noisy patches. To overcome the potential estimation problems due to the high dimension of the patches, the HDMI model adopts a parsimonious modeling which assumes that the data live in group-specific subspaces of low dimensionalities. This parsimonious modeling allows in turn to get a numerically stable computation of the conditional expectation of the image which is applied for denoising. The use of such a model also permits to rely on model selection tools, such as BIC, to automatically determine the intrinsic dimensions of the subspaces and the variance of the noise. This yields a blind denoising algorithm that demonstrates state-of-the-art performance, both when the noise level is known and unknown.

Image Denoising with Generalized Gaussian Mixture Model Patch Priors

“…Of these tasks, estimating the parameters of GGMM directly on noisy observations is a problem of particular interest, that could benefit from our approximations. Learning GMM priors on noisy patches has been shown to be useful in patch-based image restoration when clean patches are not available a priori, or to further adapt the model to the specificities of a given noisy image [66,60,26]. Another open problem is to analyze the asymptotic behavior of the minimum mean square estimator (MMSE) shrinkage with GGD prior, as an alternative to MAP shrinkage.…”

“…Alternatively, modeling the distribution of patches of an image (i.e., small windows usually of size 8×8) has proven to be a powerful solution. In particular, popular patch techniques rely on non-local self-similarity [8], fields of experts [52], learned patch dictionaries [2,19,53], sparse or low-rank properties of stacks of similar patches [12,13,34,29], patch re-occurrence priors [37], or more recently mixture models patch priors [67,66,61,60,26,56,44].…”

EPLL: An Image Denoising Method Using a Gaussian Mixture Model Learned on a Large Set of Patches

“…Zoran and Weiss [19] proposed the values of β to be (β 1 , β 2 , β 3 , β 4 , β 5 ) = (1,4,8,16,32,64). In this section we verify that these betas are indeed the best.…”

“…We kept N = 2 · 10 6 and K = 200 but we now use a smaller patch size √ d = 6 because of memory limitations. Four components of the GMM are represented in Figures 6,7,8,9. In Table 10, we compare all the denoising methods previously introduced: channel by channel with the 3 different color bases and with the prior learned in color. The study was conducted on 10 test images from the test set of images.…”

“…In other words, we wish to find a reconstructed image in which every patch is likely under our prior while keeping the reconstructed image still close to the corrupted one. This variational approach is still popular as shown by recent denoising papers [5,8].…”