High-Dimensional Mixture Models for Unsupervised Image Denoising (HDMI)
Antoine Houdard, Charles Bouveyron, Julie Delon · SIAM Journal on Imaging Sciences · 2018
This work addresses the problem of patch-based image denoising through the unsupervised learning of a probabilistic high-dimensional mixture model on the noisy patches. The model, called 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 us 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 us 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 denoising algorithm that can be used both when the noise level is known and is unknown.