Compressive Learning for Patch-Based Image Denoising

Abstract

The Expected Patch Log-Likelihood algorithm (EPLL) and its extensions have shown good performances for image denoising. The prior model used by EPLL is usually a Gaussian Mixture Model (GMM) estimated from a database of image patches. Classical mixture model estimation methods face computational issues as the high dimensionality of the problem requires training on large datasets. In this work, we adapt a compressive statistical learning framework to carry out the GMM estimation. With this method, called sketching, we estimate models from a compressive representation (the sketch) of the training patches. The cost of estimating the prior from the sketch no longer depends on the number of items in the original large database. To accelerate further the estimation, we add another dimension reduction technique (low-rank modeling of the covariance matrices) to the compressing learning framework. To demonstrate the advantages of our method, we test it on real large-scale data. We show that we can produce denoising performances similar to performances obtained with models estimated from the original training database using GMM priors learned from the sketch with improved execution times.

PatchNR: learning from very few images by patch normalizing flow regularization

“…However, GMMs have a limited expressiveness and can only hardly approximate complicated probability distributions induced by patches [23]. Further, the reconstruction process proposed in [93] is computationally very costly even though a reduction of the computational effort was considered in several papers [61,72]. Indeed, we will show in our numerical examples that the patchNR clearly outperforms the reconstructions from EPLL.…”

“…In particular, [93] proposed the negative log likelihood of all patches of an image as a regularizer, where the underlying patch distribution was assumed to follow a Gaussian mixture model (GMM) which parameters were learned from few clean images. This method is still competitive to many approaches based on deep learning and several extensions were suggested recently [22,61,72]. However, even though GMMs can approximate any probability density function if the number of components is large enough, they suffer from limited flexibility in case of a fixed number of components, see [23] and the references therein.…”

ASTRA kernelkit: GPU-accelerated projectors for computed tomography using cupy

“…For example, it can mitigate GPU memory exhaustion and reduce training time. This approach has proven successful in various image tasks such as superresolution and denoising [47,5].…”

The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension

“…Often, a low-rank approximation is made (flat-tail) to reduce the number of estimated parameters. For example, an unknown low-rank covariances model was used in [32,33] to learn an image patch model from a compressed database. This model is then used to perform patch based image denoising.…”