Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning

We show that denoising of 3D point clouds can be learned unsupervised, directly from noisy 3D point cloud data only. This is achieved by extending recent ideas from learning of unsupervised image denoisers to unstructured 3D point clouds. Unsupervised image denoisers operate under the assumption that a noisy pixel observation is a random realization of a distribution around a clean pixel value, which allows appropriate learning on this distribution to eventually converge to the correct value. Regrettably, this assumption is not valid for unstructured points: 3D point clouds are subject to total noise, i. e., deviations in all coordinates, with no reliable pixel grid. Thus, an observation can be the realization of an entire manifold of clean 3D points, which makes a na\"ive extension of unsupervised image denoisers to 3D point clouds impractical. Overcoming this, we introduce a spatial prior term, that steers converges to the unique closest out of the many possible modes on a manifold. Our results demonstrate unsupervised denoising performance similar to that of supervised learning with clean data when given enough training examples - whereby we do not need any pairs of noisy and clean training data.Comment: Proceedings of ICCV 201

Unsupervised training of deep learning based image denoisers from undersampled measurements

Department of Electrical EngineeringCompressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity, minimal total-variation, or self-similarity of images. Recently, deep learning based compressive image recovery methods have been proposed and have yielded state-of-the-art performances. They used data-driven approaches instead of hand-crafted image priors to regularize ill-posed inverse problems with undersampled data. Ironically, training deep neural networks (DNNs) for them requires ???clean??? ground truth images, but obtaining the best quality images from undersampled data requires well-trained DNNs. To resolve this dilemma, we propose novel methods based on two well-grounded theories: denoiser-approximate message passing (D-AMP) and Stein???s unbiased risk estimator (SURE). Our proposed methods, LDAMP SURE and LDAMP SURE-T, were able to train deep learning based image denoisers from undersampled measurements without ground truth images and without additional image priors and to recover images with state-of-the-art qualities from undersampled data. We evaluated our methods for various compressive sensing recovery problems with Gaussian random, coded diffraction pattern, and compressive sensing MRI (CS-MRI) measurement matrices. Our proposed methods yielded state-of-the-art performances for all cases without ground truth images. Our methods also yielded comparable performances to the approaches with ground truth data. Moreover, we have extended our methods to deal with a Gaussian noise in a measurement domain and further enhance reconstruction quality by developing an image refining method called LDAMP SURE-FT.clos

Unsupervised Image Restoration Using Partially Linear Denoisers.

Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the output of the restoration model and the ground truth, clean images is minimized. The ground truth images, however, are often unavailable or very expensive to acquire in real-world applications. We circumvent this problem by proposing a class of structured denoisers that can be decomposed as the sum of a nonlinear image-dependent mapping, a linear noise-dependent term and a small residual term. We show that these denoisers can be trained with only noisy images under the condition that the noise has zero mean and known variance. The exact distribution of the noise, however, is not assumed to be known. We show the superiority of our approach for image denoising, and demonstrate its extension to solving other restoration problems such as image deblurring where the ground truth is not available. Our method outperforms some recent unsupervised and self-supervised deep denoising models that do not require clean images for their training. For deblurring problems, the method, using only one noisy and blurry observation per image, reaches a quality not far away from its fully supervised counterparts on a benchmark dataset