Benefiting From Bicubically Down-Sampled Images for Learning Real-World Image Super-Resolution

Super-resolution (SR) has traditionally been based on pairs of high-resolution images (HR) and their low-resolution (LR) counterparts obtained artificially with bicubic downsampling. However, in real-world SR, there is a large variety of realistic image degradations and analytically modeling these realistic degradations can prove quite difficult. In this work, we propose to handle real-world SR by splitting this ill-posed problem into two comparatively more well-posed steps. First, we train a network to transform real LR images to the space of bicubically downsampled images in a supervised manner, by using both real LR/HR pairs and synthetic pairs. Second, we take a generic SR network trained on bicubically downsampled images to super-resolve the transformed LR image. The first step of the pipeline addresses the problem by registering the large variety of degraded images to a common, well understood space of images. The second step then leverages the already impressive performance of SR on bicubically downsampled images, sidestepping the issues of end-to-end training on datasets with many different image degradations. We demonstrate the effectiveness of our proposed method by comparing it to recent methods in real-world SR and show that our proposed approach outperforms the state-of-the-art works in terms of both qualitative and quantitative results, as well as results of an extensive user study conducted on several real image datasets.

From Classical to Unsupervised-Deep-Learning Methods for Solving Inverse Problems in Imaging.

Harshit Gupta

In this thesis, we propose new algorithms to solve inverse problems in the context of biomedical images. Due to ill-posedness, solving these problems require some prior knowledge of the statistics of the underlying images. The traditional algorithms, in the field, assume prior knowledge related to smoothness or sparsity of these images. Recently, they have been outperformed by the second generation algorithms which harness the power of neural networks to learn required statistics from training data. Even more recently, last generation deep-learning-based methods have emerged which require neither training nor training data. This thesis devises algorithms which progress through these generations. It extends these generations to novel formulations and applications while bringing more robustness. In parallel, it also progresses in terms of complexity, from proposing algorithms for problems with 1D data and an exact known forward model to the ones with 4D data and an unknown parametric forward model. We introduce five main contributions. The last three of them propose deep-learning-based latest-generation algorithms that require no prior training. 1) We develop algorithms to solve the continuous-domain formulation of inverse problems with both classical Tikhonov and total-variation regularizations. We formalize the problems, characterize the solution set, and devise numerical approaches to find the solutions. 2) We propose an algorithm that improves upon end-to-end neural-network-based second generation algorithms. In our method, a neural network is first trained as a projector on a training set, and is then plugged in as a projector inside the projected gradient descent (PGD). Since the problem is nonconvex, we relax the PGD to ensure convergence to a local minimum under some constraints. This method outperforms all the previous generation algorithms for Computed Tomography (CT). 3) We develop a novel time-dependent deep-image-prior algorithm for modalities that involve a temporal sequence of images. We parameterize them as the output of an untrained neural network fed with a sequence of latent variables. To impose temporal directionality, the latent variables are assumed to lie on a 1D manifold. The network is then tuned to minimize the data fidelity. We obtain state-of-the-art results in dynamic magnetic resonance imaging (MRI) and even recover intra-frame images. 4) We propose a novel reconstruction paradigm for cryo-electron-microscopy (CryoEM) called CryoGAN. Motivated by generative adversarial networks (GANs), we reconstruct a biomolecule's 3D structure such that its CryoEM measurements resemble the acquired data in a distributional sense. The algorithm is pose-or-likelihood-estimation-free, needs no ab initio, and is proven to have a theoretical guarantee of recovery of the true structure. 5) We extend CryoGAN to reconstruct continuously varying conformations of a structure from heterogeneous data. We parameterize the conformations as the output of a neural network fed with latent variables on a low-dimensional manifold. The method is shown to recover continuous protein conformations and their energy landscape.

EPFL2020

On the coupling of 1D and 3D Diffusion-Reaction Equations: Application to Tissue Pefusion Problems

Alfio Quarteroni

In this paper we consider the coupling between two diffusion-reaction problems, one taking place in a three-dimensional domain Ω, the other in a one-dimensional subdomain Λ. This coupled problem is the simplest model of fluid flow in a three-dimensional porous medium featuring fractures that can be described by one-dimensional manifolds. In particular this model can provide the basis for a multiscale analysis of blood flow through tissues, in which the capillary network is represented as a porous matrix, while the major blood vessels are described by thin tubular structures embedded into it: in this case, the model allows the computation of the 3D and 1D blood pressures respectively in the tissue and in the vessels. The mathematical analysis of the problem requires non-standard tools, since the mass conservation condition at the interface between the porous medium and the one-dimensional manifold has to be taken into account by means of a measure term in the 3D equation. In particular, the 3D solution is singular on Λ. In this work, suitable weighted Sobolev spaces are introduced to handle this singularity: the well-posedness of the coupled problem is established in the proposed functional setting. An advantage of such an approach is that it provides a Hilbertian framework which may be used for the convergence analysis of finite element approximation schemes. The investigation of the numerical approximation will be the subject of a forthcoming work.

2008

Extraction of network topology from multi-electrode recordings: is there a small-world effect?

Joao Emanuel Felipe Gerhard, Wulfram Gerstner

The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting generalized linear models on the neural responses, incorporating effects of the neurons' self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks' observed small-world-ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings.