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Deep learning networks have shown state-of-the-art performance in many image reconstruction problems. However, it is not well understood what properties of representation and learning may improve the generalization ability of the network.…

Generalization to unseen degradations remains a fundamental challenge for low-level vision models. This paper aims to investigate the underlying mechanism of this failure, using image deraining as a primary case study due to its…

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

Predicting measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying…

We propose a general framework for neural network compression that is motivated by the Minimum Description Length (MDL) principle. For that we first derive an expression for the entropy of a neural network, which measures its complexity…

Image compression is one of the essential methods of image processing. Its most prominent advantage is the significant reduction of image size allowing for more efficient storage and transfer. However, lossy compression is associated with…

A rapidly increasing portion of Internet traffic is dominated by requests from mobile devices with limited- and metered-bandwidth constraints. To satisfy these requests, it has become standard practice for websites to transmit small and…

In the past few decades, to reduce the risk of X-ray in computed tomography (CT), low-dose CT image denoising has attracted extensive attention from researchers, which has become an important research issue in the field of medical images.…

Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…

Recurrent Neural Networks (RNN) are widely used to solve a variety of problems and as the quantity of data and the amount of available compute have increased, so have model sizes. The number of parameters in recent state-of-the-art networks…

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently deep neural networks have been widely and successfully used in computer vision tasks and attracted…

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

In this work, we seek to improve the velocity reconstruction of clusters by using Graph Neural Networks -- a type of deep neural network designed to analyze sparse, unstructured data. In comparison to the Convolutional Neural Network (CNN)…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Lensless cameras relax the design constraints of traditional cameras by shifting image formation from analog optics to digital post-processing. While new camera designs and applications can be enabled, lensless imaging is very sensitive to…

Deep convolutional neural networks (CNNs) are often of sophisticated design with numerous learnable parameters for the accuracy reason. To alleviate the expensive costs of deploying them on mobile devices, recent works have made huge…