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Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

Deep neural networks suffer from catastrophic forgetting, where performance on previous tasks degrades after training on a new task. This issue arises due to the model's tendency to overwrite previously acquired knowledge with new…

Regularization is essential when training large neural networks. As deep neural networks can be mathematically interpreted as universal function approximators, they are effective at memorizing sampling noise in the training data. This…

We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…

Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…

The Deep neural networks (DNNs) have achieved great success on a variety of computer vision tasks, however, they are highly vulnerable to adversarial attacks. To address this problem, we propose to improve the local smoothness of the…

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

In recent years, deep neural networks have emerged as a solution for inverse imaging problems. These networks are generally trained using pairs of images: one degraded and the other of high quality, the latter being called 'ground truth'.…

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications…

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

The concept of deep learning is employed for the inversion of NMR signals and it is shown that NMR signal inversion can be considered as an image-to-image regression problem, which can be treated with a convolutional neural net. It is…

Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is…

Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned…

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an…

These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…