Related papers: Deep Null Space Learning for Inverse Problems: Con…
Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently…
Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…
Image restoration tasks have achieved tremendous performance improvements with the rapid advancement of deep neural networks. However, most prevalent deep learning models perform inference statically, ignoring that different images have…
Regularization plays a major role in modern deep learning. From classic techniques such as L1,L2 penalties to other noise-based methods such as Dropout, regularization often yields better generalization properties by avoiding overfitting.…
Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…
Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…
Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…
The image reconstruction process in medical imaging can be treated as solving an inverse problem. The inverse problem is usually solved using time-consuming iterative algorithms with sparsity or other constraints. Recently, deep neural…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning,…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…
Neural networks have become a prominent approach to solve inverse problems in recent years. While a plethora of such methods was developed to solve inverse problems empirically, we are still lacking clear theoretical guarantees for these…
Path regularization has shown to be a very effective regularization to train neural networks, leading to a better generalization property than common regularizations i.e. weight decay, etc. We propose a first near-complete (as will be made…
We present a computational method for empirically characterizing the training loss level-sets of deep neural networks. Our method numerically constructs a path in parameter space that is constrained to a set with a fixed near-zero training…
In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for precise characterization of correctness and reliability of data-driven methods in critical use-cases,…