Related papers: Neural-network-based regularization methods for in…
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…
Deep learning-based methods have revolutionized the field of imaging inverse problems, yielding state-of-the-art performance across various imaging domains. The best performing networks incorporate the imaging operator within the network…
There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…
Several image processing tasks, such as image classification and object detection, have been significantly improved using Convolutional Neural Networks (CNN). Like ResNet and EfficientNet, many architectures have achieved outstanding…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
Synthesizing photo-realistic images and videos is at the heart of computer graphics and has been the focus of decades of research. Traditionally, synthetic images of a scene are generated using rendering algorithms such as rasterization or…
There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…
Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available.…
Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…
We study the problem of computing the preimage of a set under a neural network with piecewise-affine activation functions. We recall an old result that the preimage of a polyhedral set is again a union of polyhedral sets and can be…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
Deep neural networks (DNN) have achieved unprecedented performance in computer-vision tasks almost ubiquitously in business, technology, and science. While substantial efforts are made to engineer highly accurate architectures and provide…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
We introduce a novel framework for solving inverse problems using NeRF-style generative models. We are interested in the problem of 3-D scene reconstruction given a single 2-D image and known camera parameters. We show that naively…
While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach,…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…