Related papers: Regularization of Inverse Problems by Filtered Dia…
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…
Image de-blurring is important in many cases of imaging a real scene or object by a camera. This project focuses on de-blurring an image distorted by an out-of-focus blur through a simulation study. A pseudo-inverse filter is first explored…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries…
Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all…
In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep…
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.…
A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving…
It is well-known that in inverse problems, end-to-end trained networks overfit the degradation model seen in the training set, i.e., they do not generalize to other types of degradations well. Recently, an approach to first map images…
Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
Designing appropriate variational regularization schemes is a crucial part of solving inverse problems, making them better-posed and guaranteeing that the solution of the associated optimization problem satisfies desirable properties.…