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The purpose of this work is to implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. The ConvDecoder neural network was trained with a…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
This paper proposes a precise signal recovery method with multilayered non-convex regularization, enhancing sparsity/low-rankness for high-dimensional signals including images and videos. In optimization-based signal recovery, multilayered…
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…
An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…
Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…
In image denoising problems, one widely-adopted approach is to minimize a regularized data-fit objective function, where the data-fit term is derived from a physical image acquisition model. Typically the regularizer is selected with two…
Classical model-based imaging methods for ultrasound elasticity inverse problem require prior constraints about the underlying elasticity patterns, while finding the appropriate hand-crafted prior for each tissue type is a challenge. In…
In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…
Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…
The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
Regularization for denoising in magnetic resonance imaging (MRI) is typically achieved using convex regularization functions. Recently, deep learning techniques have been shown to provide superior denoising performance. However, this comes…