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With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…
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…
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…
We construct custom regularization functions for use in supervised training of deep neural networks. Our technique is applicable when the ground-truth labels themselves exhibit internal structure; we derive a regularizer by learning an…
Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network…
With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being…
There has been significant recent interest in the use of deep learning for regularizing imaging inverse problems. Most work in the area has focused on regularization imposed implicitly by convolutional neural networks (CNNs) pre-trained for…
Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the…
We present a deep neural network to reduce coherent noise in three-dimensional quantitative phase imaging. Inspired by the cycle generative adversarial network, the denoising network was trained to learn a transform between two image…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…
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.…
This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…
This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…
This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear…