Related papers: Implicit Regularization Effects of the Sobolev Nor…
Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of…
We address the problem of network calibration adjusting miscalibrated confidences of deep neural networks. Many approaches to network calibration adopt a regularization-based method that exploits a regularization term to smooth the…
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
In this paper, we propose a novel approach for implicit data representation to evaluate similarity of input data using a trained neural network. In contrast to the previous approach, which uses gradients for representation, we utilize only…
We propose a semantic similarity metric for image registration. Existing metrics like Euclidean Distance or Normalized Cross-Correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our…
Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to…
We propose a semantic similarity metric for image registration. Existing metrics like euclidean distance or normalized cross-correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our…
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…
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of…
While deep neural networks (DNNs) have proven to be efficient for numerous tasks, they come at a high memory and computation cost, thus making them impractical on resource-limited devices. However, these networks are known to contain a…
We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of…
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of the training loss. Previous works indicate that the noise is…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
Large amount of image denoising literature focuses on single channel images and often experimentally validates the proposed methods on tens of images at most. In this paper, we investigate the interaction between denoising and…
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…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
Registration networks have shown great application potentials in medical image analysis. However, supervised training methods have a great demand for large and high-quality labeled datasets, which is time-consuming and sometimes impractical…
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a…