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Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized…

Deep neural networks (DNN) trained in a supervised way suffer from two known problems. First, the minima of the objective function used in learning correspond to data points (also known as rubbish examples or fooling images) that lack…

We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…

Finding sparse solutions of underdetermined linear systems commonly requires the solving of L1 regularized least squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Deep neural networks have had an enormous impact on image analysis. State-of-the-art training methods, based on weight decay and DropOut, result in impressive performance when a very large training set is available. However, they tend to…

As multimedia content often contains noise from intrinsic defects of digital devices, image denoising is an important step for high-level vision recognition tasks. Although several studies have developed the denoising field employing…

Image denoising is a classical problem in low level computer vision. Model-based optimization methods and deep learning approaches have been the two main strategies for solving the problem. Model-based optimization methods are flexible for…

Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student…

In this paper we study shallow neural network functions which are linear combinations of compositions of activation and quadratic functions, replacing standard affine linear functions, often called neurons. We show the universality of this…

Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large datasets have…

We study the theory of neural network (NN) from the lens of classical nonparametric regression problems with a focus on NN's ability to adaptively estimate functions with heterogeneous smoothness -- a property of functions in Besov or…

The resurgence of deep neural networks has created an alternative pathway for low-dose computed tomography denoising by learning a nonlinear transformation function between low-dose CT (LDCT) and normal-dose CT (NDCT) image pairs. However,…

The non-local network has become a widely used technique for semantic segmentation, which computes an attention map to measure the relationships of each pixel pair. However, most of the current popular non-local models tend to ignore the…

Deep neural networks (DNNs) with noisy weights, which we refer to as noisy neural networks (NoisyNNs), arise from the training and inference of DNNs in the presence of noise. NoisyNNs emerge in many new applications, including the wireless…

Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise…

We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…

This paper studies the properties of solutions to multi-task shallow ReLU neural network learning problems, wherein the network is trained to fit a dataset with minimal sum of squared weights. Remarkably, the solutions learned for each…

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar…

Image denoising techniques are essential to reducing noise levels and enhancing diagnosis reliability in low-dose computed tomography (CT). Machine learning based denoising methods have shown great potential in removing the complex and…