Related papers: Implicit Regularization Effects of the Sobolev Nor…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality…

In black-box optimization, noise in the objective function is inevitable. Noise disrupts the ranking of candidate solutions in comparison-based optimization, possibly deteriorating the search performance compared with a noiseless scenario.…

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…

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically…

Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may…

Logit regularization, the addition of a convex penalty directly in logit space, is widely used in modern classifiers, with label smoothing as a prominent example. While such methods often improve calibration and generalization, their…

Gradient information is widely useful and available in applications, and is therefore natural to include in the training of neural networks. Yet little is known theoretically about the impact of Sobolev training -- regression with both…

We propose a novel regularization method for compressive imaging in the context of the compressed sensing (CS) theory with coherent and redundant dictionaries. Natural images are often complicated and several types of structures can be…

Randomly perturbing networks during the training process is a commonly used approach to improving generalization performance. In this paper, we present a theoretical study of one particular way of random perturbation, which corresponds to…

This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm…

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…

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…

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…

Crucial information barely visible to the human eye is often embedded in a series of low-resolution images taken of the same scene. Super-resolution enables the extraction of this information by reconstructing a single image, at a high…

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…

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…