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Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for…

The loss function is crucial to machine learning, especially in supervised learning frameworks. It is a fundamental component that controls the behavior and general efficacy of learning algorithms. However, despite their widespread use,…

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…

In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor…

A new loss function is proposed for neural networks on classification tasks which extends the hinge loss by assigning gradients to its critical points. We will show that for a linear classifier on linearly separable data with fixed step…

Untrained Physics-based Deep Learning (DL) methods for digital holography have gained significant attention due to their benefits, such as not requiring an annotated training dataset, and providing interpretability since utilizing the…

The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based…

Dictionary learning is traditionally formulated as an $L_1$-regularized signal reconstruction problem. While recent developments have incorporated discriminative, hierarchical, or generative structures, most approaches rely on encouraging…

Image enhancement is a common technique used to mitigate issues such as severe noise, low brightness, low contrast, and color deviation in low-light images. However, providing an optimal high-light image as a reference for low-light image…

Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…

By benefiting from perceptual losses, recent studies have improved significantly the performance of the super-resolution task, where a high-resolution image is resolved from its low-resolution counterpart. Although such objective functions…

In $\ell^1$-regularization, which is an important tool in signal and image processing, one usually is concerned with signals and images having a sparse representation in some suitable basis, e.g. in a wavelet basis. Many results on…

Recently, there has been discussions on the ill-posed nature of super-resolution that multiple possible reconstructions exist for a given low-resolution image. Using normalizing flows, SRflow[23] achieves state-of-the-art perceptual quality…

We consider a continual learning (CL) problem with two linear regression tasks in the fixed design setting, where the feature vectors are assumed fixed and the labels are assumed to be random variables. We consider an $\ell_2$-regularized…

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

In image retrieval, standard evaluation metrics rely on score ranking, \eg average precision (AP), recall at k (R@k), normalized discounted cumulative gain (NDCG). In this work we introduce a general framework for robust and decomposable…

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

We first propose a novel criterion that guarantees that an $s$-sparse signal is the local minimizer of the $\ell_1/\ell_2$ objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…