Related papers: Revisiting L1 Loss in Super-Resolution: A Probabil…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
All-in-one image restoration tasks are becoming increasingly important, especially for ultra-high-definition (UHD) images. Existing all-in-one UHD image restoration methods usually boost the model's performance by introducing prompt or…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
This paper proposes a probabilistic contrastive loss function for self-supervised learning. The well-known contrastive loss is deterministic and involves a temperature hyperparameter that scales the inner product between two normed feature…
We introduce LuminanceL1Loss, a novel loss function designed to enhance the performance of image restoration tasks. We demonstrate its superiority over MSE when applied to the Retinexformer, BUIFD and DnCNN architectures. Our proposed…
The inability to acquire clean high-resolution (HR) electron microscopy (EM) images over a large brain tissue volume hampers many neuroscience studies. To address this challenge, we propose a deep-learning-based image super-resolution (SR)…
Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
Most single image super-resolution (SR) methods are developed on synthetic low-resolution (LR) and high-resolution (HR) image pairs, which are simulated by a predetermined degradation operation, e.g., bicubic downsampling. However, these…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
Generative super-resolution (GSR) currently sets the state-of-the-art in terms of perceptual image quality, overcoming the "regression-to-the-mean" blur of prior non-generative models. However, from a human perspective, such models do not…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
We examine a new form of smooth approximation to the zero one loss in which learning is performed using a reformulation of the widely used logistic function. Our approach is based on using the posterior mean of a novel generalized…
Super-resolution is aimed at reconstructing high-resolution images from low-resolution observations. State-of-the-art approaches underpinned with deep learning allow for obtaining outstanding results, generating images of high perceptual…