Related papers: Sobolev-Regularized Objective Functions for Robust…
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
We study the complexity of randomized computation of integrals depending on a parameter, with integrands from Sobolev spaces. That is, for $r,d_1,d_2\in{\mathbb N}$, $1\le p,q\le \infty$, $D_1= [0,1]^{d_1}$, and $D_2= [0,1]^{d_2}$ we are…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
We focus on tackling weakly supervised semantic segmentation with scribble-level annotation. The regularized loss has been proven to be an effective solution for this task. However, most existing regularized losses only leverage static…
Achieving high-performance in multi-object tracking algorithms heavily relies on modeling spatio-temporal relationships during the data association stage. Mainstream approaches encompass rule-based and deep learning-based methods for…
Fusing and balancing multi-modal inputs from novel sensors for dense prediction tasks, particularly semantic segmentation, is critically important yet remains a significant challenge. One major limitation is the tendency of multi-modal…
We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(\nu_q)}$, that is known to linearize the…
The renormalization group (RG) method is an important tool for studying critical phenomena. In this paper, we employ stochastic analysis techniques to investigate the stochastic partial differential equation (SPDE) derived by regularizing…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…
Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
Noisy, partially overlapping data and the need for real-time processing pose major challenges for rigid registration. Considering that feature-based matching can handle large transformation differences but suffers from limited accuracy,…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…