Related papers: A new reproducing kernel based nonlinear dimension…

Real-world image super-resolution (RISR) has received increased focus for improving the quality of SR images under unknown complex degradation. Existing methods rely on the heavy SR models to enhance low-resolution (LR) images of different…

For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for…

This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data-adaptive (SIDA) RKHS, whose norm…

Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…

We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…

In recent years, deep neural networks, including Convolutional Neural Networks, Transformers, and State Space Models, have achieved significant progress in Remote Sensing Image (RSI) Super-Resolution (SR). However, existing SR methods…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…

Single image super-resolution (SISR), which aims to reconstruct a high-resolution (HR) image from a low-resolution (LR) observation, has been an active research topic in the area of image processing in recent decades. Particularly, deep…

Previous super-resolution reconstruction (SR) works are always designed on the assumption that the degradation operation is fixed, such as bicubic downsampling. However, as for remote sensing images, some unexpected factors can cause the…

Sufficient dimension reduction (SDR) is a popular class of regression methods which aim to find a small number of linear combinations of covariates that capture all the information of the responses i.e., a central subspace. The majority of…

In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…

Existing convolutional neural networks (CNN) based image super-resolution (SR) methods have achieved impressive performance on bicubic kernel, which is not valid to handle unknown degradations in real-world applications. Recent blind SR…

Adapting the Diffusion Probabilistic Model (DPM) for direct image super-resolution is wasteful, given that a simple Convolutional Neural Network (CNN) can recover the main low-frequency content. Therefore, we present ResDiff, a novel…

We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the…

Dynamic convolution demonstrates outstanding representation capabilities, which are crucial for natural image segmentation. However, it fails when applied to medical image segmentation (MIS) and infrared small target segmentation (IRSTS)…

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…