Related papers: Deep Fourier Up-Sampling
Deep neural networks have exhibited remarkable performance in a variety of computer vision fields, especially in semantic segmentation tasks. Their success is often attributed to multi-level feature fusion, which enables them to understand…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…
$R$-limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region $R\subset\mathbb{R}^{n}$. In this work, we generalize sampling and interpolation theorems for…
Convolutional neural networks typically contain several downsampling operators, such as strided convolutions or pooling layers, that progressively reduce the resolution of intermediate representations. This provides some shift-invariance…
Recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large image dataset can be used as a universal image descriptor, and that doing so leads to impressive performance for a variety of image…
Large-scale numerical simulations are capable of generating data up to terabytes or even petabytes. As a promising method of data reduction, super-resolution (SR) has been widely studied in the scientific visualization community. However,…
We propose a novel deep-learning framework for super-resolution ultrasound images and videos in terms of spatial resolution and line reconstruction. We up-sample the acquired low-resolution image through a vision-based interpolation method;…
Recently, deep neural networks have demonstrated comparable and even better performance with board-certified ophthalmologists in well-annotated datasets. However, the diversity of retinal imaging devices poses a significant challenge:…
A typical 2D-to-3D pipeline takes multi-view images as input, where a Vision Foundation Model (VFM) extracts features that are spatially upsampled to dense representations for 3D reconstruction. If dense features across views preserve…
Foundation Vision Encoders have become essential for a wide range of dense vision tasks. However, their low-resolution spatial feature outputs necessitate feature upsampling to produce the high-resolution modalities required for downstream…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
A number of recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large dataset can be adopted as a universal image description which leads to astounding performance in many visual classification tasks.…
Image inpainting has earned substantial progress, owing to the encoder-and-decoder pipeline, which is benefited from the Convolutional Neural Networks (CNNs) with convolutional downsampling to inpaint the masked regions semantically from…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…