Related papers: Fourier Features for Identifying Differential Equa…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

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)…

Existing single-image denoising algorithms often struggle to restore details when dealing with complex noisy images. The introduction of near-infrared (NIR) images offers new possibilities for RGB image denoising. However, due to the…

In recent years, decentralized sensor networks have garnered significant attention in the field of state estimation owing to enhanced robustness, scalability, and fault tolerance. Optimal fusion performance can be achieved under fully…

Change detection aims to identify remote sense object changes by analyzing data between bitemporal image pairs. Due to the large temporal and spatial span of data collection in change detection image pairs, there are often a significant…

Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…

Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…

The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

Supervised learning-based methods yield robust denoising results, yet they are inherently limited by the need for large-scale clean/noisy paired datasets. The use of unsupervised denoisers, on the other hand, necessitates a more detailed…

Deep learning methods have been considered promising for accelerating molecular screening in drug discovery and material design. Due to the limited availability of labelled data, various self-supervised molecular pre-training methods have…

Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise…

Recent advancements in machine learning have transformed the discovery of physical laws, moving from manual derivation to data-driven methods that simultaneously learn both the structure and parameters of governing equations. This shift…

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

Decoherence induced by the laser frequency noise is one of the most important obstacles in the quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In…

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits…

As our ability to sense increases, we are experiencing a transition from data-poor problems, in which the central issue is a lack of relevant data, to data-rich problems, in which the central issue is to identify a few relevant features in…

This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…

Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…