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Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
The challenge in few-shot learning is that available data is not enough to capture the underlying distribution. To mitigate this, two emerging directions are (a) using local image representations, essentially multiplying the amount of data…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Single-photon light detection and ranging (LiDAR) has been widely applied to 3D imaging in challenging scenarios. However, limited signal photon counts and high noises in the collected data have posed great challenges for predicting the…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
In recent years, histopathology images have been increasingly used as a diagnostic tool in the medical field. The process of accurately diagnosing a biopsy sample requires significant expertise in the field, and as such can be…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
The goal of image oversegmentation is to divide an image into several pieces, each of which should ideally be part of an object. One of the simplest and yet most effective oversegmentation algorithms is known as local variation (LV)…
Automatic estimation of cardiac ultrasound image quality can be beneficial for guiding operators and ensuring the accuracy of clinical measurements. Previous work often fails to distinguish the view correctness of the echocardiogram from…
This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…
In this short note, we consider the worst case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors $\mathbf{x} \in \mathbb{C}^d$ (up to a single global phase multiple) from the magnitudes of…
We provide an overview of results relating to estimation and weak-instrument-robust inference in instrumental variables regression. Methods are implemented in the ivmodels software package for Python, which we use to illustrate results.
This paper presents a new approach on stretch processing for a fine range estimation using MPM (Matrix Pencil Method). The conventional method utilizes FFT (Fast Fourier Transform) with limited range resolution with its fixed number of…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
The local least squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Both theoretical and empirical evidence suggests that residuals often exhibit distributional properties different…