Related papers: Spatial-Slepian Transform on the Sphere
Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
The image-based rendering approach using Shearlet Transform (ST) is one of the state-of-the-art Densely-Sampled Light Field (DSLF) reconstruction methods. It reconstructs Epipolar-Plane Images (EPIs) in image domain via an iterative…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…
The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By…
Spectral interference, the frequency counterpart of the beating phenomenon in the time domain, can severely distort time-frequency representations (TFRs) in physical applications. We study this phenomenon for the short-time Fourier…
Despite the recent progress of fully-supervised action segmentation techniques, the performance is still not fully satisfactory. One main challenge is the problem of spatiotemporal variations (e.g. different people may perform the same…
We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and also allows for interpolation of gene expression. The method…
In this paper, we investigate in detail the structures of the variational characterization $A_{N,t}$ of the spherical $t$-design, its gradient $\nabla A_{N,t}$, and its Hessian $\mathcal{H}(A_{N,t})$ in terms of fast spherical harmonic…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
We propose a novel Bayesian framework for changepoint detection in large-scale spherical spatiotemporal data, with broad applicability in environmental and climate sciences. Our approach models changepoints as spatially dependent…
Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp localization in both time and frequency is inherently…
Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…
The sea surface temperature (SST), a key environmental parameter, is crucial to optimizing production planning, making its accurate prediction a vital research topic. However, the inherent nonlinearity of the marine dynamic system presents…
Finding the minimum spanning tree (MST) of a graph is an important task in computer vision, as it enables a sparse and low-cost representation of connectivity among elements (such as superpixels, points, or regions), which is useful for…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
In this work, we introduce an optimal transport framework for inferring power distributions over both spatial location and temporal frequency. Recently, it has been shown that optimal transport is a powerful tool for estimating spatial…
3D occupancy prediction is critical for comprehensive scene understanding in vision-centric autonomous driving. Recent advances have explored utilizing 3D semantic Gaussians to model occupancy while reducing computational overhead, but they…