Related papers: Variably Scaled Kernels for the regularized soluti…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently…
When simulating sky images, one often takes a galaxy image $F(x)$ defined by a set of pixelized samples and an interpolation kernel, and then wants to produce a new sampled image representing this galaxy as it would appear with a different…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…
Increasing the angular resolution of an interferometric array requires placing its elements at large separations. This often leads to sparse coverage and introduces challenges to reconstructing images from interferometric data. We introduce…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the…
Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…
We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which…
We develop and analyze a class of matrix-valued spherical-convolution kernels stemming from scaled zonal functions on $\mathbb{S}^2,$ the unit sphere embedded in $\mathbb{R}^3$. The construct of these kernels utilizes the Legendre…
We describe a scalable distributed imaging algorithm framework for next-generation radio telescopes, managing the Fourier transform from apertures to sky (or vice versa) with a focus on minimising memory load, data transfers, and…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
We present a new approach for image reconstruction and weak lensing measurements with interferometers. Based on the shapelet formalism presented in Refregier (2001), object images are decomposed into orthonormal Hermite basis functions. The…
We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
The standard wide-field imaging technique, the $w$-projection, allows correction for wide-fields of view for non-coplanar radio interferometric arrays. However, calculating exact corrections for each measurement has not been possible due to…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…