Related papers: Mapped Variably Scaled Kernels: Applications to So…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Ground-based astronomical observations at thermal infrared wavelengths face the problem of extracting the weak astronomical signal from the large and rapidly variable background flux. The observing strategy most commonly used, the so-called…
We study the constructions of piecewise rational interpolation kernels that are supported on the interval $[-2,2]$, and present one novel rational cubic/linear and five quartic/linear interpolation kernels. All proposed kernels are…
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
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…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
Generation of photo-realistic images, semantic editing and representation learning are a few of many potential applications of high resolution generative models. Recent progress in GANs have established them as an excellent choice for such…
We address the question of astronomical image processing from data obtained with array detectors. We define and analyze the cases of evenly, regularly, and irregularly sampled maps for idealized (i.e., infinite) and realistic (i.e., finite)…
Kernel phase interferometry is an approach to high angular resolution imaging which enhances the performance of speckle imaging with adaptive optics. Kernel phases are self-calibrating observables that generalize the idea of closure phases…
Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…
There are many methods for image enhancement. Image inpainting is one of them which could be used in reconstruction and restoration of scratch images or editing images by adding or removing objects. According to its application, different…
The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by…
Speckles arise when coherent light interacts with biological tissues. Information retrieval from speckles is desired yet challenging, requiring understanding or mapping of the multiple scattering process, or reliable capability to reverse…
Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
With the rise of big data sets, the popularity of kernel methods declined and neural networks took over again. The main problem with kernel methods is that the kernel matrix grows quadratically with the number of data points. Most attempts…
The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…