Related papers: Samplets: Wavelet concepts for scattered data
Both pixel-based scale saliency (PSS) and basis project methods focus on multiscale analysis of data content and structure. Their theoretical relations and practical combination are previously discussed. However, no models have ever been…
This paper is concerned with a conceptual gesture-based instruction/input technique using electromagnetic wave detection. The gestures are modelled as the shapes of some impenetrable or penetrable scatterers from a certain admissible class,…
In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets and show that they nearly attain optimal…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
Prior to adjustment, accounting conditions between national accounts data sets are frequently violated. Benchmarking is the procedure used by economic agencies to make such data sets consistent. It typically involves adjusting a high…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
Submovements are ballistic components of human motion constituting a large part of motor interaction and arising from the cyclical and overlapping cognitive processes of perception, motor planning, and motor execution. Extracting…
Scattering obscures information carried by wave by producing a speckle pattern, posing a common challenge across various fields, including microscopy and astronomy. Traditional methods for extracting information from speckles often rely on…
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness.…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal…