Related papers: Multiresolution local smoothness detection in non-…
Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…
Video prediction is a pixel-wise dense prediction task to infer future frames based on past frames. Missing appearance details and motion blur are still two major problems for current predictive models, which lead to image distortion and…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
In this paper we present a multiresolution-based method for period determination that is able to deal with unevenly sampled data. This method allows us to detect superimposed periodic signals with lower signal-to-noise ratios than in…
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…
In this work, we propose a new detector function based on wavelet transform to discriminate between turbulent and non-turbulent regions in an intermittent velocity signal. The derivative-based detector function, which is commonly used in…
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…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
We propose efficient algorithms for two key tasks in the analysis of large nonuniform networks: uniform node sampling and cluster detection. Our sampling technique is based on augmenting a simple, but slowly mixing uniform MCMC sampler with…
Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…
We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized…
Unsupervised fault detection in multivariate time series plays a vital role in ensuring the stable operation of complex systems. Traditional methods often assume that normal data follow a single Gaussian distribution and identify anomalies…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
We develop a kernel-based approach for estimating the spatially varying Sobolev regularity~$s$ of an unknown $d$-variate function~$f$ from scattered sampling data, which quantifies the degree of local differentiability supported by the…