Related papers: Haar wavelets as a tool for the statistical charac…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
A new thresholding strategy for the estimation of a deterministic image immersed in noise is introduced. The threshold is combined with a wavelet decomposition, where the wavelet coefficient of the image at any fixed value of the…
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…
Temporal and spectral information extracted from a stream of photons received from astronomical sources is the foundation on which we build understanding of various objects and processes in the Universe. Typically astronomers fit a number…
We present a new detection algorithm based on the wavelet transform for the analysis of high energy astronomical images. The wavelet transform, due to its multi-scale structure, is suited for the optimal detection of point-like as well as…
The quality of images captured in outdoor environments can be affected by poor weather conditions such as fog, dust, and atmospheric scattering of other particles. This problem can bring extra challenges to high-level computer vision tasks…
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and…
Variational Autoencoders (VAEs) are powerful generative models capable of learning compact latent representations. However, conventional VAEs often generate relatively blurry images due to their assumption of an isotropic Gaussian latent…
This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
Given a random sample from some unknown density $f_0: \mathbb R \to [0, \infty)$ we devise Haar wavelet estimators for $f_0$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny…
In this paper, a new efficient feature extraction method based on the adaptive threshold of wavelet package coefficients is presented. This paper especially deals with the assessment of autonomic nervous system using the background…
A variety of statistical methods for understanding variability in the time domain for low count rate X-ray and gamma-ray sources are explored. Variability can be detected using nonparametric (Anderson-Darling and overdispersion tests) and…
Astronomy light curves are sparse, gappy, and heteroscedastic. As a result standard time series methods regularly used for financial and similar datasets are of little help and astronomers are usually left to their own instruments and…
The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency…
Abrupt change detection based on the wavelet transform and threshold method is very effective in detecting the abrupt changes and hence segmenting the signals recorded during disturbances in the electrical power network. The wavelet method…
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer. Vice versa, image and video restoration techniques, such as inpainting or…
In this paper we present a wavelet based algorithm that is able to detect superimposed periodic signals in data with low signal-noise ratio. In this context, the results given by classical period determination methods highly depend on the…
A variational Bayesian inference for measured wave intensity, such as X-ray intensity, is proposed in this paper. The data is popular to obtain information about unobservable features of an object, such as a material sample and the…