Publications related to Wavelet

Multidimensional Lévy White Noise in Weighted Besov Spaces

Michaël Unser, Julien René Pierre Fageot, Alireza Fallah

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrab ...

Elsevier2017

Signal Analysis Based on Complex Wavelet Signs

Martin Kurt Storath

We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signat ...

Elsevier2017

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

Pedram Pad

We establish in the world of stochastic processes a theoretical relation between sparsity and wavelets. The underlying principle is to treat stochastic processes as generalized functions, which facilitates the study of their properties in a transform domai ...

EPFL2017

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Nikola Besic, Urs Martin Germann, Daniele Nerini

In this paper we present a non-stationary stochastic generator for radar rainfall fields based on the short-space Fourier transform (SSFT). The statistical properties of rainfall fields often exhibit significant spatial heterogeneity due to variability in ...

Copernicus GmbH2017

Localized orthogonal decomposition method for the wave equation with a continuum of scales

Assyr Abdulle, Patrick Henning

In this paper we propose and analyze a new multiscale method for the wave equation. The proposed method does not require any assumptions on space regularity or scale-separation and it is formulated in the framework of the Localized Orthogonal Decomposition ...

American Mathematical Society2017

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Volkan Cevher, Mikhail Kapralov, Jonathan Mark Scarlett, Amir Zandieh

The problem of approximately computing the

k

dominant Fourier coefficients of a vector

X

quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in ...

2017

Learning the weight matrix for sparsity averaging in compressive imaging

Jean-Philippe Thiran, Dimitris Perdios, Adrien Georges Jean Besson

We propose to map the fast iterative shrinkage-thresholding algorithm to a deep neural network (DNN), with a sparsity prior in a concatenation of wavelet bases, in the context of compressive imaging. We exploit the DNN architecture to learn the optimal wei ...

2017

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Martin Vetterli, Thierry Blu, Hanjie Pan

It is a classic problem to estimate continuous-time sparse signals, like point sources in a direction-of-arrival problem, or pulses in a time-of-flight measurement. The earliest occurrence is the estimation of sinusoids in time series using Prony's method. ...

Institute of Electrical and Electronics Engineers2017

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

Jan Skaloud, Stéphane Guerrier, Philipp Clausen

The proliferation of (low-cost) sensors provokes new challenges in data fusion. This is related to the correctness of stochastic characterization that is a prerequisite for optimal estimation of parameters from redundant observations. Different (statistica ...

2017

Multiresolution Subdivision Snakes

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Anaïs Laure Marie-Thérèse Badoual

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

2017

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Multidimensional Lévy White Noise in Weighted Besov Spaces

Signal Analysis Based on Complex Wavelet Signs

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Localized orthogonal decomposition method for the wave equation with a continuum of scales

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Learning the weight matrix for sparsity averaging in compressive imaging

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

Multiresolution Subdivision Snakes

Multidimensional Lévy White Noise in Weighted Besov Spaces

Learning the weight matrix for sparsity averaging in compressive imaging

Towards Generalized FRI Sampling with an Application to Source Resolution in Radioastronomy

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

Signal Analysis Based on Complex Wavelet Signs

Localized orthogonal decomposition method for the wave equation with a continuum of scales

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Multiresolution Subdivision Snakes

Parameter Determination of Sensor Stochastic Models under Covariate Dependency