Publications related to Orthogonal Quincunx Wavelets with Fractional Orders

A New Channel-Base Lightning Current Formula With Analytically Adjustable Parameters

The article provides a new channel-based current function, which aims at faithfully reproducing the salient parameters of lightning currents. All the model parameters can be set in a fully analytical way, guaranteeing the possibility of changing them (acco ...

2021

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Fabio Nobile, Simone Brugiapaglia

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

2020

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

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

On the Continuous Steering of the Scale of Tight Wavelet Frames

Michaël Unser, Daniel Sage, Zsuzsanna Püspöki, John Paul Ward

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering ste ...

SIAM2016

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in L-2(R-d) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account ...

Academic Press Inc Elsevier Science2014

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in

L _{ 2 }

(\mathbb{R} ^{ d }

) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...

Elsevier2014

Decay Properties of Riesz Transforms and Steerable Wavelets

Michaël Unser, John Paul Ward, Kunal Narayan Chaudhury

The Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construc ...

Siam Publications2013

Operator-Like Wavelet Bases of L-2(R-d)

Michaël Unser, John Paul Ward, Ildar Khalidov

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

Springer Birkhauser2013

Orthogonal Quincunx Wavelets with Fractional Orders

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A New Channel-Base Lightning Current Formula With Analytically Adjustable Parameters

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

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

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

On the Continuous Steering of the Scale of Tight Wavelet Frames

Divergence-Free Wavelet Frames

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Decay Properties of Riesz Transforms and Steerable Wavelets

Operator-Like Wavelet Bases of L-2(R-d)

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

A New Channel-Base Lightning Current Formula With Analytically Adjustable Parameters

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

On the Continuous Steering of the Scale of Tight Wavelet Frames

Decay Properties of Riesz Transforms and Steerable Wavelets

Optimal Representations of Sparse Stochastic Processes with Applications in Image Processing

Divergence-Free Wavelet Frames

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Operator-Like Wavelet Bases of L-2(R-d)