Publications related to A Theoretical Analysis of the Projection Error onto Discrete Wavelet Subspaces

Higher-Order Riesz Transforms and Steerable Wavelet Frames

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce an Nth-order extension of the Riesz transform in d dimensions. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing con ...

IEEE2009

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming

Philip Neil Garner, Weifeng Li

This paper presents new filter bank design methods for sub- band adaptive beamforming. In this work, we design analysis and synthesis prototypes for modulated filter banks so as to minimize each aliasing term individually. We then drive the total response ...

2008

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

Performance of Sigma-Delta Quantizations in Finite Frames

In this paper, we consider sigma-delta (SD) quantization of geometrically uniform (GU) finite frames. In the first part, we prove that under some conditions, the variant I and II permutation modulation (PM) codes, first introduced by Slepian (1968, 1965), ...

2008

Adaptive optics in speckle interferometry and in super-resolution

Phanindra Narayan Gundu

This thesis describes innovative techniques for reducing speckle noise and improving the intensity profile of the speckle correlation fringes. The methods are based on reducing the range of the modulation intensity values of the speckle interference patter ...

EPFL2007

What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

Bettina Schaefli

Extreme hydrological events are often triggered by exceptional co-variations of the relevant hydrometeorological processes and in particular by exceptional co-oscillations at various temporal scales. Wavelet and cross wavelet spectral analysis offers promi ...

Elsevier2007

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Michaël Unser, Cédric René Jean Vonesch

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

A Theoretical Analysis of the Projection Error onto Discrete Wavelet Subspaces

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Higher-Order Riesz Transforms and Steerable Wavelet Frames

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming

The Marr Wavelet Pyramid

Performance of Sigma-Delta Quantizations in Finite Frames

Adaptive optics in speckle interferometry and in super-resolution

What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Directionlets: Anisotropic Multidirectional representation with separable filtering

Fast directional correlation on the sphere with steerable filters

Adaptive optics in speckle interferometry and in super-resolution

Directionlets: Anisotropic Multidirectional representation with separable filtering

Fast directional correlation on the sphere with steerable filters

What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

Performance of Sigma-Delta Quantizations in Finite Frames

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

The Marr Wavelet Pyramid

Higher-Order Riesz Transforms and Steerable Wavelet Frames

Filter Bank Design based on Minimization of Individual Aliasing Terms for Minimum Mutual Information Subband Adaptive Beamforming