Publications related to Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

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

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Michaël Unser, Theo Lasser

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a mono ...

SPIE2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Wavelet and footprint sampling of signals with a finite rate of innovation

Martin Vetterli, Pier Luigi Dragotti

In this paper, we consider classes of not bandlimited signals, namely, streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution ...

2004

Guest Editorial: Wavelets in Medical Imaging

Michaël Unser

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...

2003

Wavelet Theory Demystified

Michaël Unser, Thierry Blu

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wa ...

IEEE2003

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

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Fast directional correlation on the sphere with steerable filters

Low-Rate Reduced Complexity Image Compression using Directionlets

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Wavelets on the 2-Hyperboloid

Wavelet and footprint sampling of signals with a finite rate of innovation

Guest Editorial: Wavelets in Medical Imaging

Wavelet Theory Demystified

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Low-Rate Reduced Complexity Image Compression using Directionlets

Fast directional correlation on the sphere with steerable filters

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelets on the 2-Hyperboloid

Wavelet and footprint sampling of signals with a finite rate of innovation

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Guest Editorial: Wavelets in Medical Imaging

Wavelet Theory Demystified