Publications related to Why Restrict Ourselves to Compactly Supported Basis Functions?

Sparse Image Representation by Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertic ...

Elsevier2010

A multiscale approximation scheme for explicit model predictive control with stability, feasibility, and performance guarantees

Colin Neil Jones, John Lygeros

In this paper, an algorithm is introduced based on classical wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolating wavelets. It is proven that the resulting i ...

IEEE2009

A Differential Motion Estimation Method for Image Interpolation in Distributed Video Coding

Thomas Maugey

Motion estimation methods based on differential techniques proved to be very useful in the context of video analysis, but have a limited employment in classical video compression because, though accurate, the dense motion vector field they produce requires ...

2009

Image Interpolation with Dense Disparity Estimation in Multiview Distributed Video Coding

Thomas Maugey

This paper deals with the side information (SI) generation problem in multiview distributed video coding (MDVC). For inter-view interpolation, we propose a novel dense disparity estimation (DE) approach combined with a popular distributed video coding (DVC ...

2009

Fractional Laplacian Pyramids

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We provide an extension of the L-2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyha ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Short Basis Functions for Constant-Variance Interpolation

Michaël Unser, Philippe Thévenaz, Thierry Blu

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...

SPIE2008

Locally Adaptive Wavelet-Based Image Interpolation

Martin Vetterli

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local s ...

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

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Michaël Unser, Thierry Blu

ICIP'05 Best Student Paper Award We investigate the use of quasi-interpolating approximation schemes, to construct an estimate of an unknown function from its given discrete samples. We show theoretically and with practical experiments that such methods pe ...

IEEE2005

Why Restrict Ourselves to Compactly Supported Basis Functions?

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Sparse Image Representation by Directionlets

A multiscale approximation scheme for explicit model predictive control with stability, feasibility, and performance guarantees

A Differential Motion Estimation Method for Image Interpolation in Distributed Video Coding

Image Interpolation with Dense Disparity Estimation in Multiview Distributed Video Coding

Fractional Laplacian Pyramids

Short Basis Functions for Constant-Variance Interpolation

Locally Adaptive Wavelet-Based Image Interpolation

Fast directional correlation on the sphere with steerable filters

Generalized L-Spline Wavelet Bases

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

A multiscale approximation scheme for explicit model predictive control with stability, feasibility, and performance guarantees

Image Interpolation with Dense Disparity Estimation in Multiview Distributed Video Coding

Sparse Image Representation by Directionlets

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Fast directional correlation on the sphere with steerable filters

Short Basis Functions for Constant-Variance Interpolation

Generalized L-Spline Wavelet Bases

Fractional Laplacian Pyramids

Locally Adaptive Wavelet-Based Image Interpolation

A Differential Motion Estimation Method for Image Interpolation in Distributed Video Coding