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Learning Sparse Systems at Sub-Nyquist Rates: A Frequency-Domain Approach

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Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

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

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-s ...

IEEE2005

Hex-Splines: A Novel Spline Family for Hexagonal Lattices

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

This paper proposes a new family of bivariate, non-separable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural ...

IEEE2004

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

A new expression for the ground transient resistance matrix elements of multiconductor overhead transmission lines

Michel Ianoz

The ground impedance matrix elements of a multiconductor overhead transmission line do not have analytical inverse Fourier transforms in the time domain. Thus, in general, the ground transient resistance matrix elements are to be determined numerically. Us ...

2003

An embedding approach to frequency-domain and subband adaptive filtering

Ali H. Sayed, Ricardo Merched

Frequency-domain and subband implementations improve the computational efficiency and the convergence rate of adaptive schemes. The well-known multidelay adaptive filter (MDF) belongs to this class of block adaptive structures and is a DFT-based algorithm. ...

IEEE2000

Properties of Smoothing with Time Gating

Marten Sjöström

Estimates of transfer functions from measurements contain undesired information -- noise -- whose effect can partly be taken away by applying different smoothing techniques. One such smoothing technique suggests to remove the noise by gating the impulse re ...

2000

High Order Balanced MultiWavelets: Theory, Factorization and Design

Martin Vetterli, Jérôme Lebrun

This paper deals with multiwavelets and the different properties of approximation and smoothness that are associated with them. In particular, we focus on the important issue of the preservation of discrete time polynomial signals by multiwavelet based fil ...

1999

Tight Weyl-Heisenberg frames in l2(Z)

Martin Vetterli

Tight Weyl–Heisenberg frames in l^2 (Z ) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short ...

1998

Discrete- and continuous-time local cosine bases with multiple overlapping

Martin Vetterli

Cosine-modulated filter banks (CMFB’s) are filter banks whose impulse responses are obtained by modulating a window with cosines. Among their applications are video and audio compression and multitone modulation. Their continuous- time counterpart is known ...

1998

Oversampled Filter Banks

Martin Vetterli

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in t(2)(Z), These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame exp ...

1998