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Signal Processing in Space and Time

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A sampling theorem for periodic piecewise polynomial signals

Martin Vetterli, Pina Marziliano, Thierry Blu

We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampli ...

2001

High-order balanced multiwavelets: theory, factorization, and design

Martin Vetterli, Jérôme Lebrun

This correspondence deals with multiwavelets, which are a recent generalization of wavelets in the context of time-varying filter banks and with their applications to signal processing and especially com- pression. By their inherent structure, multiwavelet ...

2001

An Error Analysis for the Sampling of Periodic Signals

Michaël Unser, Thierry Blu, Mathews Jacob

We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form ex ...

SampTA2001

Periodic c-axis modulation and crystallographic Fourier analysis of Bi2Sr2Cun+1O6+2n+x (n=0,1) single crystals with excess Bi

Giorgio Margaritondo, Davor Pavuna, Helmuth Berger

We report on a distortion of Bi2Sr2CanCun+1 O6+2n+x (n = 0,1) single crystals, perpendicular to the CuO2 planes (the c-axis), for non-stoichiometric samples containing an excess of Bi. The distortion involves two parts: (a) symmetric displacements in the S ...

2001

Contourlets

Martin Vetterli, Minh Do

This chapter focuses on the development of a new \true" two- dimensional representation for images that can capture the intrinsic geo- metrical structure of pictorial information. Our emphasis is on the discrete framework that can lead to algorithmic imple ...

Academic Press2001

Spectral processing of point-sampled geometry

Mark Pauly

We present a new framework for processing point-sampled objects using spectral methods. By establishing a concept of local frequencies on geometry, we introduce a versatile spectral representation that provides a rich repository of signal processing algori ...

2001

Generalized Sampling: A Variational Approach

Michaël Unser, Thierry Blu

We consider the problem of reconstructing a multidimensional and multivariate function ƒ:

ℜ ^{ m }

\rightarrow

ℜ ^{ n }

from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which r ...

SampTA2001

Spatial filtering and aperture apodization in digital holographic microscopy

Christian Depeursinge, Etienne Cuche, Pierre Marquet

We present two digital image processing methods for image quality enhancement in Digital Holographic Microscopy (DHM). With the first method, the Fourier transform of an off-axis hologram is spatially filtered in order to eliminate the zero order of diffra ...

OSA2000

Linear Estimation

Ali H. Sayed

This textbook is intended for a graduate-level course and assumes familiarity with basic concepts from matrix theory, linear algebra, and linear system theory. Six appendices at the end of the book provide the reader with enough background and review mater ...

Prentice Hall2000

A Conversation with John W. Tukey and Elizabeth Tukey

Stephan Morgenthaler

John Wilder Tukey, Donner Professor of Science Emeritus at Princeton University, was born in New Bedford, Massachusetts, on June 16, 1915. After earning bachelor's and master's degrees in chemistry at Brown University in 1936 and 1937, respectively, he sta ...

2000

Generalized Sampling: A Variational Approach

Michaël Unser, Thierry Blu

We consider the problem of reconstructing a multidimensional and multivariate function ƒ:

ℜ ^{ m }

\rightarrow

ℜ ^{ n }

from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which r ...

SampTA2001