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Wavelet footprints and frames for signal processing and communication

Publications associées (86)

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Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Michaël Unser, Thierry Blu

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of

L _{ 2 }

to which we apply a unitar ...

IEEE2003

Framing pyramids

Martin Vetterli, Minh Do

In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filter ...

2003

Optimal Filter Banks for Multiple Description Coding: Analysis and Synthesis

Martin Vetterli, Pier Luigi Dragotti

Multiple description (MD) coding is a source coding technique for information transmission over unreliable networks. In MD coding, the coder generates several different descriptions of the same signal and the decoder can produce a useful reconstruction of ...

Institute of Electrical and Electronics Engineers2002

Oligoquantization in low-rate lossy source coding

The theory of high rate lossy source coding is well developed both with respect to the practice of quantization and its fundamental rate distortion limits. But many modern compression systems for natural signals such as audio and images operate at lower ra ...

EPFL2002

Continuous Wavelet Transform with Arbitrary Scales and O(N) Complexity

Michaël Unser

Summary The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that ...

Elsevier2002

Lossy to lossless object-based coding of 3-D MRI data

Jean-Philippe Thiran, Gloria Menegaz

We propose a fully three-dimensional object-based coding system exploiting the diagnostic relevance of the different regions of the volumetric data for rate allocation. The data are first decorrelated via a 3D discrete wavelet transform. The implementation ...

2002

A generalized Rate-Distortion limit for edge representation

Pierre Vandergheynst, Lorenzo Granai

This paper presents a rate-distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed in this kind of image, giving a toy model for a non-linear adaptive coding technique, and its rate-distortion behavio ...

2002

R-D Analysis of Adaptive Edge Representations

Pierre Vandergheynst, Lorenzo Granai

This paper presents a Rate-Distortion analysis for a simple horizon edge image model. A quadtree with anisotropy and rotation is performed on this kind of image, giving a toy model for a non-linear adaptive coding technique, and its Rate-Distortion behavio ...

IEEE2002

The distributed Karhunen-Loeve transform

Martin Vetterli, Michael Christoph Gastpar, Pier Luigi Dragotti

The Karhunen-Loeve transform is a key element of many signal processing tasks, including classification and compression. In this paper, we consider distributed signal processing scenarios with limited communication between correlated sources, and we invest ...

2002

Wavelets, approximation, and compression

Martin Vetterli

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of the unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become st ...

2001

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Michaël Unser, Thierry Blu

L _{ 2 }

to which we apply a unitar ...

IEEE2003