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Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

Frame Domain Signal Processing: Framework and Applications

Martin Vetterli, Amina Chebira

Besides basis expansions, frames representations play a key role in signal processing. We thus consider the problem of frame domain signal processing, which is more complex and challenging than transform domain processing. Examples of such processing aboun ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

On Sampling Lattices with Similarity Scaling Relationships

Dimitri Nestor Alice Van De Ville, Thierry Blu

We provide a method for constructing regular sampling lattices in arbitrary dimensions together with an integer dilation matrix. Subsampling using this dilation matrix leads to a similarity-transformed version of the lattice with a chosen density reduction ...

LATP2009

Dimensionality Reduction for Distributed Estimation in the Infinite Dimensional Regime

Martin Vetterli, Olivier Roy

Distributed estimation of an unknown signal is a common task in sensor networks. The scenario usually envisioned consists of several nodes, each making an observation correlated with the signal of interest. The acquired data is then wirelessly transmitted ...

Institute of Electrical and Electronics Engineers2008

Enhancement of extended depth of field by digital focusing

Theo Lasser, Rainer Leitgeb, Martin Villiger, Cédric Blatter

With the use of a Bessel-like illumination beam produced by an axicon lens an extended depth of field can be achieved. The resulting illumination pattern exhibits a strong central lobe extending over 300um along the optical axis without diffraction. Here w ...

2008

Consensus and collision detectors in radio networks

Seth Gilbert

We consider the fault-tolerant consensus problem in radio networks with crash-prone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in single-hop radios networks, where all nodes are located within broadcast range of ...

2008

The SURE-LET Approach to Image Denoising

Thierry Blu, Florian Luisier

We propose a new approach to image denoising, based on the image-domain minimization of an estimate of the mean squared error—Stein's unbiased risk estimate (SURE). Unlike most existing denoising algorithms, using the SURE makes it needless to hypothesize ...

Institute of Electrical and Electronics Engineers2007

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

Rate-Distortion Problem for Physics Based Distributed Sensing

Martin Vetterli, Robert Konsbruck

We consider the rate-distortion problem for sensing the continuous space-time physical temperature in a circular ring on which a heat source is applied over space and time, and which is allowed to cool by radiation or convection. The heat source is modelle ...

2004