Publications by Martin Vetterli

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We present a general framework for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over the reals, but is shown to be valid over more general fields. We show that these basefield transforms can be viewed as “projections” of the discrete Fourier transform (DFT). Furthermore, by imposing an additional condition on the projections, one may obtain self-inverse versions of the basefield transforms. Applying the theory to the real and compl

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the performance of pop ...

Many communication systems are {\em bandwidth-expanding}: the transmitted signal occupies a bandwidth larger than the {\em symbol rate}. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. shows that in order to represent a bandlimited signal, it is necessary to sample at what is popularly referred to as the Shannon or Nyquist rate. However, in many systems, the required sampling rate is very high and expensive to implement. In this work we show that it is possible to get suboptimal performance by

We address the problem of efficient bit allocation in a dependent coding environment. While optimal bit allocation for independently coded signal blocks has been studied in the literature, we extend these techniques to the more general temporally and spatially dependent coding scenarios. Of particular interest are the topical MPEG video coder and multiresolution coders. Our approach uses an operational rate-distortion (R-D) framework for arbitrary quantizer sets. We show how a certain monotonicity property

In this paper we present FRIDA—an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state- of-the-art resolution at extremely low signal-to-noise ratios. It work ...

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[link weight]. The minimization is achieved by jointly optimizing the transmission structure, which we show consists of a superposition of trees from each of the source nodes to its co

In this paper, we consider the minimization of a relevant energy consumption related cost function in the context of sensor networks where correlated sources are generated at various sets of source nodes and have to be transmitted to some set of sink nodes. The cost function we consider is given by the product [rate] × [link weight]. The minimization is achieved by jointly optimizing the transmission structure, which we show consists of a superposition of trees from each of the source nodes to its correspon

Classical digital signal processing (DSP) lore tells us the tale of a continuous-time primeval signal, of its brutal sampling, and of the magic sinc interpolation that, under the aegis of bandlimitedness, brings the original signal back to (continuous) lif ...

Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex wavelets, the redundancy of most current transforms hinders their application in compression and related problems. In this paper we introduce a new orthonormal complex wavelet transform with no redundancy for both real— and complex-valued signals. The trans

We consider the problem of reconstructing a diffusion field, such as temperature, from samples collected by a sensor network. Motivated by the fast decay of the eigenvalues of the diffusion equation, we approximate the field by a truncated series. We show ...

Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we study a well-known and influential demosaicking algorithm based on alternating projections (AP), proposed by Gunturk, Altunbasak and Mersereau in 2002. Since its p ...

A framework supported by a set of tools for turning digital signal processing algorithms into custom chips is proposed. The framework, called MOVAL, integrates analysis, layout synthesis and validation and is based on a structured top-down design methodology covering seven succinct abstraction levels: the behavioral, data representation, space/time, hardware, symbolic and geometric (mask) descriptions, and the chip. The top four levels efficiently cope with the implementation trade-offs and are all written

The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient co

We consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a Slepian-Wolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. Thi

In this paper, we present a super-resolution method to approximately double image resolution in both dimensions from a set of four low resolution, aliased images. The camera is shifted and rotated by small amounts between the different image captures. Only the low frequency, aliasing-free part of the images is used to find the shift and rotation parameters. When the images are registered, it is possible to reconstruct a higher resolution, aliasing-free image from the four low resolution images using cubic i

We consider data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information, collected by the nodes, to the sink node. This problem requires a joint optimization of the data representation at the nodes and of the transmission structure. First, we study the case when the measured data are correlated random variables, both in the lossless scenario with Slepian-Wolf coding, and in the high-resolution loss

Multichannel sound field reproduction techniques, such as Wave Field Synthesis (WFS) and Sound Field Reconstruction (SFR), define loudspeaker filters in the frequency domain. However, in order to use these techniques in practical systems, one needs to convert these frequency-domain characteristics to practical and efficient time-domain digital filters. Additional limitation of SFR comes from the fact that it uses a numerical matrix pseudoinversion procedure, where the obtained filters are sensitive to numer

In this paper, we present a simple method to almost quadruple the spatial resolution of aliased images. From a set of four low resolution, undersampled and shifted images, a new image is constructed with almost twice the resolution in each dimension. The resulting image is aliasing-free. A small aliasing-free part of the frequency domain of the images is used to compute the exact subpixel shifts. When the relative image positions are known, a higher resolution image can be constructed using the Papoulis-Ger

Reducing energy cost is crucial for energy-constrained smart wireless cameras. Existing platforms impose two main challenges: First, most commercial smart phones have a closed platform, which makes it impossible to manage low-level circuits. Since the samp ...

This paper presents an efficient simplification method for regular meshes obtained with a binary subdivision scheme. Our mesh connectivity is constrained with a quadtree data structure. We propose a quadtree built especially for this class of meshes having a constant-time traversal property. We introduce a rate-distortion (RD) framework to decimate the mesh and build a progressive representation for the model. We propose to achieve the RD-optimal solutions for our quadtree-restricted setting: to obtain the

Martin Vetterli

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Basefield transforms with the convolution property

The regularized tau estimator: A robust and efficient solution to ill-posed linear inverse problems

Sampling of communications systems with bandwidth expansion

Bit allocation for dependent quantization with applications to multiresolution and MPEG video coders

FRIDA: FRI-Based DOA Estimation For Arbitrary Array Layouts

Networked Slepian-Wolf: Theory and Algorithms

Networked Slepian-Wolf: Theory and Algorithms

From Lagrange to Shannon...and Back: Another Look at Sampling

Orthogonal Hilbert transform filter banks and wavelets

Sensor Networks for Diffusion Fields: Detection of Sources in Space and Time

Demosaicking by Alternating Projections: Theory and Fast One-Step Implementation

MOVAL: a framework for turning digital signal processing algorithms into custom chips

Wavelets and Filter Banks: Theory and Design

On Network Correlated Data Gathering

Double resolution from a set of aliased images

On the interaction of data representation and routing in sensor networks

Designing Practical Filters For Sound Field Reconstruction

Superresolution images reconstructed from aliased images

Sensorcam: An Energy-Efficient Smart Wireless Camera for Environmental Monitoring

Progressive Meshes in an Operational Rate-Distortion Sense with Application to Terrain Data