Publications by Martin Vetterli

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Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we showthat they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theo

The ﬁeld of signal processing has known tremendous progress with the The field of signal processing has known tremendous progress with the development of digital signal processing. The first foundation of digital signal processing is due to Shannon's sampling theorem which shows that any bandlimited analog signal can be reduced to a discrete-time signal. However, digital signals assume a second digitization operation in amplitude. While this operation, called quantization, is as deterministic as time sampli

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

In this paper, we design a new iterative low-complexity algorithm for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT. We suppose that N is a power of two and K = O(N^α), scales sub-linearly in N for some α ∈ (0, ...

We study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as a function of their spatial positions. We observe that the multidimensional spectrum of the solution of the wave equation has an almost bandlimited character. Therefore sampling and interpolation can easily be applied using signals on an array. The decay of the spectrum is studied on both temporal and spatial frequency axes. We study how this decay influences the performance of the interpolatio

In many applications, the sampling frequency is limited by the physical characteristics of the components: the pixel pitch, the rate of the A/D converter, etc. A low-pass filter is then often applied before the sampling operation to avoid aliasing. However, when multiple copies are available, it is possible to use the information that is inherently present in the aliasing to reconstruct a higher resolution signal. If the different copies have unknown relative offsets, this is a non-linear problem in the off

The issue of how to efficiently represent the data collected by a network of microphones recording spatio-temporal acoustic wave fields is addressed. Each sensor node in the network samples the sound field, quantizes the samples and transmits the encoded s ...

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining a ...

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize point ...

Consider a nonparametric representation of acoustic wave fields that consists of observing the sound pressure along a straight line or a smooth contour L defined in space. The observed data contains implicit information of the surrounding acoustic scene, b ...

Sound or acoustic tomography is a type of inverse problem. The idea of estimating physical quantities that influence sound propagation by measuring the parameters of sound propagation has proven to be successful in several practical domains, including medicine, seismology, oceanography. The use of acoustic tomography for estimating temperature and wind fields in the atmosphere has been shown to be possible as well and, moreover, its potentials have been demonstrated in field experiments. However, in most of

Detection of defective members of large populations has been widely studied in the statistics community under the name ``group testing'', a problem which dates back to World War~II when it was suggested for syphilis screening. There the main interest is to ...

In the present paper, we study the spatialization of the soundfield in a room, in particular the evolution of room impulse responses as function of their spatial positions. The presented technique allows us to completely characterize the sound field in any arbitrary location if the sound field is known in a certain finite number of positions. The existing techniques make usually use of room models to recreate the sound field present at some point in the space. Our technique simply starts from the measuremen

Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such as efficient processing, compact storage and numerical robustness. A mesh having subdivision connectivity can be described using a tree structure and recent work exploits this inherent hierarchy in applications such as progressive terrain visualization, sur

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weig ...

We consider the joint estimation of multipath channels obtained with a set of receiving antennas and uniformly probed in the frequency domain. This scenario fits most of the modern outdoor communication protocols for mobile access (ETSI Std. 125 913) or di ...

Lensless imaging can provide visual privacy due to the highly multiplexed characteristic of its measurements. However, this alone is a weak form of security, as various adversarial attacks can be designed to invert the one-to-many scene mapping of such cameras. In this work, we enhance the privacy provided by lensless imaging by (1) downsampling at the sensor and (2) using a programmable mask with variable patterns as our optical encoder. We build a prototype from a low-cost LCD and Raspberry Pi components,

Traditional sampling results assume that the sample locations are known. Motivated by simultaneous localization and mapping (SLAM) and structure from motion (SfM), we investigate sampling at unknown locations. Without further constraints, the problem is of ...

The plenoptic function (POF) provides a powerful conceptual tool for describing a number of problems in image/video processing, vision, and graphics. For example, image based-rendering can be seen as sampling and interpolation of the POF. In such applicati ...

Martin Vetterli

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Sampling signals with finite rate of innovation

Consistent Signal Reconstruction and Convex Coding

Coordinate Difference Matrices

A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain

The Plenacoustic Function and its Sampling

Aliasing is Good for You: Joint Registration and Reconstruction for Super-Resolution

On Sampling and Coding for Distributed Acoustic Sensing

Sequences with Minimal Time-Frequency Uncertainty

Kinetic Euclidean Distance Matrices

Space/time-frequency processing of acoustic wave fields: theory, algorithms, and applications

Acoustic tomography for scalar and vector fields: theory and application to temperature and wind estimation

Compressed Sensing with Probabilistic Measurements: A Group Testing Solution

The Plenacoustic Function, Sampling and Reconstruction

Mesh Optimization Using Global Error with Application to Geometry Simplification

Networked Slepian-Wolf: Theory, Algorithms and Scaling Laws

Fast and Robust Parametric Estimation of Jointly Sparse Channels

Privacy-Enhancing Optical Embeddings for Lensless Classification

Computational Analysis of Mesh Simplification Using Global Error

Sampling at unknown locations: Uniqueness and reconstruction under constraints

On the Bandwidth of the Plenoptic Function