Publications by Martin Vetterli

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Most users of online services have unique behavioral or usage patterns. These behavioral patterns can be used to identify and track users by using only the observed patterns in the behavior. We study the task of identifying users from statistics of their behavioral patterns. Specifically, we focus on the setting in which we are given histograms of users’ data collected in two different experiments. In the first dataset, we assume that the users’ identities are anonymized or hidden and in the second dataset

The connectivity of a neuronal network has a major effect on its functionality and role. It is generally believed that the complex network structure of the brain provides a physiological basis for information processing. Therefore, identifying the network’ ...

We study a multichannel sampling scheme, where different channels observe scaled and shifted versions of a common bandlimited signal. The channel gains and offsets are unknown a priori, and each channel samples at sub-Nyquist rates. This setup appears in many practical signal processing applications, including time-interleaved ADC with timing skews, unsynchronized distributed sampling in sensor networks, and superresolution imaging. In this paper, we propose a new algorithm to efficiently estimate the unkno

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies ...

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 ...

The ridgelet transform (Candes and Donoho, 1999) was introduced as a new multiscale representation for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we present several discrete versions of the ridgelet transform that lead to algorithmic implementations. The resulting transforms are invertible, non-redundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional orthonormal bases for digital images. Numerical re

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from the magnitude of i ...

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one dimensional methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the hori ...

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 polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom ...

We study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. To analyze its performance, we formulate the oversam ...

Lippmann (or interferential) photography is the first and only analog photography method that can capture the full color spectrum of a scene in a single take. This technique, invented more than a hundred years ago, records the colors by creating interferen ...

In recent years the ``Internet Multicast Backbone'', or MBone, has risen from a small, research curiosity to a large scale and widely used communications infrastructure. A driving force behind this growth was the development of multipoint audio, video, and shared whiteboard conferencing applications. Because these real-time media are transmitted at a uniform rate to all the receivers in the network, a source must either run at the bottleneck rate or overload portions of its multicast distribution tree. We o

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining the next one, and b) recursive decoding, where the signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization scheme applied to decode the new one. To remove estimation bias, a two-step estimation proc

Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of ...

Tree structures for computing orthogonal transforms are introduced. Two cases, delay trees and decimation trees, are investigated. A simple condition, namely the orthogonality of branches with a common root, is shown to be necessary and sufficient for the overall transform to be orthogonal. Main advantages are structural simplicity and a number of operations proportional to N Log2N. Application of the tree structures to the Walsh-Hadamard Transform (in natural, sequency and dyadic order) is presented. A sin

The authors consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. They show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. The method is based on the construction of boundary and transition filters; these allow us to construct essentially arbitrary tilings. Time-var

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it raises questions when the linearized problem is solvable and what is the cost of linearization. In this work, we study a few specific cases of this general problem and show when the bilinear problem is solvable. Using this result and certain properties of

The goal of a class of sensor networks is to monitor an underlying physical reality at the highest possible fidelity. Sensors acquire noisy measurements and have to communicate them over a power- and possibly bandwidth-constrained interference channel to a set of base stations. The goal of this paper is to analyze, as a function of the number of sensors, the trade-offs between the degrees of freedom of the underlying physical reality, the communication resources (power, temporal and spatial bandwidth), and

We consider the problem of full-duplex video transmission over the Internet, under real-time delay constraints. In this work we present the design of a complete communications system, whose salient features are: (a) a soft real-time transport protocol, whose generated traffic characteristics are identical to those of bulk transfers using TCP/IP, thus ensuring complete fairness to other flows in the network; (b) a video coder resilient to moderate amounts of loss of data that are induced by the soft real-tim

Martin Vetterli

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Where You Are is Who You Are: User Identification by Matching Statistics

Learning Neural Connectivity from Firing Activity: Scalable Algorithms with Provable Guarantees

Multichannel Sampling with Unknown Gains and Offsets: A Fast Reconstruction Algorithm

Shapes from pixels

Super-Resolution from Unregistered and Totally Aliased Signals Using Subspace Methods

Discrete Ridgelet Transforms for Image Representation

Phase Retrieval for Sparse Signals: Uniqueness Conditions

Sampling at unknown locations, with an application in surface retrieval

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Exact Local Reconstruction Algorithms for Signals with Finite Rate of Innovation

Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics

Lippmann Photography: A Signal Processing Perspective

Low-complexity video coding for receiver-driven layered multicast

Recursive Compressed Sensing

Which Distributed Averaging Algorithm Should I Choose for my Sensor Network?

Tree structures for orthogonal transform and application to the Hadamard transform

Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms

Matrix recovery from bilinear and quadratic measurements

Power-bandwidth-distortion scaling laws for sensor networks

High-bandwidth internet video telephony