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Differences between observation and sampling error in sparse signal reconstruction

Related publications (39)

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Sampling Bounds for Sparse Support Recovery in the Presence of Noise

Michael Christoph Gastpar

It is well known that the support of a sparse signal can be recovered from a small number of random projections. However, in the presence of noise all known sufficient conditions require that the per-sample signal-to-noise ratio (SNR) grows without bound w ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Compressed Sensing and Bayesian Experimental Design

Matthias Seeger

We relate compressed sensing (CS) with Bayesian experimental design and provide a novel efficient approximate method for the latter, based on expectation propagation. In a large comparative study about linearly measuring natural images, we show that the si ...

2008

Sampling methods for parametric non-bandlimited signals

Irena Maravic

Sampling theory has experienced a strong research revival over the past decade, which led to a generalization of Shannon's original theory and development of more advanced formulations with immediate relevance to signal processing and communications. For e ...

EPFL2004

Embedding Motion in Model-Based Stochastic Tracking

Daniel Gatica-Perez, Jean-Marc Odobez, Silèye Oumar Ba

Particle filtering is now established as one of the most popular method for visual tracking. Within this framework, two assumptions are generally made. The first is that the data are temporally independent given the sequence of object states. In this paper ...

IDIAP2003

Sampling With Finite Rate of Innovation: Channel and Timing Estimation for UWB and GPS

Martin Vetterli, Irena Maravic

Abstract—In this work, we consider the problem of channel estimation by using the recently developed theory for sampling of signals with a finite rate of innovation [1]. We show a framework which allows for lower than Nyquist rate sampling applicable ...

2003

Sampling signals with finite rate of innovation: the noisy case

Martin Vetterli, Andrea Ridolfi, Irena Maravic

Recently a sampling theorem for a certain class of signals with finite rate of innovation (which includes for example stream of Diracs) has been developed. In essence, such non band-limited signals can be sampled at or above the rate of innovation. In the ...

2002

Sampling innovations

Pina Marziliano

Sampling theory has prospered extensively in the last century. The elegant mathematics and the vast number of applications are the reasons for its popularity. The applications involved in this thesis are in signal processing and communications and call out ...

EPFL2002

Sampling of communications systems with bandwidth expansion

Martin Vetterli, Andrea Ridolfi

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 ...

2002

Sampling signals with finite rate of innovation

Martin Vetterli, Pina Marziliano, Thierry Blu

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 ...

Institute of Electrical and Electronics Engineers2002