Sparse Sampling of Signal Innovations

By Thierry Blu, Pier Luigi Dragotti, Martin Vetterli, Pina Marziliano, Lionel Coulot. IEEE Signal Processing Magazine, 2008

455 citations recorded by the source corpus.

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, proposing methods reaching the optimal performance given by the Cramer-Rao bounds. Finally, a number of applications have been discussed where sparsity can be taken advantage of. The comprehensive coverage given in this article should lead to further research in sparse sampling, as well as new applications. One main application to use the theory presented in this article is ultra-wide band (UWB) communications.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/e67cb5c0775ebd598226d6c722425c10b5e26051

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

In Signal Processing

Citations in the corpus

Sparsity and Compressed Sensing in Radar Imaging (2010, methodology): “Resolution is the ability to detect two objects in close proximity [ 73 ], [101], [102], while accuracy refers to the mean squared error in estimating the object’s parameters (location, amplitude, etc.).”
Comparing Measures of Sparsity (2008, methodology): “…and techniques such as matrix factorization [7], signal recovery/extraction [8], denoising [9], [10], compressed sensing [11], dictionary learning [12], signal representation [13], [14], support vector machines [15], sampling theory [16], [17] and source separation/localization [18], [19].”
On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data (2014, unknown): “This system of equations can be solved using Prony's method for which readers are referred to [52].”
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals (2009, background): “We believe that these applications will be easier to achieve in the near future because suitable ADC and DSP technology is already available.”
Exact Support Recovery for Sparse Spikes Deconvolution (2013, unknown): “This includes for instance greedy [26, 25], root finding [3, 11], matrix pencils [13] and compressed sensing [18, 16] approaches.”
Structured Compressed Sensing: From Theory to Applications (2011, methodology): “This has also led to parallel low-rate sampling schemes that combine the principles of CS with the rich theory of sampling such as the ﬁnite rate of innovation (FRI) [6]–[8] and Xampling frameworks [9], [10].”
Compressed Sensing Off the Grid (2012, background): “A survey of these methods can be found in [42] and an extensive list of references is given in [23].”
Atomic Norm Denoising With Applications to Line Spectral Estimation (2012, methodology): “Cadzow’s method has been identified as a fruitful preprocessing step for linear prediction methods [46].”
Foundations of Signal Processing (2014, background): “Rather, the sampling rate for exact reconstruction of a function is related to its rate of innovation, which is defined as the function’s number of degrees of freedom per unit time; an overview can be found in [8].”
Super-Resolution from Noisy Data (2012, unknown): “These techniques are typically based on the eigendecomposition of a sample covariance matrix of the data [4, 5, 33, 36].”
Spectral compressive sensing (2013, methodology): “In fact, noise-tolerant line spectral estimation algorithms [66, 67] have been proposed to extend FROI to noisy sampling settings [30, 31, 32], albeit without performance guarantees to date.”