Download Compressed Sensing & Sparse Filtering by Avishy Y. Carmi, Lyudmila Mihaylova, Simon J. Godsill PDF

By Avishy Y. Carmi, Lyudmila Mihaylova, Simon J. Godsill

This booklet is aimed toward featuring options, tools and algorithms ableto do something about undersampled and restricted facts. One such development that lately received acceptance and to a point revolutionised sign processing is compressed sensing. Compressed sensing builds upon the remark that many signs in nature are approximately sparse (or compressible, as they're quite often spoke of) in a few area, and therefore they are often reconstructed to inside excessive accuracy from some distance fewer observations than typically held to be necessary.

except compressed sensing this ebook comprises different similar ways. every one method has its personal formalities for facing such difficulties. as an instance, within the Bayesian technique, sparseness selling priors similar to Laplace and Cauchy are as a rule used for penalising inconceivable version variables, hence selling low complexity ideas. Compressed sensing strategies and homotopy-type suggestions, resembling the LASSO, utilise l1-norm consequences for acquiring sparse options utilizing fewer observations than conventionally wanted. The ebook emphasizes at the position of sparsity as a equipment for selling low complexity representations and in addition its connections to variable choice and dimensionality aid in a variety of engineering problems.

This e-book is meant for researchers, teachers and practitioners with curiosity in a number of elements and purposes of sparse sign processing.

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Extra resources for Compressed Sensing & Sparse Filtering

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In:Proceedings of the IEEE international conference on acoustics, speech and signal processing, pp 393–396 38. Szarek SJ (1991) Condition numbers of random matrices. J Complex 7:131–149 39. Tibshirani R (1996) Regression shrinkage and selection via the LASSO. J Roy Stat Soc Ser B, 58(1):267–288 40. Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1:211–244 41. Tropp JA, Gilbert AC (2007) Signal recovery from random measurements via orthogonal matching pursuit.

Candes E, Tao T (2007) The Dantzig selector: statistical estimation when p is much larger than n. Ann Stat 35:2313–2351 10. Candes EJ (2006) Compressive sampling. In: Proceedings of the international congress of mathematicians, European Mathematical Society,Madrid, pp 1433–1452 11. Candes EJ (2008) The restricted isometry property and its implications for compressed sensing. C R Math 346:589–592 12. Candes EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information.

Carmi et al. 1007/978-3-642-38398-4_2, © Springer-Verlag Berlin Heidelberg 2014 25 26 T. 1 Introduction How do we know something is there, if we haven’t seen it, or, to use the cliche, how do we know that the falling tree still makes a sound even if there is no one to listen? This is far more than a purely philosophical question. It is at the heart of all of scientific discovery, indeed, one could say that all of science is ultimately a quest for rules that allow us to predict the unobserved. In science, this is done by observing certain aspects of nature which are then used to build models which in turn allow us to make predictions about things we have not yet seen.

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