In this article an information-based method for the selection of expansion coefficients of functions in a Hilbert basis is presented. An information-based measure, namely Entropic NID (ENID), is presented; the optimal separation point between more informative coefficients and less informative ones is selected by evaluating the information contribution of two competing sets of expansion coefficients. A consistent numerical scheme is given to approximate ENID and the numerical error is studied. Numerical simulations are provided to test the behaviour of ENID in different wavelet bases, as well as to perform comparative studies.

An automatic and parameter-free information-based method for sparse representation in wavelet bases / Bruni, Vittoria; Della Cioppa, Lorenzo; Vitulano, Domenico. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - 176:(2020), pp. 73-95. [10.1016/j.matcom.2019.09.016]

An automatic and parameter-free information-based method for sparse representation in wavelet bases

Vittoria Bruni;DELLA CIOPPA, LORENZO
;
Domenico Vitulano
2020

Abstract

In this article an information-based method for the selection of expansion coefficients of functions in a Hilbert basis is presented. An information-based measure, namely Entropic NID (ENID), is presented; the optimal separation point between more informative coefficients and less informative ones is selected by evaluating the information contribution of two competing sets of expansion coefficients. A consistent numerical scheme is given to approximate ENID and the numerical error is studied. Numerical simulations are provided to test the behaviour of ENID in different wavelet bases, as well as to perform comparative studies.
Information measure; non-linear approximation; normalized Information distance (NID); sparse representation; differential entropy
01 Pubblicazione su rivista::01a Articolo in rivista
An automatic and parameter-free information-based method for sparse representation in wavelet bases / Bruni, Vittoria; Della Cioppa, Lorenzo; Vitulano, Domenico. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - 176:(2020), pp. 73-95. [10.1016/j.matcom.2019.09.016]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1341612
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