caa a22 4500 606205136 CHVBK 20210128101006.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00034-015-9985-8 doi (NATIONALLICENCE)springer-10.1007/s00034-015-9985-8 Sabri Khalid STIC Laboratory, Department of Physics, Faculty of Sciences, University Chouaïb Doukkali, El Jadida, Morocco aut New Cyclic Sparsity Measures for Deconvolution Based on Convex Relaxation [Elektronische Daten] [Khalid Sabri] Periodic random impulse signals are powerful tools for various situations of interest and are a natural way for modeling highly localized events occurring randomly at given times. However, the measured impulses are often masked because of unwanted convolution and eventually drowned in noise. Thus, the resulting signal is not legible and may lead to poor or even erroneous analysis and, hence, the need of deconvolution to recover the random periodic impulses. As a matter of fact, periodic random impulse signals are sparse and the sparse coefficients are periodically correlated. It has thus emerged as to how to combine the data structure and the sparsity jointly for a best description. The originality of this study lies in the design of new measures of cyclic sparsity property for the deconvolution of signals that are simultaneously sparse and cyclostationary. To our knowledge, all related works in this field exploit only one property, either sparsity or cyclostationarity and never both properties together. The key feature of cyclic sparsity deconvolution is that it combines the cyclic structure and the sparsity together which implies a significantly enhanced performance. Finally, we include examples of computer simulations to illustrate the behavior in deconvolution context of the proposed algorithms against an $$\ell _1$$ ℓ 1 sparse deconvolution through convex optimization. We show that deconvolution based on cyclic sparsity hypothesis increases the performance and reduces significantly the computation cost as well. Springer Science+Business Media New York, 2015 Deconvolution nationallicence Periodic random impulses nationallicence Cyclic sparsity nationallicence Cyclostationary nationallicence Convex relaxation nationallicence Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/9(2015-09-01), 2911-2934 0278-081X 34:9<2911 2015 34 34 https://doi.org/10.1007/s00034-015-9985-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-015-9985-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sabri Khalid STIC Laboratory, Department of Physics, Faculty of Sciences, University Chouaïb Doukkali, El Jadida, Morocco aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/9(2015-09-01), 2911-2934 0278-081X 34:9<2911 2015 34 34