caa a22 4500 463246993 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s00041-006-6006-0 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6006-0 Exact Solutions of Some Discrete Deconvolution Problems [Elektronische Daten] [Abderrazek Karoui, Amara Ammari, Belgacem Selmi] In this work, we study the existence of solutions of the deconvolution problems in the discrete setting. More precisely, we prove the existence of solutions of the discrete multichannel deconvolution problems DMDP with convolvers being the characteristic functions of finite sets of positive integers. Also, we provide the reader with a simple method and a fast algorithm for finding the closed forms of the discrete deconvolvers with minimal supports that constitute exact solutions of the DMDP. Moreover, we show that unlike the singular value decomposition scheme, the multichannel deconvolution scheme based on the use of these discrete deconvolvers is not very sensitive to small 2-norm perturbation of the data. Finally, we show how to generalize our method for solving the 2-D version of the DMDP. Birkhauser Boston, 2007 Karoui Abderrazek Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna 7021, Tunisia aut Ammari Amara Institut Préparatoire d'Ingénieur de Bizerte, Jarzouna 7021, Tunisia aut Selmi Belgacem Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna 7021, Tunisia aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 533-550 1069-5869 13:5<533 2007 13 41 https://doi.org/10.1007/s00041-006-6006-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6006-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karoui Abderrazek Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna 7021, Tunisia aut NATIONALLICENCE 700 1- Ammari Amara Institut Préparatoire d'Ingénieur de Bizerte, Jarzouna 7021, Tunisia aut NATIONALLICENCE 700 1- Selmi Belgacem Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna 7021, Tunisia aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 533-550 1069-5869 13:5<533 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer