<html><body><div style="font-family: arial, helvetica, sans-serif; font-size: 12pt; color: #000000"><div><br data-mce-bogus="1"></div><div data-marker="__QUOTED_TEXT__"><div><br><div><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="font-size: 16pt; font-family: 'calibri';" data-mce-style="font-size: 16pt; font-family: 'calibri';">Séminaire</span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="font-size: 16pt; font-family: 'calibri';" data-mce-style="font-size: 16pt; font-family: 'calibri';"> <span style="font-size: 24pt;" data-mce-style="font-size: 24pt;">Neuromathématiques</span></span><span style="font-family: 'calibri'; font-size: 20pt; text-indent: 0cm;" data-mce-style="font-family: 'calibri'; font-size: 20pt; text-indent: 0cm;"> </span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><br></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">Organisé par</span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">Giovanna Citti </span><i style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;">(University of Bologna)</i></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">JP Nadal (<i style="color: #000000; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; background-color: #ffffff;" data-mce-style="color: #000000; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; background-color: #ffffff;">CAMS - EHESS)</i></span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">Jean Petitot</span><i style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;"> (CAMS - EHESS)</i></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">Jerome Ribot </span><em style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;">(Collège de France)</em><em style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;"></em></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0cm; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-style: normal; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff; float: none; display: inline !important;">Alessandro Sarti </span><i style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;" data-mce-style="color: #000000; font-family: 'times new roman' , 'new york' , 'times' , serif; font-size: 17.3333px; font-weight: 400; letter-spacing: normal; text-align: center; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: normal; background-color: #ffffff;">(CAMS - EHESS/CNRS) (reférent) </i></p><p align="center" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times'; font-size: 10pt;" data-mce-style="color: #000000; font-family: 'times'; font-size: 10pt;"><br></span></p><p align="center" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="color: #000000; font-family: 'times'; font-size: 10pt;" data-mce-style="color: #000000; font-family: 'times'; font-size: 10pt;"></span><span style="text-align: center; text-indent: 0px; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="text-align: center; text-indent: 0px; background-color: #ffffff; float: none; display: inline !important;"><span style="font-family: calibri;"><span style="font-size: 18.6667px;" data-mce-style="font-size: 18.6667px;"> mardi 8 avril 14h30-16h30</span></span></span></p><p align="center" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><br data-mce-bogus="1"></p><p align="center" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="text-align: center; text-indent: 0px; background-color: #ffffff; float: none; display: inline !important;" data-mce-style="text-align: center; text-indent: 0px; background-color: #ffffff; float: none; display: inline !important;"><span style="color: #000000; font-family: 'calibri'; font-size: 18.6667px;" data-mce-style="color: #000000; font-family: 'calibri'; font-size: 18.6667px;">Salle D2.2, </span></span><span style="color: #000000; font-family: 'calibri'; font-size: 14pt;" data-mce-style="color: #000000; font-family: 'calibri'; font-size: 14pt;"><strong>Collège de France</strong>, 11, Place Marcelin-Berthelot, 75005, Paris</span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="font-size: 14pt; font-family: 'calibri';" data-mce-style="font-size: 14pt; font-family: 'calibri';">On se retrouve à l'accueille à 14h15 et on y va à la salle tous ensemble</span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="font-size: 14pt; font-family: 'calibri';" data-mce-style="font-size: 14pt; font-family: 'calibri';"><br></span></p><p align="center" style="text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="color: rgb(0, 0, 0); font-family: calibri; font-size: 12pt;"><span style="font-size: 18.6667px;" data-mce-style="font-size: 18.6667px;">Lien Zoom: </span></span><font face="calibri"><span style="font-size: 18.6667px;">https://cnrs.zoom.us/j/97625468512?pwd=MwulsVF5QP6THQalI2s0PaaYCbzpYa.1</span></font></p><p align="center" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><br></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><span style="font-size: 12pt; font-family: 'calibri';" data-mce-style="font-size: 12pt; font-family: 'calibri';">______________ </span><span style="font-size: 10pt; font-family: 'times';" data-mce-style="font-size: 10pt; font-family: 'times';"></span></p><p align="center" style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;" data-mce-style="color: #000000; font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; text-indent: 0cm; margin: 0px; text-align: center;"><br></p><div style="text-align: center;" data-mce-style="text-align: center;"><div dir="ltr"><div dir="ltr" style="color: #000000; font-family: times; font-size: 14px;" data-mce-style="color: #000000; font-family: times; font-size: 14px;"><span style="font-size: 24pt;" data-mce-style="font-size: 24pt;"><strong>Davide Barbieri</strong></span><br></div><div dir="ltr" style="color: #000000; font-family: times; font-size: 14px;" data-mce-style="color: #000000; font-family: times; font-size: 14px;"><br></div><div dir="ltr" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;"><strong style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;"><span style="font-family: 'times';" data-mce-style="font-family: 'times';"><span style="font-size: 16pt;" data-mce-style="font-size: 16pt;"> Universidad Autonoma de Madrid </span></span></strong><strong style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;"><span style="font-family: 'times';" data-mce-style="font-family: 'times';"><span style="font-size: 16pt;" data-mce-style="font-size: 16pt;"></span></span></strong></div><div dir="ltr" style="color: #000000; font-family: times; font-size: 14px;" data-mce-style="color: #000000; font-family: times; font-size: 14px;"><span style="font-size: 14pt;" data-mce-style="font-size: 14pt;"><strong><br></strong></span></div><div dir="ltr"><div class=""><p style="margin: 0px;" data-mce-style="margin: 0px;"><span style="font-family: times;"><span style="font-size: 24px;" data-mce-style="font-size: 24px;"><b><i>On the completeness of orientation preference maps in primary visual cortex</i></b></span></span><span style="color: #000000; font-family: times; font-size: 12pt;" data-mce-style="color: #000000; font-family: times; font-size: 12pt;"><span style="font-size: 24px;" data-mce-style="font-size: 24px;"><b><i></i></b></span></span></p><p style="margin: 0px; text-align: left;" data-mce-style="margin: 0px; text-align: left;"><span style="background-color: rgb(253, 253, 253); font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt; text-align: start;"><br data-mce-bogus="1"></span></p><p style="margin: 0px; text-align: left;" data-mce-style="margin: 0px; text-align: left;"><span style="background-color: rgb(253, 253, 253); font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt; text-align: start;">We want to consider the model of classical receptive fields of simple cells in primary visual cortex, given by translations and rotations of a two-dimensional modulated gaussian function, with parameters of positions and orientations distributed according to a two-dimensional pinwheel-like orientation preference map, from the point of view of harmonic analysis.</span></p><div class="page" title="Page 1" style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-family: arial, helvetica, sans-serif; font-size: 12pt;"><div style="text-align: center;" data-mce-style="text-align: center;"><div class="column"><div class="page" title="Page 1"><div class="layoutArea"><div class="" style="text-align: left;" data-mce-style="text-align: left;"><div class=""><div class="elementToProof" style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;">The aim is to discuss the problem of completeness of the set of receptive fields parametrized by orientation preference maps, the question being: can the visual stimulus be reconstructed in a stable way from such a set of cells, and how can this reconstruction be performed?</div><div class="elementToProof" style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;">We will start by introducing the model and the basic properties of its linear processing described by a group wavelet transform.</div><div class="elementToProof" style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;">We will then provide a mathematical proof that completeness can be achieved depending on the relationship between the receptive field size and the correlation length of the pinwheel distribution. The argument makes use of a construction of frames of exponentials from a Fuglede-type theorem for lattices and will be presented in elementary terms as an adaptation of the classical Shannon sampling theorem.</div><div class="elementToProof" style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: #fdfdfd; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; font-family: aptos, aptos_embeddedfont, aptos_msfontservice, calibri, helvetica, sans-serif; font-size: 12pt;">Finally, we will show an iterative reconstruction algorithm in the form of a classical population dynamics equation, where the iteration kernel contains both the structure of the group wavelet and that of the pinwheel distribution. We will show the results of the reconstruction on natural images, for a properly discretized model.</div></div></div><div class="" style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;" data-mce-style="color: #000000; font-family: 'arial' , 'helvetica' , sans-serif; font-size: 12pt;"><br></div></div></div></div></div></div></div></div></div></div><div class="x11i5rnm xat24cr x1mh8g0r x1vvkbs xtlvy1s x126k92a" style="color: #080809; font-family: arial, helvetica, sans-serif; font-size: 15px; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: pre-wrap; margin: 0.5em 0px 0px; background-color: #ffffff;" data-mce-style="color: #080809; font-family: arial, helvetica, sans-serif; font-size: 15px; font-style: normal; font-weight: 400; letter-spacing: normal; text-indent: 0px; text-transform: none; word-spacing: 0px; white-space: pre-wrap; margin: 0.5em 0px 0px; background-color: #ffffff;"><div dir="auto" style="font-family: inherit; 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