Vehkapera, M.Kabashima, Y.Chatterjee, S.Aurell, E.Skoglund, M.Rasmussen, L.2025-12-172025-12-172012Information theory workshop, 2012, iss.6404757, pp.647-6519781467302241https://hdl.handle.net/1959.8/124268The sparse representation problem of recovering an N dimensional sparse vector x from M <; N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and identically distributed (IID) zero-mean Gaussian and minimize the l1-norm of x under the constraint y = Dx. In this paper, the performance of l1-reconstruction is analyzed, when the dictionary is bi-orthogonal D = [O1 O2], where O1, O2 are independent and drawn uniformly according to the Haar measure on the group of orthogonal M × M matrices. By an application of the replica method, we obtain the critical conditions under which perfect l1-recovery is possible with bi-orthogonal dictionaries.enCopyright 2012 IEEE Access Condition Notes: Accepted manuscript is availableConference paper10.1109/ITW.2012.64047572-s2.0-84873181807