Recoverability And Stability Of L_q Minimization For Compressive Sensing Without RIP

A model is thought to have recoverability if an n-dimensional signal can be recoveredfrom its m sample (m n) via this model. The model has stability if it has recover-ability when measurements are nosiy and/or sparsity is inexact. So far§most analysesabout the recoverability and stability rely on the Restricted Isometry Property(RIP) forthe measurement matrices. The recoverability and stability for lqminimization withoutRIP had been proved by Chartrand and other authors. In2008, the recoverability andstability for lqminimization without RIP had been proved by Yin Zhang. We mainlydiscuss the recoverability and stability for lqminimization without RIP.