Consistent sparse signal ensemble recovery restricted on feasible dependent access routings

In this paper, motivated by the requirement of efficient information transmission with limited network resources, we study the problem of sparse signal vectors recovery over the generalized access network structure consisting of feasible access routings. In particular, we first utilize a feasible encoding mechanism to gather a small collection of linear projections of sparse signal ensemble with consistent sparsity. Then we develop a centralized reconstructing method to recover sparse vectors by applying not only the traditional compressive sensing properties but the characteristics of the generalized access network structure. For strictly sparse signals obeying ensemble and single sparsity restrictions, we deduce sufficient conditions that ensure the signals are jointly recoverable in noiseless scenario respectively, and provide an upper-bound on the estimation error in noise scenario.