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In this paper, the joint spectrum sensing and resource allocation problem is investigated in a multi-band-multi-user cognitive radio (CR) network. Assuming imperfect spectrum sensing information, our goal is to jointly optimize the sensing threshold and power allocation strategy such that the average total throughput of secondary users (SUs) is maximized. In Addition, the power of SUs is constrained to keep the interference introduced to primary users under certain limit, which gives rise to a nonconvex mixed integer non-linear programming (MINLP) optimization problem. Our contribution in this paper is threefold. First, it is illustrated that the dimension of the nonconvex MINLP problem can be significantly reduced, which helps to re-formulate the optimization problem without resorting to integer variables. Second, it is demonstrated that the simplified formulation admits the canonical form of a monotonic optimization, and an $\epsilon $ -optimal solution can be achieved using the polyblock outer approximation algorithm. Third, a practical low-complexity spectrum sensing and resource allocation algorithm is developed to reduce the computational cost. Finally, the effectiveness of proposed algorithms is verified by simulations. [ABSTRACT FROM AUTHOR]