This paper studies robust resource-allocation algorithm design for a multiuser multiple-input-single-output (MISO) cognitive radio (CR) downlink communication network. We focus on a secondary system that provides wireless unicast secure layered video information to multiple single-antenna secondary receivers. The resource-allocation algorithm design is formulated as a nonconvex optimization problem for the minimization of the total transmit power at the secondary transmitter. The proposed framework takes into account a quality-of-service (QoS) requirement regarding video communication secrecy in the secondary system, the imperfection of the channel state information (CSI) of potential eavesdroppers (primary receivers) at the secondary transmitter, and a limit for the maximum tolerable received interference power at the primary receivers. Thereby, the proposed problem formulation exploits the self-protecting architecture of layered transmission and artificial noise generation to ensure communication secrecy. The considered nonconvex optimization problem is recast as a convex optimization problem via semidefinite programming (SDP) relaxation. It is shown that the global optimal solution of the original problem can be constructed by exploiting both the primal and the dual optimal solutions of the SDP-relaxed problem. In addition, two suboptimal resource-allocation schemes are proposed for the case when the solution of the dual problem is unavailable for constructing the optimal solution. Simulation results demonstrate significant transmit power savings and robustness against CSI imperfection for the proposed optimal and suboptimal resource-allocation algorithms employing layered transmission compared to baseline schemes employing traditional single-layer transmission.