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Achieving robustness, imperceptibility and high capacity simultaneously is of great importance in digital watermarking. This paper presents a new informed image watermarking scheme with high robustness and simplified complexity at an information rate of 1/64 bit/pixel. Firstly, a Taylor series approximated locally optimum test (TLOT) detector based on the hidden Markov model (HMM) in the wavelet domain is developed to tackle the problem of unavailability of exact embedding strength in the receiver due to informed embedding. Then based on the TLOT detector and the concept of dirty-paper code design, new HMM-based spherical codes are constructed to provide an effective tradeoff between robustness and distortion. The process of informed embedding is formulated as an optimization problem under the robustness and distortion constraints and the genetic algorithm (GA) is then employed to solve this problem. Moreover, the perceptual distance in the wavelet domain is also developed and incorporated into the GA-based optimization. Simulation results demonstrate that the proposed informed watermarking algorithm has high robustness against common attacks in signal processing and shows a comparable performance to the state-of-the-art scheme with a greatly reduced arithmetic complexity.