A joint design of source coding and channel coding is proposed to transmit images over error-prone wireless channels. First, the importance of each source output bit is quantified in bit error sensitivity (BES). Next, clustered set partitioning in hierarchical trees (C-SPIHT) is adopted to cluster SPIHT output bits so that the resultant bit-clusters have distinct BES. Then, we prove that equalizing the mean BES of bit-clusters provides the optimal assignment of channel coding rates for the unequal error protection. Besides, to achieve the best PSNR performance under a transmission rate, we use a heuristic method to allocate the source coding rate and channel coding rate. Simulation results show that, under different channel bit error rates, our design not only improves the mean PSNR performance, but also reduces the variations of PSNR performance, i.e. the robustness of PSNR to the channel noise interference is improved. [Copyright &y& Elsevier]