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The explosive demands for high quality mobile video services have caused heavy overload to the existing cellular networks. Although the small cell has been proposed to alleviate such a problem, the network operators may not be interested in deploying numerous base stations (BSs) due to expensive infrastructure construction and maintenance. The unmanned aerial vehicles (UAVs) can provide the low-cost and quick deployment, which can support high-quality line-of-sight communications and have become promising mobile BSs. In this paper, we propose a quality-of-experience (QoE)-driven UAV-enabled pseudo-analog wireless video broadcast scheme, which provides mobile video broadcast services for ground users (GUs). Due to limited energy available in UAV, the aim of the proposed scheme is to maximize the minimum peak signal-to-noise ratio (PSNR) of GUs' video reconstruction quality by jointly optimizing the transmission power allocation strategy and the UAV trajectory. Firstly, the reconstructed video quality at GUs is defined under the constraints of the UAV's total energy and motion mechanism, and the proposed scheme is formulated as a complex non-convex optimization problem. Then, the optimization problem is simplified to obtain a tractable suboptimal solution with the help of the block coordinate descent model and the successive convex approximation model. Finally, the experimental results are presented to show the effectiveness of the proposed scheme. Specifically, the proposed scheme can achieve over 1.6dB PSNR gains in terms of GUs' minimum PSNR, compared with the state-of-the-art schemes, e.g., DVB, SoftCast, and SharpCast.