Unmanned aerial vehicle (UAV) imaging is a dynamically developing field, where the effectiveness of imaging applications highly depends on quality of the acquired images. No-reference image quality assessment is widely used for quality control and image processing management. However, there is a lack of accuracy and adequacy of existing quality metrics for human visual perception. In this paper, we demonstrate that this problem persists for typical applications of UAV images. We present a methodology to improve the efficiency of visual quality assessment by existing metrics for images obtained from UAVs, and introduce a method of combining quality metrics with the optimal selection of the elementary metrics used in this combination. A combined metric is designed based on a neural network trained to utilize subjective assessments of visual quality. The metric was tested using the TID2013 image database and a set of real UAV images with embedded distortions. Verification results have demonstrated the robustness and accuracy of the proposed metric.