In many Earth observation missions, a large amount of data is collected by the on-board sensors, and must be transmitted to ground through a channel with limited capacity; in this case, besides lossy compression, one often has to select a subset of the original images for ground transmission. It is then desirable that the discarded images are those with a minor information content. In this paper we propose an algorithm for on-board image selection, which is fully integrated within a wavelet-based image compression scheme. The algorithm selects images possibly containing straight patterns, and uses the Hough transform, performed in the wavelet domain, for the detection task. It is shown that this method achieves a notable complexity reduction at the expenses of a limited performance degradation, strongly increasing the sustainable real-time data throughput.