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Most of the images transmitted from deep space probes to Earth are subject to lossy compression. Recent NASA missions (such as Mars rovers Spirit and Opportunity) have used the ICER progressive wavelet image compressor to achieve state of-the-art compression performance. The purpose of the research described in this paper was to demonstrate that it is possible to evolve wavelet and scaling numbers describing novel transforms that outperform the most commonly used ICER wavelet for the reconstruction of images of the Martian landscape that had previously been subjected to lossy compression. Because our technique only modifies the image reconstruction transform, it requires no modification of deployed mission hardware. We thus present a technique to provide improved reconstruction of images received from existing rover missions.