Hyperspectral data acquired by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) have allowed for unparalleled mapping of the surface mineralogy of Mars. Due to sensor degradation over time, a significant portion of the recently acquired data is considered unusable. Here a new data-driven model architecture, Noise2Noise4Mars (N2N4M), is introduced to remove noise from CRISM images. Our model is self-supervised and does not require zero-noise target data, making it well suited for use in Planetary Science applications where high quality labelled data is scarce. We demonstrate its strong performance on synthetic-noise data and CRISM images, and its impact on downstream classification performance, outperforming benchmark methods on most metrics. This allows for detailed analysis for critical sites of interest on the Martian surface, including proposed lander sites.