Inpainting vs denoising for dose reduction in scanning-beam microscopies

We consider sampling strategies for reducing the radiation dose during image acquisition in scanning-beam microscopies, such as SEM, STEM, and STXM. Our basic assumption is that we may acquire subsampled image data (with some pixels missing) and then inpaint the missing data using a compressed-sensing approach. Our noise model consists of Poisson noise plus random Gaussian noise. We include the possibility of acquiring fully-sampled image data, in which case the inpainting approach reduces to a denoising procedure. We use numerical simulations to compare the accuracy of reconstructed images with the "ground truths." The results generally indicate that, for sufficiently high radiation doses, higher sampling rates achieve greater accuracy, commensurate with well-established literature. However, for very low radiation doses, where the Poisson noise and/or random Gaussian noise begins to dominate, then our results indicate that subsampling/inpainting can result in smaller reconstruction errors. We also present an information-theoretic analysis, which allows us to quantify the amount of information gained through the different sampling strategies and enables some broader discussion of the main results.