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The ability to sense, count, and size microscopic and nanoscopic particles is important in air quality monitoring, biomedical diagnostics, and nanomaterials synthesis. Lensfree holographic microscopy is an attractive sensing platform due to its ultra-large field of view, compact form factor, and cost-effective components. Although submicron resolution has been previously demonstrated using lensfree holographic microscopy, the ability to detect individual microscale and nanoscale objects can pose a challenge due to limited signal to noise ratio (SNR). Previously, we have used vapor-deposited nanoscale polymer lenses to boost the SNR in sensing experiments, however this adds experimental complexity and is not compatible with all types of samples. Here we present a computational approach for boosting SNR in lensfree holographic microscopy. This approach optimizes a sparsity-promoting cost function in conjunction with a pixel superresolution method for synthesizing a high resolution hologram out of multiple low-resolution holograms captured at slightly different angles. The resulting high-resolution hologram can be computationally reconstructed to provide an in-focus image of the sample. We find that a sparsity-promoting cost function yields ~8 dB of improvement over conventional pixel superresolution approaches that involve cardinal neighbor regularization, provided that the surface coverage is below ~4%. The impacts of the sparsity-promoting cost function on image resolution and computational time will be presented, as well as a guide to which regularization parameters work best for given target sizes and coverage densities. These computational approaches can be used to extend the limit of detection of lensfree holographic microscopes in sensing applications.
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