Digital holographic lens-free imaging is based on recording the diffraction pattern of light after it passes through a specimen and post-processing the recorded diffraction pattern to reconstruct an image of the specimen. If the full, complex-valued wave-front of the diffraction pattern could be recorded then the image reconstruction process would be straight-forward, but unfortunately image sensors typically only record the amplitude of the diffraction pattern but not the phase. As a result, many conventional reconstruction techniques suffer from substantial artifacts and degraded image quality. This paper presents a computationally efficient technique to reconstruct holographic lens-free images based on sparsity, which improves image quality over existing techniques, allows for the possibility of reconstructing images over a 3D volume of focal-depths simultaneously from a single recorded hologram, provides a robust estimate of the missing phase information in the hologram, and automatically identifies the focal depths of the imaged objects in a robust manner.
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