High-resolution imaging of densely connected samples such as pathology slides using digital in-line holographic microscopy requires the acquisition of several holograms, e.g., at >6–8 different sample-to-sensor distances, to achieve robust phase recovery and coherent imaging of specimen. Reducing the number of these holographic measurements would normally result in reconstruction artifacts and loss of image quality, which would be detrimental especially for biomedical and diagnostics-related applications. Inspired by the fact that most natural images are sparse in some domain, here we introduce a sparsity-based phase reconstruction technique implemented in wavelet domain to achieve at least 2-fold reduction in the number of holographic measurements for coherent imaging of densely connected samples with minimal impact on the reconstructed image quality, quantified using a structural similarity index. We demonstrated the success of this approach by imaging Papanicolaou smears and breast cancer tissue slides over a large field-of-view of ~20 mm2 using 2 in-line holograms that are acquired at different sample-to-sensor distances and processed using sparsity-based multi-height phase recovery. This new phase recovery approach that makes use of sparsity can also be extended to other coherent imaging schemes, involving e.g., multiple illumination angles or wavelengths to increase the throughput and speed of coherent imaging.