Conventional microscopy has been a revolutionary tool for biomedical applications since its invention several centuries ago. Ability to non-destructively observe very fine details of biological objects in real time enabled to answer many important questions about their structures and functions. Unfortunately, most of these advance microscopes are complex, bulky, expensive, and/or hard to operate, so they could not reach beyond the walls of well-equipped laboratories. Recent improvements in optoelectronic components and computational methods allow creating imaging systems that better fulfill the specific needs of clinics or research related biomedical applications. In this respect, lensfree computational microscopy aims to replace bulky and expensive optical components with compact and cost-effective alternatives through the use of computation, which can be particularly useful for lab-on-a-chip platforms as well as imaging applications in low-resource settings. Several high-throughput on-chip platforms are built with this approach for applications including, but not limited to, cytometry, micro-array imaging, rare cell analysis, telemedicine, and water quality screening.-
The lack of optical complexity in these lensfree on-chip imaging platforms is compensated by using computational techniques. These computational methods are utilized for various purposes in coherent, incoherent and fluorescent on-chip imaging platforms e.g. improving the spatial resolution, to undo the light diffraction without using lenses, localization of objects in a large volume and retrieval of the phase or the color/spectral content of the objects.,  For instance, pixel super resolution approaches based on source shifting are used in lensfree imaging platforms to prevent under sampling, Bayer pattern, and aliasing artifacts. Another method, iterative phase retrieval, is utilized to compensate the lack of lenses by undoing the diffraction and removing the twin image noise of in-line holograms. This technique enables recovering the complex optical field from its intensity measurement(s) by using additional constraints in iterations, such as spatial boundaries and other known properties of objects. Another computational tool employed in lensfree imaging is compressive sensing (or decoding), which is a novel method taking advantage of the fact that natural signals/objects are mostly sparse or compressible in known bases. This inherent property of objects enables better signal recovery when the number of measurement is low, even below the Nyquist rate, and increases the additive noise immunity of the system.