Figure 1. Sparsity-based algorithm to enhance the spatial resolution in lens-free digital inline holography (LDIH).

(A) Imaging schematic of a typical LDIH system. The system consists of a light-emitting diode (LED), a pinhole, and an imager. A sample is placed directly above the imager, and the hologram coming from the sample is recorded. (B) Block diagram of the developed algorithm. The measured hologram (y₀) and its numerical reconstruction (x₀) via diffraction theory are used as an initial input. The sparsity-based routine executes an iterative minimization. In each iteration, the algorithm first increases the sparsity of the spatial image (x) by removing the weakest pixel and generates a new hologram (y). The algorithm then minimizes the difference (ε) between y and y₀ by adjusting the pixel values of the spatial image at a given sparsity. The combination of pixel values that produces smallest ε is selected to update x. The iteration stops when ε becomes smaller than the threshold value ε₀, and the final output (x_ε) is obtained.