Developing variants of the Lucy–Richardson algorithm for coded aperture imaging: tutorial

Deconvolution methods, originally developed for image deblurring, are foundational to coded aperture imaging (CAI) technologies. Among these, the Lucy-Richardson algorithm (LRA), first introduced over half a century ago, has seen renewed interest in CAI applications in recent years. Uniquely, LRA incorporates both convolution and cross-correlation operations, with the latter effectively functioning as an internal deconvolution step, offering a versatile platform for innovation. This tutorial presents the fundamentals of CAI alongside a detailed formulation of LRA. Strategies for enhancing LRA performance through modifications to the cross-correlation step are explored in depth. Both established variants, such as LRA with power-law transformation and limited support constraint, the Lucy-Richardson-Rosen algorithm, and novel extensions, including the interlooped LRA, are introduced. Future directions for designing LRA variants tailored to specific imaging scenarios are also discussed. Step-by-step MATLAB code examples are provided to guide researchers in developing custom LRA-based deconvolution approaches for advanced imaging applications.