Inter-Looped Lucy-Richardson-Rosen Algorithm for Coded Aperture Imaging : a Tutorial

Deconvolution methods are central to coded aperture imaging, with recent advancements aiming to achieve signal-to-noise ratios comparable to those of direct imaging systems. The Lucy-Richardson-Rosen Algorithm (LRRA), a recent development, combines the classical Lucy-Richardson algorithm (LRA) with Rosen’s non-linear reconstruction (NLR) method. Uniquely, LRA involves both convolution and correlation operations, where the correlation component effectively functions as a form of deconvolution—providing a foundation for further innovation. LRRA improves upon LRA by substituting this correlation step with NLR, leading to significantly enhanced performance. Over the past three years, LRRA has been widely adopted and continuously refined. In this work, I introduce a novel extension: the Inter-looped LRRA (I-LRRA), in which LRRA is recursively embedded within LRA. I present the theoretical basis and simulation results across various optical fields, demonstrating improved performance over NLR and similar performance to LRRA. The concept is presented in a tutorial format, facilitating further exploration by replacing LRA’s correlation step with other deconvolution techniques. MATLAB code is included to support implementation and adaptation for future research.