Lucy-Richardson-Rosen algorithm

Lucy-Richardson-Rosen algorithm is an advanced deconvolution algorithm based on Lucy-Richardson algorithm.

Lucy-Richardson algorithm (LRA) is a widely used deconvolution methods. It is available within MATLAB by the syntax 'deconvlucy' [1,2]. However, the convergence rate of LRA is slow requiring hundreds and somtimes thousands of iterations making it not suitable for imaging rapid events. Lucy-Richardson-Rosen algorithm (LRRA) is an advanced version of LRA with rapid convergence requiring only few iterations such as 5 instead of 500 iterations - two orders of magnitude lower. In LRA, there is a forward convolution and a backward correlation [3]. In LRRA, the backward correlation of LRA is replaced by non-linear reconstrution method developed by Prof. Joseph Rosen of Ben Gurion University, Israel [4]. In 'deconvlucy' there is only three inputs - object intensity, PSF and number of iterations. In LRRA, there are five inputs - object intensity, PSF, alpha (between -1 and 1), beta (between -1 and 1) and number of iterations. The values of alpha, beta and number of iterations can be tuned to achieve rapid convergence. Recently, LRRA has been tested against many different optical fields and existing algorithms including Wiener reconstruction method and found that LRRA has better performances for wide range of inputs and scenarios.

References

1. Richardson WH. Bayesian-based iterative method of image restoration. J Opt Soc Am 62, 55–59 (1972).
2. Lucy LB. An iterative technique for the rectification of observed distributions. Astron J 79, 745–754 (1974).
3. Anand V, Han ML, Maksimovic J, Ng SH, Katkus T et al. Singleshot mid-infrared incoherent holography using Lucy–Richardson–Rosen algorithm. Opto-Electron Sci 1, 210006 (2022).
4. Rai MR, Vijayakumar A, Rosen J. Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH). Opt Express 26, 18143–18154 (2018).
5. Xavier API, et. al. Single-Shot 3D Incoherent Imaging Using Deterministic and Random Optical Fields with Lucy–Richardson–Rosen Algorithm. Photonics 10, 987 (2023).