Improved vector extrapolation based Richardson-Lucy algorithm used for wavefront coded imaging and experimental demonstration

Abstract

Wave-front coding is a mile-stone technique that can be used to greatly extend the DOF (depth of field) of incoherent imaging system. Besides the phase mask design, the digital restoration is very crucial to obtain clear image with largely extended DOF. Richardson-Lucy (RL) algorithm is a kind of nonlinear image restoration method which is based on Poisson noise model and maximum likelihood estimation. Because RL algorithm can generate high quality restoration result and own the capability to realize super-resolution construction, it has been widely applied in the field of astronomy, macroscopic imaging and et.al. However, classical RL algorithm converges very slowly and have to be run many times to achieve an acceptable restoration result when it is applied to wave-front coded imaging system whose point spread function has quite a large support region. Our previously published results demonstrate that at least 60 times iterations are needed for each color channel, which severely prohibits real-time implementation of classical RL algorithm.. Therefore in this manuscript, an improved vector extrapolation based RL algorithm is designed by embedding the modified exponent into the framework of traditional vector extrapolation based RL algorithm. Not only a bigger iteration step indicating a bigger acceleration ratio is obtained, but also the noise amplification is effectively prohibited. Experimental results demonstrate that with the same number of iterations, the restored image corresponding to the improved vector extrapolation based RL algorithm has a better visual quality. At the same time, the structural similarity index (SSIM) is used as a criterion to determine the optimum iterations for each color channel and optimum combinations of algorithm parameters, based on which total iterations for color images are reduced approxiamately 78.9% and visually satisfactory restoration results can be obtained without denoising the restored image further. It could be considered that the work reported in this manuscript paves the way for realization of the embedded processing based real-time wave-front coded imaging in the future.