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.
In wave-front coded imaging system, the phase mask placed in the pupil plane of the imaging system aims to reshape the PSF (point spread function) or OTF (optical transfer function) to realize DOF (depth of field) extension. How to design a suitable phase mask to provide a highly controlled response of system PSF or OTF is crucial to computational imaging application. Traditionally, AF (ambiguity function) is a powerful tool to assess the DOF extension effect generated by phase masks with known phase function. However, in this paper, we investigate an iterative optimization based procedure to recover the unknown phase mask using AF in a backward way. First, a set of desired PSFs or OTFs at different defocus planes is combined together to construct an initial estimate of AF. Second, the corresponding mutual function is calculated through Fourier transform. Third, SVD (singular value decomposition) is applied to the mutual function. Fourth, only the term corresponding to the biggest eigenvalue is kept and inverse Fourier transform is used to generate a new estimate of AF. Fifth, the input desired OTFs are used to update the newly estimated AF. This procedure iterates until the OTFs extracted from the estimated AF are highly consistent with the input ones using the MSE (meansquare-error) as criterion. In the paper, we systematically study this powerful procedure using numerical simulation and investigate the probability of recovering the rectangular non-separable phase masks. After that, experiments are carried out to justify the effectiveness of the procedure.
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