Zhao Hui, Xia JingJing, Zhang Ling, Fan Xuewu
Appl Opt. 2019 May 1;58(13):3630-3638. doi: 10.1364/AO.58.003630.
The Richardson-Lucy (RL) algorithm is a well-known nonlinear restoration method and has been widely applied in the fields of astronomical image restoration, microscopic image restoration, and so on because of its capability of generating high-quality restoration results and potential in realizing super-resolution. However, when being applied to restore the wavefront coded blurry images, the classical RL algorithm converges very slowly and has to be iterated many times before obtaining a satisfactory result, which severely prohibits its real-time application. Vector-extrapolation-based RL algorithm was invented to solve this problem, but the noise amplification increases fast, and additional post-processing is needed to further improve the signal-to-noise ratio. Therefore, in this paper, an improved RL algorithm is proposed by introducing an exponential modified correction term into the framework of the original vector-extrapolation-based RL algorithm. It not only results in a bigger iteration step, which ensures a faster convergence can be obtained, but also the noise amplification is effectively prohibited. Besides that, we design a structure-similarity-index-metric-based stopping criterion, based on which the optimum number of iterations for each color channel is obtained. Experimental results reveal that the total iterations decreases approximately 78.9%, and the restored images demonstrate a superior visual quality without denoising additionally.
理查森 - Lucy（RL）算法是一种著名的非线性恢复方法，因其能够生成高质量的恢复结果以及在实现超分辨率方面的潜力，已广泛应用于天文图像恢复、显微图像恢复等领域。然而，当应用于恢复波前编码模糊图像时，经典的RL算法收敛非常缓慢，必须迭代多次才能获得满意的结果，这严重限制了其实时应用。基于向量外推的RL算法被发明出来解决这个问题，但噪声放大增长很快，需要额外的后处理来进一步提高信噪比。因此，本文通过在基于向量外推的原始RL算法框架中引入指数修正项，提出了一种改进的RL算法。它不仅导致更大的迭代步长，确保能够获得更快的收敛速度，而且有效地抑制了噪声放大。除此之外，我们设计了一种基于结构相似性指数度量的停止准则，基于此获得每个颜色通道的最佳迭代次数。实验结果表明，总迭代次数减少了约78.9%，并且恢复的图像在无需额外去噪的情况下展现出卓越的视觉质量。
