Liu Yiming, Panezai Spozmai, Wang Yutong, Stallinga Sjoerd
Department of Imaging Physics, Delft University of Technology, Delft, The Netherlands.
Nat Commun. 2025 Jan 21;16(1):911. doi: 10.1038/s41467-025-56241-x.
Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent.
理查森-露西（RL）反卷积优化了非相干成像系统中目标估计的似然性。它可以提高对比度，但收敛性较差，并且随着迭代的进行，噪声会增强。我们通过克拉美-罗下界（CRLB）分析发现了这种有问题的收敛行为的根本原因。对于从下方接近衍射极限的空间频率分量，CRLB的解析表达式发散。对于大图像，每个像素的平均噪声方差会发散。这些结果表明不存在似然性的常规最优解，并且RL反卷积必然收敛性不佳。
