Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized into a few bins, measurement statistics can be high, and instrument performance can be well understood. In such circumstances, it is essential to understand the deblurring first without any explicit noise considerations. We employ singular value decomposition for the blurring matrix in a low-count pixel system. A strong blurring may yield a null space for the blurring matrix. Yet, a nonnegativity constraint for images built into the deblurring may help restore null-space content in a high-contrast image with zero or low intensity for a sufficient number of pixels. For low-contrast images, control over null-space content can be achieved through regularization. When regularization is applied, the blurred image is, in practice, restored to one that is still blurred but less than the starting image.

翻译：本文在核物理与高能物理应用的背景下，分析了迭代去模糊方法，特别是带正则化与不带正则化的Richardson-Lucy算法。在这些应用中，概率分布可能被离散化为少量区间，测量统计量可能较高，且仪器性能通常可被充分理解。在此类情况下，首先在不考虑任何显式噪声的条件下理解去模糊过程至关重要。我们针对低计数像素系统中的模糊矩阵采用了奇异值分解。强模糊可能导致模糊矩阵存在零空间。然而，去模糊过程中内置的图像非负约束，可在足够多像素强度为零或较低的高对比度图像中，帮助恢复零空间内容。对于低对比度图像，可通过正则化实现对零空间内容的调控。当应用正则化时，实际中模糊图像被恢复为仍带有模糊但比初始图像模糊程度更低的图像。