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, the control over null-space content may be gained through regularization. When the regularization is applied, the blurred image is, in practice, restored to an image that is still blurred but less than the starting one.

翻译：本文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，在核物理与高能物理应用中的表现。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，且仪器性能通常已被充分掌握。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。我们在低计数像素系统中对模糊矩阵采用奇异值分解。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性约束，可能有助于在足够多像素强度为零或较低的高对比度图像中恢复零空间内容。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。当施加正则化时，实际中被模糊的图像将恢复为仍带有模糊但程度低于原始图像的图像。