重新思考无需迭代截断的Richardson-Lucy算法：物理驱动的贝叶斯反卷积
Re-thinking Richardson-Lucy without Iteration Cutoffs: Physically Motivated Bayesian Deconvolution
AI总结：
针对Richardson-Lucy反卷积的稀疏偏好和噪声过拟合问题，提出一种物理驱动的贝叶斯反卷积框架，在空间域建模噪声、无需参数调整或迭代截断，产生严格正解且支持并行计算。
摘要：
Richardson-Lucy反卷积被广泛用于恢复由点扩散函数的展宽效应和光子散粒噪声污染而退化的图像，以恢复潜在目标。在实践中，这通过迭代最大化泊松发射似然来实现。然而，已知RL算法偏好稀疏解并过拟合噪声，导致高频伪影。这些伪影的结构对RL迭代次数敏感，且该参数通常通过手动调整以获得推断目标的合理感知质量。过拟合可以通过引入可调正则化器或优化中的其他临时迭代截断来缓解，否则纳入完全逼真的模型可能引入计算瓶颈。为解决这些问题，我们提出了贝叶斯反卷积，一个严谨的反卷积框架，结合了物理精确的图像形成模型，避免了RL方法固有的挑战。我们的方法在满足以下期望的同时实现反卷积：I 反卷积在空间域（而非频率域）执行，其中所有已知噪声源被准确建模并整合，以提供对恢复的潜在目标密度的完整概率分布；II 概率分布的估计不对潜在目标的稀疏性或连续性做假设；III 无监督推断执行并收敛到稳定解，无需用户依赖的参数调整或迭代截断；IV 反卷积产生严格正解；V 实现适合快速、可并行化的计算。
英文摘要：
Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is achieved by iteratively maximizing a Poisson emission likelihood. However, the RL algorithm is known to prefer sparse solutions and overfit noise, leading to high-frequency artifacts. The structure of these artifacts is sensitive to the number of RL iterations, and this parameter is typically hand-tuned to achieve reasonable perceptual quality of the inferred object. Overfitting can be mitigated by introducing tunable regularizers or other ad hoc iteration cutoffs in the optimization as otherwise incorporating fully realistic models can introduce computational bottlenecks. To resolve these problems, we present Bayesian deconvolution, a rigorous deconvolution framework that combines a physically accurate image formation model avoiding the challenges inherent to the RL approach. Our approach achieves deconvolution while satisfying the following desiderata: I deconvolution is performed in the spatial domain (as opposed to the frequency domain) where all known noise sources are accurately modeled and integrated in the spirit of providing full probability distributions over the density of the putative object recovered; II the probability distribution is estimated without making assumptions on the sparsity or continuity of the underlying object; III unsupervised inference is performed and converges to a stable solution with no user-dependent parameter tuning or iteration cutoff; IV deconvolution produces strictly positive solutions; and V implementation is amenable to fast, parallelizable computation.
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