arXiv:2411.00991cs.CVastro-ph.IM2024-11

提出无需调参的贝叶斯去卷积方法,解决传统算法过拟合噪声问题。

Re-thinking Richardson-Lucy without Iteration Cutoffs: Physically Motivated Bayesian Deconvolution

  • 基于物理成像模型,在空间域进行概率化去卷积
  • 无需迭代次数限制,自动收敛到稳定解
  • 适合需要高保真重建且不想调参的科研与工程场景

Richardson-Lucy去卷积广泛用于恢复因点扩散函数展宽和光子散粒噪声导致退化的图像,以还原原始物体。实际中通过迭代最大化泊松发射似然实现,但该算法倾向于稀疏解并过拟合噪声,产生高频伪影。这些伪影结构对迭代次数敏感,通常需人工调参以获得合理视觉质量。可通过引入可调正则项或人为截断迭代缓解过拟合,但完整建模会带来计算瓶颈。为此,我们提出贝叶斯去卷积框架,结合物理准确的图像形成模型,避免RL方法固有缺陷。本方法满足:一、在空间域进行去卷积,精确建模所有已知噪声源,并提供恢复物体密度的完整概率分布;二、概率分布估计不假设底层物体的稀疏性或连续性;三、无监督推断,自动收敛且无需用户调参或迭代截止;四、输出严格正解;五、实现支持快速并行计算。

原文摘要 · Abstract (English)

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.

去卷积贝叶斯推断图像恢复

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