The identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric model of the blur and introduce an 1D state-space model to describe the statistical dependence among the neighboring kernels. We apply a Bayesian approach to estimate the posterior distribution of the kernel parameters given the available data. Since this posterior is intractable for most realistic models, we propose to approximate it through a sequential Monte Carlo approach by processing all data in a sequential and efficient manner. Additionally, we propose a new sampling method to alleviate the particle degeneracy problem, which is present in approximate Bayesian filtering, particularly in challenging concentrated posterior distributions. The considered method allows us to process sequentially image patches at a reasonable computational and memory costs. Moreover, the probabilistic approach we adopt in this paper provides uncertainty quantification which is useful for image restoration. The practical experimental results illustrate the improved estimation performance of our novel approach, demonstrating also the benefits of exploiting the spatial structure the parametric blurs in the considered models.

中文翻译：

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序列空变模糊识别的概率建模和推理

在给定清晰图像及其模糊噪声版本的情况下，识别空间变化模糊的参数是许多应用领域（例如生物显微镜和天文成像）中感兴趣的具有挑战性的逆问题。在本文中，我们考虑模糊的参数模型并引入一维状态空间模型来描述相邻内核之间的统计依赖性。我们应用贝叶斯方法来估计给定可用数据的内核参数的后验分布。由于这种后验对于大多数现实模型来说是难以处理的，我们建议通过以顺序和有效的方式处理所有数据，通过顺序蒙特卡罗方法来近似它。此外，我们提出了一种新的采样方法来缓解粒子简并问题，它存在于近似贝叶斯过滤中，特别是在具有挑战性的集中后验分布中。所考虑的方法允许我们以合理的计算和内存成本顺序处理图像块。此外，我们在本文中采用的概率方法提供了对图像恢复有用的不确定性量化。实际实验结果说明了我们新方法的改进估计性能，也证明了利用所考虑模型中参数模糊的空间结构的好处。我们在本文中采用的概率方法提供了对图像恢复有用的不确定性量化。实际实验结果说明了我们新方法的改进估计性能，也证明了利用所考虑模型中参数模糊的空间结构的好处。我们在本文中采用的概率方法提供了对图像恢复有用的不确定性量化。实际实验结果说明了我们新方法的改进估计性能，也证明了利用所考虑模型中参数模糊的空间结构的好处。