低剂量影像重建中，高斯代理模型也能达到与泊松模型相当的精度。
Gaussian Surrogates for Poisson Imaging: Some Theoretical and Empirical Results
- 用高斯替代泊松似然，设计两种简化目标函数。
- 在低剂量下，两种代理模型的均方误差接近泊松最大后验估计。
- 适用于计算断层扫描等低剂量医学成像任务的快速重建。
在泊松噪声下的成像反问题中，通常采用基于泊松似然的目标函数，但性能常以均方误差（MSE）评估。这引发一个实际问题：泊松目标对MSE的影响有多大？我们分析了泊松和高斯代理重建目标在泊松噪声下的MSE。在简化的对角模型中，未正则化的泊松最大似然估计在低剂量下会带来显著的高均方误差，而泊松最大后验（MAP）通过正则化缓解了这种不稳定性。随后研究了两种高斯代理目标：一种基于泊松数据的正态近似，具有异方差二次形式；另一种同方差二次形式，对应简单线性估计器。我们证明，这两种代理在低剂量条件下均可实现与泊松MAP相近的均方误差，尽管它们偏离了泊松似然。数值计算断层扫描实验表明，这些结论可推广至理论分析之外的复杂场景。
原文摘要 · Abstract (English)
In imaging inverse problems with Poisson-distributed measurements, it is common to use objectives derived from the Poisson likelihood. But performance is often evaluated by mean squared error (MSE), which raises a practical question: how much does a Poisson objective matter for MSE, even at low dose? We analyze the MSE of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise. In a stylized diagonal model, we show that the unregularized Poisson maximum-likelihood estimator can incur large MSE at low dose, while Poisson MAP mitigates this instability through regularization. We then study two Gaussian surrogate objectives: a heteroscedastic quadratic objective motivated by the normal approximation of Poisson data, and a homoscedastic quadratic objective that yields a simple linear estimator. We show that both surrogates can achieve MSE comparable to Poisson MAP in the low-dose regime, despite departing from the Poisson likelihood. Numerical computed tomography experiments indicate that these conclusions extend beyond the stylized setting of our theoretical analysis.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。