用噪声估计分数函数,实现无需重训练的通用信号检测。
Score-Based Ideal Observer Approximation via Denoising Score Matching for Signal-Known-Exactly Detection Tasks

- 基于分数函数重构理想观测器统计量,避免逐图像采样。
- 仅用无信号图像训练网络,即可适配任意已知信号的检测任务。
- 在随机斑块背景模型下逼近理想观测器性能,适用于医学影像等场景。
贝叶斯理想观测器(IO)为二元检测任务提供了理论性能上限,但其测试统计量的解析计算通常不可行。基于马尔可夫链蒙特卡洛(MCMC)的数值方法,包括最近的深度生成模型扩展,通常需要对每张测试图像进行大量后验采样。监督学习也被用于近似IO性能,但这类方法通常针对特定检测任务和信号训练,当任务或信号改变时需重新训练。分数函数(即对数概率密度的梯度)编码了数据分布的局部几何结构,是现代分数生成建模的核心。本文将理想观测器测试统计量重构为分数函数形式,提出分数基理想观测器(SIO)。SIO使用仅在无信号图像上训练的去噪卷积神经网络来估计无信号分数函数。模型训练完成后,可直接用于任意加性信号的检测任务,无需逐图像后验采样或信号特定重训练。数值实验采用具有随机斑块背景的信号已知精确(SKE)检测任务,结果表明所提SIO能紧密逼近理想观测器性能。
原文摘要 · Abstract (English)
The Bayesian Ideal Observer (IO) establishes the theoretical upper bound on task performance for binary detection tasks. However, analytical computation of the IO test statistic is generally intractable. Numerical approaches based on Markov-chain Monte Carlo (MCMC) methods, including their recent deep generative model-based extensions, typically require extensive posterior sampling for each test image. Supervised learning has also been investigated to approximate the IO performance. However, such methods are typically trained for a specific detection task and signal and may require retraining when the task or signal changes. The score function, defined as the gradient of the log probability density, encodes the local geometry of the data distribution and is a fundamental quantity in modern score-based generative modeling. This work reformulates the IO test statistic in terms of the score function and introduces a score-based ideal observer (SIO). The proposed SIO uses a denoising convolutional neural network trained exclusively on signal-absent images to estimate the signal-absent score function. Once trained, the resulting score model can be used to approximate the IO test statistic for detection tasks involving arbitrary additive signals, without per-image posterior sampling or signal-specific retraining. Numerical studies consider a signal-known-exactly (SKE) detection task with a stochastic lumpy-background model. The results demonstrate that the proposed SIO can closely approximate the IO performance.
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