噪声平面：连接指数与离散度的扩散桥
The Noise Plane: A Diffusion Bridge Across Exponent and Dispersion
AI总结：
本文提出针对Tweedie噪声的统一扩散框架p-Bridge，通过指数条件网络适配不同噪声模型，实验验证其在多类图像去噪任务中具备良好鲁棒性与有效性。
摘要：
基于扩散的去噪通常使用高斯扰动，而传感器噪声遵循多样的依赖于信号的统计规律。本文提出p-Bridge，一种针对Tweedie噪声的、以测量值为索引的统一扩散框架。噪声指数p描述方差与强度的关系，累积测量值ν控制噪声水平，二者共同定义了包含高斯、泊松和伽马模型的噪声平面。随机桥通过独立增量连接测量分布，赋予去噪物理意义，即渐进式测量累积。可指定起始和停止索引，实现从观测测量水平到规定更高水平的恢复。测量叠加产生共享的反向均值更新，结合基于偏差的目标函数学习所需的条件均值。潜在复合泊松-伽马结构支持中间指数的采样。单个指数条件网络可适配不同Tweedie噪声模型，无需为每个指数单独训练。实验表明，指数条件相比固定指数模型提升了跨指数鲁棒性；使用估计的指数时，共享网络的鲁棒性可与神谕选择的5个专家模型相当。在合成图像、FMD荧光显微镜图像和多传感器SAR图像上的实验进一步证明了其在不同依赖信号的噪声 regime 中的有效性。
英文摘要：
Diffusion-based denoising commonly uses Gaussian perturbations, whereas sensor noise follows diverse signal-dependent statistical laws. In this paper, we propose $p$-Bridge, a unified measurement-indexed diffusion framework for Tweedie noise. The noise exponent $p$ describes the variance--intensity relation, while accumulated measurement $ν$ controls the noise level. Together, they define a noise plane that includes Gaussian, Poisson, and Gamma models. The stochastic bridge connects measurement distributions through independent increments, giving denoising a physical interpretation as progressive measurement accumulation. Both the starting and stopping indices can be specified, allowing restoration from an observed measurement level to a prescribed higher level. Measurement superposition yields a shared reverse-mean update, paired with a deviance-based objective for learning the required conditional mean. A latent compound Poisson--Gamma construction enables sampling at intermediate exponents. A single exponent-conditioned network adapts to different Tweedie noise models without separate training for each exponent. Experiments show that exponent conditioning improves cross-exponent robustness over fixed-exponent models. Using estimated exponents, the shared network achieves robustness comparable to an oracle-selected set of five specialist models. Experiments on synthetic images, FMD fluorescence microscopy, and multi-sensor SAR images further demonstrate its effectiveness across different signal-dependent noise regimes.
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