联合信号恢复与不确定性量化：基于残差先验变换
Joint Signal Recovery and Uncertainty Quantification via the Residual Prior Transform
AI总结：
本文提出残差先验变换方法，在分层贝叶斯框架下实现信号恢复与不确定性量化，支持多模态数据联合恢复，实验验证其高保真度与稳健性。
摘要：
用于信号恢复的传统先验通常受限于一个假设，即信号变异性类型（如分段常数或线性行为）是已知且固定的。这一假设对于在定义域内表现出不同行为的复杂信号而言是有问题的。最近开发的残差变换算子有效地在LASSO回归框架内减少了这种依赖于变异性的误差。重要的是，它不需要关于底层信号结构的先验信息。本文将残差变换算子重新表述为分层贝叶斯框架中的一种新先验。这样做，它解锁了两个强大的新能力。首先，它实现了原则性的不确定性量化，为恢复的信号提供稳健的置信区间；其次，它为从多模态测量中联合恢复信号提供了一个自然框架，通过连贯地融合来自不同数据源的信息。数值实验表明，残差先验能够从多模态数据中实现高保真度的信号和图像恢复，同时提供稳健的不确定性量化。
英文摘要：
Conventional priors used for signal recovery are often limited by the assumption that the type of a signal's variability, such as piecewise constant or linear behavior, is known and fixed. This assumption is problematic for complex signals that exhibit different behaviors across the domain. The recently developed {\em residual transform operator} effectively reduces such variability-dependent error within the LASSO regression framework. Importantly, it does not require prior information regarding structure of the underlying signal. This paper reformulates the residual transform operator into a new prior within a hierarchical Bayesian framework. In so doing, it unlocks two powerful new capabilities. First, it enables principled uncertainty quantification, providing robust credible intervals for the recovered signal, and second, it provides a natural framework for the joint recovery of signals from multimodal measurements by coherently fusing information from disparate data sources. Numerical experiments demonstrate that the residual prior yields high-fidelity signal and image recovery from multimodal data while providing robust uncertainty quantification.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
