结构驱动反演：求解反问题的新范式
Structure-Driven Inversion: A New Paradigm for Solving Inverse Problems
- School of Earth Sciences, Zhejiang University（浙江大学地球科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出结构驱动反演（SDI）新范式，通过利用数学或物理结构而非迭代搜索求解反问题，涵盖MSDI和PSDI两类方法，作为优化驱动反演的补充与扩展。
AI中文摘要：
反问题主要在优化驱动范式下求解，该范式将问题表述为目标函数最小化，并通过迭代搜索来逼近解。尽管这种方法具有普适性，但在效率、可解释性和多参数解耦方面存在局限。本文提出了一种新范式——结构驱动反演（SDI）。SDI 不采用迭代搜索，而是识别并利用问题的内在结构来构造求解方法。它包含两类结构——数学结构和物理结构——以及两种相应的驱动反演类型：数学结构驱动反演（MSDI）和物理结构驱动反演（PSDI）。目前 MSDI 的代表性方法是数学结构驱动伪逆反演（MSDPII），它通过酉对角化在谱域构造伪逆。目前 PSDI 的代表性方法包括物理结构驱动波形反演成像（PSDWII），它通过虚拟源投影进行反演，以及物理结构驱动反向传播（PSDBP），它通过物理系统类比为深度神经网络实现三种结构投影。SDI 并非对优化驱动反演（ODI）的否定，而是对其的补充和扩展。据作者所知，现有研究尚未将结构驱动反演作为独立范式进行系统阐述；本文旨在填补这一空白。
英文摘要：
Inverse problems are predominantly solved within the optimization-driven paradigm, which formulates the problem as objective-function minimization and approaches the solution by iterative search. Though universal, it suffers from limitations in efficiency, interpretability, and multi-parameter decoupling. This paper proposes a new paradigm---Structure-Driven Inversion (SDI). Instead of iterative search, SDI identifies and exploits the intrinsic structure of the problem to construct a solution method. It has two types of structure---mathematical structure and physical structure---and two corresponding driving inversion types: Mathematical Structure-Driven Inversion (MSDI) and Physical Structure-Driven Inversion (PSDI). The current representative method of MSDI is Mathematical Structure-Driven Pseudo-Inverse Inversion (MSDPII), which constructs a pseudo-inverse in the spectral domain via unitary diagonalization. The current representative methods of PSDI are Physical Structure-Driven Waveform Inversion Imaging (PSDWII), which performs inversion through virtual-source projection, and Physical Structure-Driven Back-Propagation (PSDBP), which implements three structural projections for deep neural networks via physical-system analogy. SDI is not a rejection but a complement and extension of Optimization-Driven Inversion (ODI). To the best of the author's knowledge, no existing study has systematically presented structure-driven inversion as an independent paradigm; this paper aims to fill that gap.
