手把手教非科班如何用优化方法解成像逆问题
User Manual for Model-based Imaging Inverse Problem
- 用逻辑推理代替数学推导，讲清成像逆问题的求解思路
- 分四步回答：什么是逆问题、为何用优化、怎么解、如何落地
- 适合零基础想深入理解成像反问题的人阅读
本手册旨在为成像逆问题的模型化优化提供详细说明。此类问题通常复杂且具挑战性，尤其对缺乏凸优化或逆问题理论背景的初学者而言。为此，本文以逻辑思考为核心，系统梳理成像逆问题背后的数学原理，而非追求严格的数学表述。手册分为四个部分，分别回答四个关键问题：(1) 成像逆问题是什么？(2) 为何采用优化方法求解？(3) 如何求解优化问题？(4) 如何在真实成像系统中实现优化算法？强调通过提问深化理解，帮助读者建立清晰的解决框架。
原文摘要 · Abstract (English)
This user manual is intended to provide a detailed description on model-based optimization for imaging inverse problem. Theseproblems can be particularly complex and challenging, especially for individuals without prior exposure to convex optimization orinverse problem theory, like myself. In light of this, I am writing this manual to clarify and systematically organize the mathematicalrationale underlying imaging inverse problems. This manual might not be accurate in mathmatical notion but more focus on the logicalthinking on how to solve and proceed to solve the problems. If you want to think deep about something, try to raise questions! Thismanual is seaprated into four sections, aiming to answer the following four questions: (1) What is inverse imaging problem? (2) Why optimization is used to solve the inverse imaging problem? (3) How to solve the optimization problem? (4) How to implement the optimization algorithm in real imaging system?
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