提出新方法解决可逆图像转换中的不确定性问题，实现更可靠的图像还原。
Tackling Ill-posedness of Reversible Image Conversion with Well-posed Invertible Network
- 构建过定系统并利用非零格拉姆行列式，避免随机变量采样引入的不确定性。
- 设计WIC模块与WIN网络，在多种任务中达到当前最优性能。
- 适合研究可逆图像处理、神经网络逆问题的开发者参考。
可逆图像转换（RIC）因前向转换过程为欠定系统而存在病态问题。尽管使用可逆神经网络（INN），现有方法仍因引入随机采样变量而不可避免地带来不确定性。为解决此难题，本文通过构造具有非零格拉姆行列式的过定系统，建立可靠近似左逆，确保解的良态性。基于此，提出无须随机采样的良态可逆1×1卷积（WIC），并设计WIN-Naïve与融合先进跳跃连接的WIN网络以增强长期记忆。在可逆图像隐藏、图像缩放和去色等任务上，所提方法持续取得领先性能。大量实验验证了方法的有效性，突破现有方案瓶颈，树立新基准。代码已开源：https://github.com/BNU-ERC-ITEA/WIN。
原文摘要 · Abstract (English)
Reversible image conversion (RIC) suffers from ill-posedness issues due to its forward conversion process being considered an underdetermined system. Despite employing invertible neural networks (INN), existing RIC methods intrinsically remain ill-posed as inevitably introducing uncertainty by incorporating randomly sampled variables. To tackle the ill-posedness dilemma, we focus on developing a reliable approximate left inverse for the underdetermined system by constructing an overdetermined system with a non-zero Gram determinant, thus ensuring a well-posed solution. Based on this principle, we propose a well-posed invertible $1\times1$ convolution (WIC), which eliminates the reliance on random variable sampling and enables the development of well-posed invertible networks. Furthermore, we design two innovative networks, WIN-Naïve and WIN, with the latter incorporating advanced skip-connections to enhance long-term memory. Our methods are evaluated across diverse RIC tasks, including reversible image hiding, image rescaling, and image decolorization, consistently achieving state-of-the-art performance. Extensive experiments validate the effectiveness of our approach, demonstrating its ability to overcome the bottlenecks of existing RIC solutions and setting a new benchmark in the field. Codes are available in https://github.com/BNU-ERC-ITEA/WIN.
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