Diffusion Posterior Sampling for General Noisy Inverse Problems
Diffusion Posterior Sampling for General Noisy Inverse Problems
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DOI：
10.48550/arxiv.2209.14687
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Hyungjin Chung;Jeongsol Kim;Michael T. McCann;M. Klasky;J. C. Ye
中科院分区：
文献类型：
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作者：
Hyungjin Chung;Jeongsol Kim;Michael T. McCann;M. Klasky;J. C. Ye
由于扩散模型的高质量重建和易于组合现有迭代求解器，扩散模型最近被研究为强大的生成逆问题求解器。然而，大多数工作都专注于在无噪声环境中解决简单的线性逆问题，这大大低估了现实世界问题的复杂性。在这项工作中，我们扩展了扩散求解器，通过后验采样的近似来有效地处理一般的噪声（非线性）线性逆问题。有趣的是，所得的后验采样方案是扩散采样与流形约束梯度的混合版本，没有严格的测量一致性投影步骤，与之前的研究相比，在噪声环境中产生了更理想的生成路径。我们的方法表明，扩散模型可以结合各种测量噪声统计数据，例如高斯和泊松，并且还可以有效处理噪声非线性逆问题，例如傅立叶相位检索和非均匀去模糊。代码可在 https://github.com/DPS2022/diffusion-posterior-sampling 获取
Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling