具有可调复杂度的潜在生成模型用于压缩感知及其他反问题
Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems
AI总结：
本文提出可调复杂度生成模型，用于提升压缩感知等反问题的重建性能，并通过理论分析和实验验证其有效性。
摘要：
生成模型已经发展为解决反问题的强大先验。这些模型通常使用单一固定复杂度或维度来表示一类自然信号。这可能会产生限制：根据问题的不同，固定复杂度可能导致如果太小则出现高表示误差，或者如果太大则容易过拟合噪声。我们为扩散模型、归一化流和变分自编码器开发了可调复杂度先验，利用嵌套丢弃。在包括压缩感知、修复、去噪和相位检索在内的任务中，我们证明经验上可调先验在降低重建误差方面始终优于固定复杂度基线。在线性去噪设置中，我们提供了一种理论分析，明确说明了最优调节参数如何依赖于噪声和模型结构。这项工作展示了可调复杂度生成先验的潜力，并推动了支持理论的发展以及在广泛反问题中的应用。
英文摘要：
Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.
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。
