压缩感知中可调线性生成先验的全模型最优性
Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing
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中文总结 AI 辅助
本文针对压缩感知中可调线性生成先验建立理论，证明无噪高斯场景下全维线性先验达最小期望重建误差，该可调性优势源于神经网络先验的非线性。
中文摘要 AI 辅助
生成模型作为压缩感知等逆问题的先验已得到实验与理论研究。Gunn等人近期研究了复杂度可调的生成先验的应用，该方法会维护一组复杂度各异的生成先验，在重建时可选择特定复杂度，他们通过实验证明，对多种逆问题，适当调整生成先验的复杂度可获得更低的重建误差。本文针对压缩感知中通过奇异值分解自然关联的可调线性生成先验族建立理论，证明在无噪高斯压缩感知中，全维线性先验在所有线性先验族中达到最小期望重建误差，因此在该理想线性无噪场景下，调整到更低复杂度的先验无法提升期望重建误差。该结果与去噪场景形成对比，去噪中因标准偏差-方差权衡，更低复杂度的先验可获得更低重建误差，这表明神经网络先验在压缩感知中可调性的实验优势源于生成模型的非线性特性。
英文摘要
Generative models have been studied experimentally and theoretically as priors for inverse problems such as compressed sensing. Recent work by Gunn et al. studied the use of generative priors with tunable complexity, where a family of generative priors with varying complexity is maintained and a specific complexity can be selected at inversion time. They demonstrated that lower reconstruction errors can be experimentally attained for a variety of inverse problems by appropriately tuning the complexity of the generative prior. In the present paper, we establish theory for compressed sensing in the setting of a tunable family of linear generative priors naturally related through their singular value decompositions. We prove that in noiseless Gaussian compressed sensing, the full-dimensional linear prior attains the minimum expected reconstruction error over the entire family of linear priors. Thus, in this idealized linear noiseless setting, tuning to a lower-complexity prior does not improve the expected reconstruction error. This result is in contract to the behavior of denoising, where lower complexity priors attain lower reconstruction errors due to a standard bias-variance tradeoff. This result indicates that the experimental benefits of tunability in compressed sensing with neural network priors arises due to nonlinearities in the generative models.
发表机构
- Northeastern University（东北大学）
- Khoury College of Computer Sciences（卡尔计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。
