这篇论文揭示了压缩传感中可调线性生成先验的理论边界，解释了为什么神经网络先验的可调性在实际应用中有效。
该研究建立了可调线性生成先验在压缩传感中的理论框架。研究证明在无噪声高斯压缩传感中，全维线性先验在整个线性先验家族中达到最小期望重建误差。这一结果与去噪行为形成对比，在去噪中较低复杂度的先验因偏差-方差权衡能获得更低重建误差。该研究表明神经网络先验在压缩传感中的可调性实验优势源于生成模型的非线性特性。
Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing
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.