This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.

本研究解决了压缩感知中的基本线性逆问题，提出了一种新型的正则化生成先验。该方法结合了经典字典基础的压缩感知思想与稀疏贝叶斯学习，旨在通过少量压缩和噪声数据样本进行学习，有效地进行不确定性量化，且无需优化算法解决逆问题。

稀疏贝叶斯生成建模用于压缩感知