用稀疏贝叶斯生成先验提升压缩感知重建质量
Sparse Bayesian Generative Modeling for Compressive Sensing
- 结合字典学习与稀疏贝叶斯学习，构建强稀疏正则化生成先验
- 仅需少量压缩噪声数据即可训练，无需反向优化求解
- 支持不确定性量化，适合小样本高噪声场景应用
本文针对压缩感知中的基础线性逆问题，提出一种新型的正则化生成先验。该方法融合经典字典基压缩感知与稀疏贝叶斯学习（SBL）思想，实现对稀疏解的强正则化；同时通过条件高斯性设计，保留生成模型对训练数据的适应能力。不同于大多数先进生成模型，本方法仅需少量压缩噪声样本即可训练，且无需优化算法求解逆问题。此外，类似狄利克雷先验网络，模型参数化共轭先验，可支持不确定性量化。理论分析基于变分推断，实验验证涵盖多种可压缩信号类型。
原文摘要 · Abstract (English)
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.
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