The performance of sparse signal recovery (SSR) can be enhanced by exploiting rich temporal correlation in the multiple snapshots of signal of interest. However, existing methods need to transform the temporally correlated multiple measurements SSR problem into its vectorization form, imposing huge computational cost for algorithmic realization. To overcome this drawback, we propose a novel formulation to model the temporal correlation so that variational Bayesian inference (VBI) can be applied to simplify the inference and a novel uncoupling trick is also proposed to reduce the computation. Theoretical and simulation results indicate that our method can bring a considerable computational complexity reduction and achieve a performance improvement for the temporally correlated SSR problem compared to the state of arts time-varying sparse Bayesian learning (TSBL) method.

中文翻译：

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快速变分贝叶斯推理用于暂时相关的稀疏信号恢复

通过在感兴趣的信号的多个快照中利用丰富的时间相关性，可以增强稀疏信号恢复（SSR）的性能。然而，现有方法需要将时间相关的多次测量SSR问题转换为其向量化形式，从而为算法实现带来了巨大的计算成本。为克服此缺点，我们提出了一种新颖的公式来对时间相关性进行建模，以便可以应用变分贝叶斯推理（VBI）来简化推理，并且还提出了一种新颖的解耦技巧以减少计算量。