This paper presents two novel Bayesian learning recovery algorithms for block sparse signals corresponding to two distinct cases. In the first case, the signals within each block are correlated and the block borders are known, whereas in the second case, the block borders are unknown and the signal elements are uncorrelated. For the first case, the proposed recovery algorithm differs from existing ones in two aspects. First, in each iteration, the optimal block covariances are obtained based on the data estimated in previous iterations. Hence, it does not rely on prior assumptions nor does it restrict the covariance matrices to have a particular structure. Second, the decision to declare a block as zero or non-zero is based on hypothesis testing, which ensures that the probability of erroneous detection is minimized. For the second case, we introduce a new prior model which is characterized by elastic dependencies among neighbouring signal elements. Using this model, we develop a novel Bayesian learning algorithm which iterates between estimating the dependencies among the signal elements and updating the Gaussian prior model. Numerical simulations illustrate the effectiveness of the proposed algorithms.

中文翻译：

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针对已知和未知边界的块稀疏信号的新颖恢复算法


本文提出了两种新颖的贝叶斯学习恢复算法，用于对应两种不同情况的块稀疏信号。在第一种情况下，每个块内的信号是相关的并且块边界是已知的，而在第二种情况下，块边界是未知的并且信号元素是不相关的。对于第一种情况，所提出的恢复算法在两个方面与现有算法不同。首先，在每次迭代中，根据先前迭代中估计的数据获得最佳块协方差。因此，它不依赖于先前的假设，也不限制协方差矩阵具有特定的结构。其次，将块声明为零或非零的决定基于假设检验，这确保了错误检测的概率最小化。对于第二种情况，我们引入了一种新的先验模型，其特征是相邻信号元素之间的弹性依赖性。使用该模型，我们开发了一种新颖的贝叶斯学习算法，该算法在估计信号元素之间的依赖性和更新高斯先验模型之间进行迭代。数值模拟说明了所提出算法的有效性。