Dictionaries with separable structure reduce the computational load of sparse coding and learning algorithms and ensure that patterns present in 2D data are not broken by vectorization. We propose an adaptation of the sparse Bayesian learning (SBL) framework for sparse approximation to the 2D separable case. Our algorithm has two stages. In the first, the hierarchical prior model targets the sparsity patterns occurring in each dimension, therefore focusing on the representation structure. The underlying 2D row-column structure of the sparse support is thus recovered via two separate SBL processes. Simulations show that this recovery is obtained in considerably less iterations than the non-separable method, especially in noisy setups. Since we take advantage of the separable structure, each iteration is considerably faster. In the second stage, only few iterations of standard SBL on the reduced support are needed to obtain the signal representation.

In addition to this significant improvement over SBL in numerical complexity, we demonstrate, in a series of tests carried out on synthetic data and images, that the separable formulation results also in comparable accuracy.

具有可分离结构的字典减少了稀疏编码和学习算法的计算量，并确保2D数据中存在的模式不会被矢量化破坏。我们提出了一种稀疏贝叶斯学习（SBL）框架的改编方案，用于对2D可分离情况的稀疏近似。我们的算法有两个阶段。首先，分层先验模型针对每个维度中出现的稀疏模式，因此着眼于表示结构。稀疏支持的底层2D行-列结构因此通过两个单独的SBL过程恢复。仿真表明，与不可分离方法相比，这种恢复获得的迭代次数要少得多，尤其是在嘈杂的设置中。由于我们利用了可分离的结构，因此每次迭代都快得多。在第二阶段

除了在数字复杂度上比SBL有了显着改善之外，我们还通过对合成数据和图像进行的一系列测试证明，可分离的配方也具有相当的精度。