We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyper-parameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multi-coil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.

翻译：我们提出了一种层次贝叶斯学习方法，用于从多个观测向量中推断联合稀疏的参数向量。该模型对每个参数向量使用独立的条件高斯先验，并采用共同的伽马分布超参数来强化联合稀疏性。由此产生的促联合稀疏先验与现有贝叶斯推断方法相结合，生成了一系列新算法。我们的数值实验（包括一项多线圈磁共振成像应用）表明，新方法始终优于常用的层次贝叶斯方法。