An EM-based approach for compressed sensing using dynamic dictionaries

In the current Compressed Sensing (CS) theory, signal reconstruction depends on presetting an appropriate sparsifying dictionary. For signals characterized by parametric models, this dictionary is known to be a parameterized dictionary of a certain form, but the values of the parameters are difficult to determine. If the parameters are set to a group of uniform grid points, the mismatch between the assumed and the actual sparsifying dictionaries will cause the performance of conventional CS reconstruction methods to degrade considerably. To address this, a CS reconstruction method that utilizes dynamic dictionaries is proposed. By iteratively optimizing dictionary parameters, the method refines the dictionary dynamically during signal reconstruction. To achieve joint sparse recovery and dictionary refinement, the method alternates between steps of signal coefficients estimation and dictionary parameters optimization under the framework of the variational Expectation-Maximization (EM) algorithm. Experimental results demonstrate the effectiveness of the proposed method.