Abstract
In this article, we propose an efficient method for solving analysis-l1-TV regularization problems with a multi-step alternating direction method of multipliers (ADMM) approach as the fast solver. Additionally, we apply it to a real-data magnetoen-cephalography (MEG) brain imaging problem as well as to signal reconstruction. In our approach, the inverse problem arising in MEG or signal reconstruction is formulated as an optimization problem which we regularize using a combination of analysis-l1 prior together with a total variation (TV) regularization term. We then formulate an optimization algorithm based on ADMM which can effectively be used to solve the optimization problems. The performance of the algorithm is illustrated in practical scenarios.
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