Reconstructions of Analytic Signals via Alternating Direction Method of Multipliers

In this paper, we introduce a sparse reconstruction strategy for analytic signals in Hardy space ${H^2}\left( \mathbb{D} \right)$ where $\mathbb{D}$ denotes the unit disk of the complex plane. The representation strategy is based on the optimization technique which is called Alternating Direction Method of Multipliers (ADMM). The dictionary matrix and discrete signals are investigated. The author also gives two numerical examples to illustrate the idea.