Reconstruction of Non- Stationary Signals with Missing Samples Using S-method and a Gradient Based Reconstruction Algorithm

This paper addresses the reconstruction problem of non-stationary signals with missing samples. The reconstruction is achieved by using concentration measures of time-frequency representations in combination with a gradient-based iterative algorithm. As an example of time-frequency representation, the S-method is used in the proposed approach. The sparsity of the transform domain, needed for a successful reconstruction, is interpreted through the concept of concentration measures, and limits for successful reconstruction are discussed. Several examples with nonstationary signals which exhibit different concentrations in the time-frequency domain illustrate the presented theoretical concepts.