Performance Evaluation of a Missing Data Recovery Approach Based on Compressive Sensing

In this paper, a Compressive Sensing-based approach is proposed to recover missing data in time series signals. The presented technique is based on the combined application of two mathematical techniques: the Discrete Cosine Transform (DCT) and a ℓ 1 -minimization algorithm. The former allows representing the system under test with reference to a new sparse base, while the latter is one of the possible approaches to solve a Compressive Sensing problem, well-known for the capability of recovering undersampled sparse signals. After presenting the state of the art and the steps characterizing the proposed approach, the recovery performances are tested on real voltage and current Root Mean Square (rms) signals, stored on a database. In particular, the different impact on the recovery of random discontinuous values and wide missing signals is evaluated by means of the Mean Absolute Percentage Error (MAPE).