Prior Structure-Based Sparsity Representation for Compressive Signal Feature Recovery

Compressive sampling is a promising solution to reduce required sampling rates for signal reconstruction. In many scenarios, such as cognitive radio and modulation recognition, there are only expecting to acquire useful features rather than original signals. To reconstruct these features from compressive measurements, Compressive Sensing (CS) requires features to be sparse and have a one-dimensional relationship with those measurements. Since most of features are nonlinearly transformed from signals, selecting one with high sparsity and then building a linear mapping between it and measurements become the main challenges. This work proposed a new method to find sparsity representations for signals based on their intra-structure. With this method, two common features, autocorrelation function and fourth order time-varying moment are respectively expressed as another two sparse representations called structure-based sparsity representations. Simulation shows that these representations can work effectively in reducing reconstruction iterations, computing consumption, and memory cost for sensing matrices.