Sparse Representation and Reconstruction of Signals Based on the Peak Transform
基于峰值变换的信号稀疏表示及重建

The appearance of Compressed Sensing (CS) has been paid a great deal of attention over the world in the recent years. A basic requirement of CS is that a signal should be sparse or it can be sparsely represented in some orthogonal bases. Based on the Peak Transform (PT), a new algorithm called PTCS algorithm is proposed for the signals (such as the Linear Frequency Modulated signal) that are non-sparse themselves and can not be sparsely represented by wavelet transform. For the peak sequence produced by the Peak Transform, value expansion approach of reversible watermarking is exploited such that the peak sequence can be embedded into the measurements of the signal, which avoids increasing additional points for the transmission. By using the Peak Transform, non-sparse wavelet coefficients can be transformed into sparse coefficients, which greatly improves the reconstruction result of CS. Comparing with the original CS algorithm, simulation results show that the reconstruction results of the proposed PTCS algorithm significantly improves the reconstruction quality of signals.