Compressed sensing to short duration voltage variation signal sparse in redundant dictionary

Compressed sensing (CS) is a novel data acquisition method that makes full use of the sparsity of signal. This paper presents a number of results regarding the construction of redundant dictionary for short duration voltage variation (SDVV) signal compressed sensing. The redundant dictionary was the union of three orthonormal bases: Discrete Fourier Transform (DFT), db1 wavelet transform (WT) and db4 WT bases. To getting a small number of measurements, the Gaussian random matrix was chosen for linear non-adaptive measurements of SDVV signals, due to its small restricted isometry constants. The orthogonal matching pursuit, a kind of greedy algorithms, was used for reconstruction finally. Numerical experiments showed that the compression results obtained using the CS concept based on redundant dictionary are better than that those using the orthonormal bases such as DFT and WT bases. The SNR of recovered signals were higher than 25dB in the redundant dictionary, while fewer iterations were used with respected to the orthonormal bases.