Sparse Representation and Reconstruction of Signals on Wavelet Modulus Maxima Searching

As a basic requirement of compressed sensing theory, sparse representation requires that a signal is sparse itself or it can be sparsely represented in some orthogonal basis. A new sparse representation algorithm based on modulus maxima is proposed for the signals that are non-sparse themselves and cannot be sparsely represented by wavelet transform. According to the structure of the wavelet transform, the high frequency coefficients of every level could be represented more sparsely via the method of modulus maxima searching. Then the measurement matrix could be applied to the sparse coefficients to obtain the measurement values. Entropy encoding of the measurement values is followed for data compression and transmission. For the decoding, orthogonal matching pursuit algorithm is used for recovering the modulus maxima of every level. Then the original signal is reconstructed by alternating projection algorithm. Compared with the classical compressed sensing algorithm with wavelet transform, simulation results show that since the sparsity of the wavelet coefficients is significantly improved according to our proposed algorithm, the compression ratio could be improved. Also, our proposed algorithm significantly improves the quality of the reconstructed signal, especially for the complex signal.