Channelized-Based Denoising Generalized Orthogonal Matching Pursuit for Reconstructing Structural Sparse Signal Under Noise Background

This paper proposed a channelized-based denoising generalized orthogonal matching pursuit algorithm (gOMP) for reconstructing structural sparse signal in engineering application. The algorithm combines the compressive sensing channelization method, the pre-estimation-based adaptive method with the gOMP. By channelizing the observation matrix, the algorithm first eliminates most of the channels that only contain noise with a residual-based detection method. Then, according to a pre-estimated sparsity level, the signal can be accurately and adaptively reconstructed by re-screening the redundant support obtained by the gOMP. The two steps of the algorithm effectively reduce the deterioration of the reconstruction caused by noise, thereby significantly improving the output signal-to-noise ratio (SNR). A mathematical derivation of the reconstruction conditions is given. Also, the computational complexity and the theoretical SNR improvement are discussed. Besides, the upper bound of the reconstruction error in the noise environment is mathematically analyzed. Finally, the experiments verified the performance analysis and detailedly demonstrated the advantages of the proposed algorithm for recovering structural sparsity signals under noise interference. The results show that the proposed scheme considerably outperforms any existing adaptive and denoising greedy algorithm in the sense of the reconstruction accuracy and the output SNR.