Signal Spectrum Estimation Algorithm Based On Structural Sparsity

Compressed sensing theorem break the traditional sampling theorem. Based on thesparse of signal, the original signal can be reconstructed accurately with fewer samplingpoints. And the structure sparsity of signal which has been proposed recently has beenwidely followed. And its transform domain is constituted by non-zero elements whichaccord with aggregated distribution. Using the characteristics of the signal’s distributioncan achieve better spectrum estimation. But the sparse problem within the sparsitystructure of the signal is often ignored. Based on the above theory and research, theinternal structure sparse of the signal has been study further.Firstly, the theoretical framework and the main content of compressed sensing hadbeen analyzed in this paper, which including the observation matrix, designing the sparsematrix and the reconstruction algorithm of the signal and some important theorems ofcompressed sensing: restricted isometry property and incoherence theorem. Then thestructure sparsity of the signal has been studied.Secondly, structure sparse signals can be reconstructed by the traditional groupsparsity optimization problem based on the structural features. But the problem ofmismatched basis has been ignored. Based on the analysis of the signal’s structure andsparisity, signal estimation algorithm based on block structure and redundant frame hasbeen proposed, which introducing the redundant dictionary to the group-lasso algorithm,and estimating signal by combining coherent inhibition model and frequency interpolation.The experimental results show that, the algorithm reconstructing and estimating thefrequency of the mismatched basis signal with block structure is superior to theconventional signal reconstruction algorithm in both robustness and accuracy, because ofintegrating the advantages of the redundant frame and signal structure.Finally, the sampling rate of the Block sparse-signal can be reduced by using theblock characteristics of the signal, but the sparisity in the block has been ignoredfrequently. When dealing with random signals, according the translation-invariant of thecomplex exponentials, the redundant dictionary is often mapped to the surface of a hypersphere by a polar interpolation. This algorithm will manage the whole frequency, andhave a high estimation precision, but the running time is too long. Based on the aboveissues, the signal and spectrum estimation of block structure based on polar interpolationis proposed in this paper, which combining the block characteristics and polarinterpolation, and removing the non-zero block, therefore the computational complexity isreduced. Simulation results show that the proposed algorithm can effectively reduce thecomputing time and spectrum estimation error, and realize better robustness.