Investigation on 1-D and 2-D Signal Sparsity Using the Gini Index, L1-Norm and L2-Norm for the Best Sparsity Basis Selection

摘要

Sparsity of signals is a crucial fundamental concept in diverse fields such as compressed sensing, image processing, dictionary learning, blind source separation and sampling theory. The objective of this paper is to present sparsity analysis of 1-D speech signal and 2-D image using Gini index, L1-norm and L2-norm, for the best sparsity basis selection. The DWT families, FFT, DCT, LPC and PCA are used as sparsifying basis. The result shows that the dmey wavelet (1-level decomposition) and bior3.7 wavelet (3-level decomposition) show the greatest value of Gini index for speech. Furthermore, the bior5.5 wavelet shows the lowest value of L1-norm and L2-norm. The DCT exhibits largest Gini index compared to FFT, LPC and PCA for speech. For image signals, the bior3.7 (1-level decomposition) and bior3.1 (3-level decomposition) exhibits highest Gini index. Moreover, the bior3.1 and the bior5.5 wavelet show the lowest value of L1-norm and L2-norm. The PCA exhibits the highest Gini index for image.