Sparsity-Enhanced Constrained Least-Squares Spectral Analysis with Greedy-FISTA

Abstract

The utilization of the inversion-based algorithm for spectral decomposition using constrained least-squares spectral analysis (CLSSA) facilitates a time–frequency spectrum with higher temporal and frequency resolution. The conventional CLSSA algorithm is solved by optimizing an L2-norm regularized least-squares misfit function using Gaussian elimination, which suffers from intensive computational cost. Instead of solving an L2-norm regularized misfit function, we propose to use an L1-norm regularized objective function to enhance the sparsity of the resulting time–frequency spectra. Then, we utilize a faster, smarter, and greedier algorithm named greedy-FISTA to enhance the computational efficiency. Compared to the short-time Fourier transform, continuous wavelet transform, and the conventional CLSSA method, the sparsity-enhanced CLSSA with the greedy-FISTA is capable of achieving time–frequency spectra with higher resolution but with much less computational cost. The applicability of this sparsity-enhanced CLSSA method is demonstrated through synthetic and real data examples.

Keywords

• least-squares spectral analysis
• FISTA
• time–frequency spectrum