Complex trace analysis provides seismic interpreters with a view to identify the nature of challenging subsurface geologic features. However, the conventional procedure based on the Hilbert transform (HT) is highly sensitive to random noise and sudden frequency variations in seismic data. Generally, conventional filtering methods reduce the spectral bandwidth while stabilizing complex trace analysis, whereas obtaining high-resolution images of multiple thin-bed layers requires wideband data. It is thus a challenging problem to reconcile the conflict between the two purposes, and a powerful signal processing device is required. To overcome the issue, I first introduced the fast sparse S-transform (ST) as a powerful time-frequency decomposition method to improve the windowed Hilbert transform (WHT). Then, in addition to the mixed-norm higher resolution provided by the fast sparse ST, I have developed a novel sparsity-based optimization for window parameters. The process adaptively regularizes sudden changes in frequency content of nonstationary signals with the same computational complexity of the nonoptimized algorithm. The performance of the proposed windowing optimization is compared with those of available methods that have so far been used for adaptivity enhancement of Fourier-based spectral decomposition methods. The final adaptive and sparse version of WHT is used to achieve high-resolution complex trace analysis and address the above-mentioned conflict. The instantaneous complex attributes obtained by the proposed method for several synthetic and real data sets of which multiple thin-bed layers contain wedges, trapped gas reservoirs, and faults are superior to those obtained by WHT via adaptive sparse STFT, robust adaptive WHT, and conventional HT. Potential applications of the adaptive double-sparse ST as a new spectral decomposition method were also evaluated.