Resolution study on wavelets both in temporal and spectral domain

An improved version of Matching Pursuit Decomposition (MPD), called Fractional Matching Pursuit Decomposition (FMPD), which can solve the lateral instability problem caused by conventional Matching Pursuit Decomposition, is proposed. On synthetic data, including a wedge model and the Dickman field real dataset, FMPD results show better lateral continuity among all the applications than conventional MPD. \ In pursuing better resolution in spectral decomposition, the conventional uncertainty principle is not adequate for application purpose. An alternative definition of uncertainty principle, which could clearly and quantitatively define combined temporal and spectral resolution concerned in spectral decomposition, is presented. According to this, complex uncertainty principle, the lowest limit is still valid if we consider zero mean condition into wavelet selection.