Multiscale Adaptive Gabor Expansion (MAGE): Improved Detection of Transient Oscillatory Burst Amplitude and Phase

Since Denis Gabors pioneering paper on the discrete Gabor Expansion (Gabor, 1946), time-frequency signal analysis has proven to be an important tool for many fields. In neurophysiology, time-frequency analysis has often been used to characterize and describe transient bursts in local field potential data. However, these transient bursts have a wide range of variable durations, suggesting that a time-frequency-scale dictionary composed of elementary signal "atoms" may prove useful to more accurately match recorded bursts. While overcomplete multiscale dictionaries are useful, generating a sparse code over such dictionaries is a difficult computational problem. Existing adaptive algorithms for discovering a sparse description are slow and computationally intensive. Here we describe the Multiscale Adaptive Gabor Expansion (MAGE), which uses an implicit dictionary of parametric time-frequency-scale Gabor atoms to perform fast parameter reassignment to accelerate discovery of a sparse decomposition. Using analytic expressions together with numerical computation, MAGE is a greedy pursuit algorithm similar to Matching Pursuit, restricted to a dictionary of multiscale Gaussian-envelope Gabor atoms. MAGE parameter reassignment is robust in the presence of moderate noise. By expressing a unknown signal as a weighted sum of Gabor atoms, MAGE permits a more accurate estimate of the amplitude and phase of transient bursts than existing methods.