Approximations for detection of periodic signals in image sequences

摘要

This article describes our extended and generalized approach to detection of periodic signals in image sequences. These signals appear in a small number of pixels of an image sequence as periodic fluctuations in the temporal domain. Neither the shape of a signal nor its fundamental frequency is assumed to be known, but the fundamental frequency is assumed to be localized in some narrow range. The frame sequences cover only a few periods of each signal under discussion. We consider groups of these signals relative to our sampling operator that is defined by its sampling frequency and integration (exposure) time. For each group the appropriate coherent basis is used: Fourier basis or periodized gaussians. Not unusually, under the sampling operator the signals and basic functions loose periodicity, and the bases loose orthogonality. The problems that arise are treated by some version of matching pursuit. Our approach to signal accumulation from adjacent pixels by spectrum-specific version of principal components is generalized by using projection onto more general class of subspaces. Normally, the computationally expensive processing sketched above is performed for less than 1% of pixels only. The remaining 99% are rejected by simple and fast procedures. The algorithm was tested by processing simulated image sequences, as well as several real ones.