Spectral estimation in unevenly sampled space of periodically expressed microarray time series data

For evenly sampled data, methods based on the classical Fourier periodogram are often used to detect periodically expressed gene. Recently, the Lomb-Scargle algorithm has been applied to unevenly sampled gene expression data for spectral estimation. However, since the Lomb-Scargle method assumes that there is a single stationary sinusoid wave with infinite support, it introduces spurious periodic components in the periodogram for data with a finite length. In this paper, we propose a new spectral estimation algorithm for unevenly sampled gene expression data. The new method is based on signal reconstruction in a shift-invariant signal space, where a direct spectral estimation procedure is developed using the B-spline basis. Experiments on simulated noisy gene expression profiles show that our algorithm is superior to the Lomb-Scargle algorithm and the classical Fourier periodogram based method in detecting periodically expressed genes. We have applied our algorithm to the Plasmodium falciparum and Yeast gene expression data and the results show that the algorithm is able to detect biologically meaningful periodically expressed genes.We have proposed an effective method for identifying periodic genes in unevenly sampled space of microarray time series gene expression data. The method can also be used as an effective tool for gene expression time series interpolation or resampling.Periodic phenomena are widely studied in biology and there are numerous biological applications where periodicities must be detected from experimental biological data. Because the measured data are often non-ideal, efficient algorithms are needed to extract as much information as possible. Spectral estimation has been a classical research topic in digital signal processing and has recently found important applications in DNA microarray time series data analysis. Many spectral estimation methods have been proposed in the past decades, including the modified periodogram, the autoregressive (AR