Uncertainties of a window mixing estimator for the noise power spectrum of digital signals

Abstract

The statistical characteristics of several estimators of the noise power spectrum are analysed in this work. Averaged periodogram, Kim’s large subimage and small subimage methods [1] together with windowed periodogram methods using rectangular and Hamming windows and a new window mixing method are studied to obtain their biasing and standard deviation.Sample means and sample standard deviations of the NPS calculations following the different methods are obtained using synthetic images that simulate noise in digital radiography images. In addition, biasing and variance characteristics of the windowed periodograms and the window mixing methods are derived theoretically.Biasing, characteristic of estimators based in periodograms, is eliminated by modifying the periodogram in such a way that it is obtained as the discrete Fourier transform of the unbiased sampled covariance of the signal. Simulations show that Kim’s methods considerably improve the precision of the averaged periodogram, obtaining an important reduction in the sampled standard deviation. Also, the window mixing method, using a convex combination of windowed periodograms with rectangular and Hamming windows, improves the Kim’s methods in terms of standard deviation and has similar biasing.Finally, it is shown that NPS estimators based in the windowed periodogram and in the window mixing methods are unbiased and mean-square consistent, provided that the support of the autocorrelation function of the system PSF is finite.