Efficient detrending of uniform images for accurate determination of the noise power spectrum at low frequencies

Abstract

The noise power spectrum (NPS) of a digital x-ray imaging device is usually estimated from the average of periodograms of regions of interest (ROIs) in images obtained with uniform radiation fields. In order to mitigate low frequency trends, present in the images and not arising from stochastic processes, detrending methods are applied to the images before being Fourier transformed. The most common of these methods subtracts a second-order polynomial fit from the image. In this work, it is shown that the characteristics of low frequency trends can deviate from the quadratic dependence on spatial coordinates. This results in large residual trends that give rise to important correlations in the detrended images and produce an inaccurate rise of the NPS calculations at low frequencies. A new detrending method of uniform images is presented. The method operates in the subbands of a wavelet transform, removing the low frequency contents of the uniform image. To do this, the approximation subband of the highest level of the wavelet transform is cancelled. The effect on the NPS calculations for three digital detectors is shown and the importance of the parameters of the wavelet transform is discussed. The main result states that the performance of the new method improves those of two polynomial detrending methods commonly used and is close to the performance of the subtraction of uniform exposure images method. Finally, guidelines for the implementation of the procedure, like the number of levels in the wavelet decomposition, are provided. As the number of levels in the wavelet transform increases, the removal of trends is restricted to lower frequencies. The selection of the number of levels should be guided by the shape of the autocorrelation function of the detrended image, which has to resemble the shape expected from the propagation of noise through the imaging chain.