Noise characterization of frequency-distance principle (FDP) restoration filtering

We investigate the propagation of noise via the Bellini attenuation correction method and Frequency-Distance Principle (FDP) restoration filtering technique in SPECT imaging. The Bellini method, a Fourier-domain technique, is an exact solution to the attenuated Radon transform under the constraint of uniform attenuation. The FDP states that points in the object at a specified distance from the source to the center-of-rotation (COR) will contribute predominantly to particular regions of the 2D Fourier transform of the sinogram. Using this frequency distance information, the nonstationary response of the collimator can ideally be deconvolved using an inverse filter. However, in the presence of noise, the FDP filter needs to be regularized in order to control noise amplification caused by the deconvolution. The noise is characterized by calculating the population covariance matrix of the processed projection data and of the reconstructed images for a point object located near the edge of a uniformly attenuating medium. Two different implementational combinations of the Bellini attenuation correction and FDP filtering methods, which we term mirroring and no mirroring, are considered. The results show that the mirroring implementation of Bellini-FDP introduces angular noise correlations into the processed projection data, that are induced by low-pass filtering of the sinogram in the angular direction. Furthermore, mirroring is shown to highly correlate the noise in opposing projection views. The impact on the reconstructed image is the presence of arc-like noise artifacts. In contrast, implementing Bellini-FDP using no mirroring does not result in introducing low-pass angular noise correlations. However, images reconstructed using no mirroring show a higher noise variance relative to the mirroring implementation.