Sinogram bow-tie filtering in FBP PET reconstruction

Low-pass filtering of sinograms in the radial direction is the most common practice to limit noise amplification in filtered back projection (FBP) reconstruction of positron emission tomography studies. Other filtering strategies have been proposed to prevent the loss in resolution due to low-pass radial filters, although results have been diverse. Using the well-known properties of the Fourier transform of a sinogram, the authors defined a binary mask that matches the expected shape of the support region in the Fourier domain of the sinogram ("bow tie"). This mask was smoothed by a convolution with a ten-point Gaussian kernel which not only avoids ringing but also introduces a pre-emphasis at low frequencies. A new filtering scheme for FBP is proposed, comprising this smoothed bow-tie filter combined with a standard radial filter and an axial filter. The authors compared the performance of the bow-tie filtering scheme with that of other previously reported methods: Standard radial filtering, angular filtering, and stackgram-domain filtering. All the quantitative data in the comparisons refer to a baseline reconstruction using a ramp filter only. When using the smallest size of the Gaussian kernel in the stackgram domain, the authors achieved a noise reduction of 33% at the cost of degrading radial and tangential resolutions (14.5% and 16%, respectively, for cubic interpolation). To reduce the noise by 30%, the angular filter produced a larger degradation of contrast (3%) and tangential resolution (46% at 10 mm from the center of the field of view) and showed noticeable artifacts in the form of circular blurring dependent on the distance to the center of the field of view. For a similar noise reduction (33%), the proposed bow-tie filtering scheme yielded optimum results in resolution (gain in radial resolution of 10%) and contrast (1% increase) when compared with any of the other filters alone. Experiments with rodent images showed noticeable image quality enhancement when using the proposed bow-tie filtering scheme.