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An important part of the filtered backprojection (FBP) algorithm is the ramp filter. This paper derives the discrete version of the ramp filter in the Fourier domain and studies the windowing effects. When a window function is used to control the noise, the image amplitude will be affected and reduced. A simple remedy is proposed to improve the image accuracy when a window function must be used.
This paper shows that the FBP algorithm is able to provide a solution to a weighted least-squares problem. Therefore, the projection noise model can be included in the FBP reconstruction. Bayesian information can also be incorporated in the FBP reconstruction.
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