Backprojection filtering for variable orbit fan beam tomography

A backprojection filtering algorithm is presented for variable orbit fan-beam tomography. Expressions for the fan beam projection and backprojection operators are given for a fan-beam geometry with flat detector. The backprojection operator is derived such that the impulse response for the composite of the projection and backprojection operations is equal to l/r if the data are acquired over 360 degrees. The algorithm first backprojects the variable orbit fan-beam projection data using the newly derived backprojector, takes the two-dimensional (2D) Fast Fourier Transform (FFT) of the backprojected image, multiplies the transformed image by the 2D ramp filter function, and finally takes the inverse 2D FFT to obtain the reconstructed image. The backprojection operator includes a factor which is a function of the flux density along the flat detector which is a function of the rate of change of the orbit radius as a function of angle. The algorithm is verified using computer simulations