Image reconstruction is one of the most exciting borderline science in the last few decades. Many applications have become known such as in diagnostic radiology

nuclear medicine

industry checking and etc. We know that fan-beam projection is a widely used scheme in these applications. One disadvantage of fan-beam projection is the truncation problem in some case which results in ring artifacts in the reconstruction. To resolve this problem

multi focal fan-beam projection is proposed in recent years to avoid the truncation problem and at the same time in the fan-beam projection' s good sensitivity especially for imaging of small organs is maintained. But the famous filering back projection method which is quick and efficient

can not be extended to such projection. In this thesis we advance a new method based on expanding fourier series and regularization technique. The method is as simple as the famous filtering back projection method and its simplified form can be applied to parallel-beam and fan-Beam cases. In implementing it

FFT is used to reduce the time of computation. Through computer simulation

it is found that the new method is noise-insensitivity and can produce accurate reconstruction almost without any visible artifacts when intensifying projection.