Reconstruction from minimum data in helical cone-beam CT

It has been shown that images can be reconstructed exactly from knowledge of data in the Tam window in helical cone-beam CT. Recently, Katsevich proposed an algorithm for image reconstruction from helical cone-beam data. This algorithm, however, requires data more than that within the Tam window. From a practical point of view, any requisition of data additional to that in the Tam window would lead to an increased radiation dosage to patients. In this work, we re-express Katsevich´s algorithm in terms of two terms. The first term can be computed from data only within the Tam window, whereas the second term involves the Fourier transform of the object function. It is unclear whether the calculation of the second term requires data outside the Tam window. However, as we argue qualitatively and demonstrate quantitatively, for practical helical cone-beam configurations, the contribution from the second term to the final reconstruction is negligible. Therefore, in practical situations, images can be accurately obtained from the first term by use of data only within the Tam window, thus allowing potential reduction of radiation dose to the patients.