On the aliasing artifacts in airect aourier methods

Direct Fourier methods (DFMs) have the advantage of computational efficiency over filtered backprojection (FBP) algorithms. The linogram algorithm and the gridding method are two popular DFMs which can well handle the risky interpolation procedure in the Fourier space. The original implementations of the linogram and the gridding methods both encounter a weighting factor n during discretization. Without careful preprocessing, it will make reconstruction contain severe aliasing artifacts (dishing and dc shift). A substituting weight can be produced via the Fourier transform of the discrete ramp filter. Two benefits can be obtained from such a modification: it mainly avoids the dc shift; and it reduces the dishing artifacts with less computational time (an oversampling factor of two is totally enough).