Study of reprojection methods in terms of their resolution loss and sampling errors

Two reprojection methods were studied with respect to their resolution loss and sampling errors. The modulation transfer function was used to evaluate the resolution loss, and the residual sum of squares (RSS) of the difference between the reprojected sinogram and the reference sinogram was used to assess the sampling errors. The two methods studied are: area weighted convolution, (AWC) and Gaussian pixel convolution (GPC). For both methods, resolution loss was determined by the reconstruction filter, the linear interpolation in the backprojection, and the convolution kernel. Sampling errors were found to be angle-dependent, and the angular dependence was more pronounced for the GPC. To avoid significant sampling error, the width of the convolution kernel needs to be two times larger than the pixel distance. The large subbinning size of the projection array lead to interpolation error, which is more pronounced for AWC than for GPC. With pixel distance equal to half the sampling distance, the sampling error can be greatly reduced without additional resolution loss