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

Two reprojection methods are studied to their resolution loss and sampling errors. The methods are area weighted convolution (AWC), and Gaussian pixel convolution (GPC). Modulation transfer function (MTF) is used to evaluate the resolution loss, and the residual sum of squares (RSS) of the difference between the reprojected sinogram and a reference sinogram corresponding to infinite sampling is used to assess the sampling errors. The resolution loss is found to be determined by the reconstruction filter, the linear interpolation in the backprojection, and the convolution kernel. Sampling errors are found to be angle-dependent, and the angular dependency is more pronounced for the GPC. To avoid significant sampling errors, the width of the convolution kernel needs to be two times larger than the pixel distance. Large sub-binning size of the projection array leads to interpolation error, which is more pronounced for AWC than for GPC. For the GPC method, with pixel size twice the pixel distance, the sampling error can be greatly reduced. The sampling error can be reduced without additional resolution loss by using a smaller pixel distance