Can the backprojection filtering algorithm be as accurate as the filtered backprojection algorithm?

For many years people have realized that the image reconstructed by the filtered backprojection (FBP) algorithm is more accurate than the image reconstructed by the backprojection filtering (BpjF) algorithm. The FBP algorithm is implemented in two steps: (1) convolve the projections with a kernel function, then (2) backproject the modified projections. The BpjF algorithm is also implemented in two steps: (1) backproject the projections, then (2) filter the backprojected image in the frequency domain with a two-dimensional ramp filter. The major drawback of BpjF is that the mean value of the reconstruction is not correct. This error is caused by the way the two-dimensional discrete ramp-filter is formed by sampling the continuous ramp-filter, which results in zeroing the DC component. The Nyquist Theorem is used to show that this approach of forming a discrete ramp-filter is not accurate and a new method to form the discrete ramp-filter is developed. The newly developed filter is the same as the commonly used discrete ramp-filter except for the DC value and preserves the correct mean value of the image