Error analysis of tomographic reconstructions in the absence of projection data.

Error estimates for tomographic reconstructions (using Fourier transform-based algorithm) are available for cases where projection data are available. These data are used for reconstructions with different filter functions and the reliability of these reconstructions can be checked as per guidelines of those error estimates. There are cases where projection data are large (in gigabytes or terabytes) so storage of these data becomes an issue. It leads to storing of only the reconstructed images. Error estimation in such cases is presented here. Second-level projection data are calculated from the given reconstructed images ('first-level' images). These 'second-level' data are now used to generate 'second-level' reconstructed images. Different filter functions are employed to check the fidelity of these 'second-level' images. This inference is extended to first-level images in view of the characteristics of the convolution operator. This approach is validated with experimental data obtained by the X-ray micro-CT scanner installed at IIT Kanpur. Five specimens (of same material) have been scanned. Data are available in this case thus we have performed a comparative error estimate analysis for the 'first-level' reconstructions (data obtained from CT machine) and second-level reconstructions (data generated from first-level reconstructions). We observe that both approaches show similar outcome. It indicates that error estimates can also be applied to images when data are not available.