Filtered Backprojection Reconstruction with Depth-Dependent Filtering

A direct filtered-backprojection (FBP) reconstruction algorithm is presented for circular cone-beam computed tomography (CB-CT) that allows the filter operation to be applied efficiently with shift-variant band-pass characteristics on the kernel function. Our algorithm is derived from the ramp-filter based FBP method of Feldkamp et al. and obtained by decomposing the ramp filtering into a convolution involving the Hilbert kernel (global operation) and a subsequent differentiation operation (local operation). The differentiation is implemented as a finite difference of two (Hilbert filtered) data samples and carried out as part of the backprojection step. The spacing between the two samples, which defines the low-pass characteristics of the filter operation, can thus be selected individually for each point in the image volume. We here define the sample spacing to follow the magnification of the divergent-beam geometry and thus obtain a novel, depth-dependent filtering algorithm for circular CB-CT. We evaluate this resulting algorithm using computer-simulated CB data and demonstrate that our algorithm yields results where spatial resolution and image noise are distributed much more uniformly over the field-of-view, compared to Feldkamp's approach.