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To eliminate empirical trial-and-error in filtered backprojection (FBP), this work formulates the interaction between frequency-domain filtering and spatial interpolation as a unified cascaded frequency modulation process. The theoretical model demonstrates that the effective reconstruction spectrum is governed by the sequential modulation of projection data by both the filter and the interpolation kernel's continuous frequency response. Validated across numerical benchmarks and synchrotron radiation CT experiments, the framework analytically predicts structural fidelity, spatial resolution, and the operational hierarchy of filter-interpolator pairs in both clean and noisy regimes.
Decades of empirical trial-and-error in tomographic filter-interpolator selection reduce to an exact analytical cascaded frequency model that directly predicts reconstruction fidelity and noise characteristics.
The fidelity of image reconstruction from projections in linear inverse problems, such as tomography, is critically dependent on the synergistic interaction between frequency-domain filtering and spatial-domain interpolation. However, a physical model that can quantitatively describe how these two components cascade interact in the frequency domain and ultimately determine image quality is still lacking to this day. Here, we introduce a unified frequency-domain model that conceptualizes the combined effect of filtering and interpolation in the filtered backprojection (FBP) algorithm as a cascaded modulation process. This model demonstrates that the effective reconstruction spectrum is determined by the original projection data being sequentially modulated by the frequency responses of the filter and the interpolation kernel. Comprehensive numerical simulations and synchrotron radiation CT experiments validate the model, confirming its power to explain the performance hierarchy of classical filter-interpolation pairs under both ideal and noisy conditions. The model successfully predicts key performance characteristics, including spatial resolution and structural fidelity, thereby elucidating the physical principles behind the efficacy of specific combinations. This work establishes a generalizable theoretical foundation for analyzing cascaded systems in linear inverse problems, moving the practice of algorithm selection in computational imaging from empiricism to a principled, physics-based paradigm.