[Central Slice Theorem-based Relationship between 1D-NPS Obtained by the Slit Method and 2D-NPS for CT Images].

Purpose: The method using a numerical slit (slit method) is used commonly to obtain the one-dimensional (1D) noise power spectrum (NPS) in computed tomography. However, the relationship between the 1D-NPS obtained by the slit method and the original two-dimensional (2D) NPS derived by the 2D Fourier transformation has not been elucidated clearly. The purpose of this study was to clarify their relationship based on the well-known central slice theorem (projection slice theorem) and validate it using computer simulation analysis.
Methods: With the application of the central slice theorem, we described that the 1D-NPS obtained by the slit method was equal to the central slice (profile) in the 2D-NPS when we set the slit length to the maximum (i.e. the matrix size of the noise image). To verify this, we generated computer-simulated noise images with the known 2D-NPS (true 2D-NPS). From those images, we obtained the 1D-NPS that was obtained by the slit method and compared it with the central slice in the true 2D-NPS.
Results: When we set the slit length to the maximum, the 1D-NPS obtained by the slit method showed good agreement with the central slice in the true 2D-NPS.
Conclusion: We clarified the relationship between the 1D-NPS obtained by the slit method and the 2D-NPS using a theoretical approach and the computer simulation. We had to maximize the slit length to achieve the accurate measurement of the 1D-NPS using the slit method.