3D MTF estimation using sphere phantoms for cone-beam computed tomography systems

Purpose: For cone-beam computed tomography (CBCT) systems, we propose a sphere phantom based method to estimate the full three-dimensional (3D) modulation transfer function (MTF).

Methods: The FDK reconstruction of CBCT system in a local region was modeled by a triple convolution operator. Afterward, we calculated the directional projections of ideal and reconstructed sphere phantoms into a two-dimensional (2D) plane for multiple views. To estimate the projected 3D point spread function (PSF), we applied the 2D Richardson-Lucy deconvolution with Tikhonov-Miller (RL-TM). After estimating the projected 3D PSF from multiple views, the full 3D PSF was estimated by performing filtered backprojection. Then, the full 3D MTF was calculated by taking the modulus of the Fourier transform of the estimated 3D PSF. To validate the proposed method, we reconstructed sphere phantoms from simulation and experiment data. We simulated ideal 3D MTFs and compared them with the estimated 3D MTFs along the $f_z$ -, $f_x$ -, and $f_{{45}^{\circ }}$ -directions. The full-width at half-maximum (FWHM) and full-width at tenth-maximum (FWTM) values were compared between ideal and estimated 3D MTFs.

Results: The estimated 3D MTFs from both the simulation and experiment results show qualitative similarity in their shapes with the ideal 3D MTFs; FWHM and FWTM results quantitatively show that the proposed method provides reliable estimation performance. In particular, the estimated 3D MTF in a missing cone region was correctly matched with the corresponding ideal 3D MTF.

Conclusions: In this work, we proposed a full 3D MTF estimation method for CBCT systems. Based on the results, we believe that the proposed method can be used to evaluate the spatial resolution performance of CBCT systems.