Full 3-D modulation transfer function estimation of tomosynthesis system using modified Richardson-Lucy deconvolution.

BACKGROUND: Tomosynthesis systems are three-dimensional (3-D) medical imaging devices that operate over limited acquisition angles using low radiation dosages. To measure the spatial resolution performance of a tomosynthesis system, the modulation transfer function (MTF) is widely used as a quantitative evaluation metric. PURPOSE: We previously introduced a method to estimate the full 3-D MTF of a cone-beam computed tomography system using two-dimensional (2-D) Richardson-Lucy (RL) deconvolution with Tikhonov-Miller regularization. However, this method can not be applied directly to estimate the 3-D MTF of a tomosynthesis system, since the unique artifacts (i.e., shadow artifacts, spreading tails, directional blurring, and high-level noise) of the system produce several errors that lower the estimation performance. Varying positions of the negative pixels due to shadow artifacts and spreading tails cause inconsistent deconvolution performances at each of the directional projections, and the severe noise in the reconstructed images cause noise amplification during estimation. This work proposes several modifications to the previous method to resolve the inconsistent performance and noise amplification errors to increase the full 3-D MTF estimation accuracy. METHODS: Three modifications were introduced to the 2-D RL deconvolution to prevent estimation errors and improve MTF estimation performance: non-negativity relaxation function, cost function to terminate the iterative process of RL deconvolution, and regularization strength for noise control. To validate the effectiveness of the proposed modifications, we reconstructed sphere phantoms from simulation and experimental tomosynthesis studies in the iso-center and offset-center positions as well as estimated the full 3-D MTFs using the previous and proposed methods. We compared the 3-D render images, central plane images, and center profiles of the estimated 3-D MTFs and calculated the full widths at half and tenth maximum for quantitative evaluation. RESULTS: The previous method cannot estimate the full 3-D MTF of a tomosynthesis system; its inaccurate negative pixel relaxation produces circular-shaped errors, and the mean squared error based simple cost function for termination causes inconsistent estimation at each directional projection to diminish the clear edges of the low-frequency drop and missing sample regions. Noise amplification from lack of noise regularization is also seen in the previous method results. Compared to the previous method, the proposed method shows superior estimation performance at reducing errors in both the simulation and experimental studies regardless of object position. The proposed method preserves the low-frequency drop, missing sample regions from the limited acquisition angles, and missing cone region from the offset-center position; the estimated MTFs also show FWHM and FWTM values close to those of the ideal MTFs than with the previous method. CONCLUSIONS: This work presents a method to estimate the full 3-D MTF of a tomosynthesis system. The proposed modifications prevent circular-shaped errors and noise amplification due to the geometry for limited acquisition angles and high noise levels. Compared to our previous method, the proposed scheme show better performance for estimating the 3-D MTF of the tomosynthesis system.

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 ∘ -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.