Full 3‐D modulation transfer function estimation of tomosynthesis system using modified Richardson‐Lucy deconvolution
Authors: Song Hoondong , Lee Changwoo , Baek Jongduk 
Published: November 2023

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.