Determination of 3D PSFs from computed tomography reconstructed x‐ray images of spherical objects and the effects of sphere radii

Robert, Normand; Mainprize, James G.; Whyne, Cari

doi:10.1002/mp.13734

Cited by 3 publications

(8 citation statements)

References 18 publications

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“…Of particular interest are the factors that affect the MTF differently in the axial

(x, y)

and longitudinal

(z)

domains and the extent to which a 3D image reconstruction can be considered isotropic [i.e.,

M T F (f_{x}) = M T F (f_{y}) = M T F false(f_{z} false)

]. The 3D presampling MTF can be measured via the sphere phantom (from a single 3D image reconstruction) by analysis at all angles (up to the angle of the null cone, as detailed below) or the 3D post‐sampling MTF can be estimated via R‐L deconvolution of the 3D PSF 26–28 …”

Section: Methodsmentioning

confidence: 99%

“…The 3D presampling MTF can be measured via the sphere phantom (from a single 3D image reconstruction) by analysis at all angles (up to the angle of the null cone, as detailed below) or the 3D post-sampling MTF can be estimated via R-L deconvolution of the 3D PSF. [26][27][28]…”

Section: A5 Interpretation and Implicationsmentioning

confidence: 99%

“…A second category of methodology aims to estimate the 3D PSF and MTF using a spherical test object and deconvolution [e.g., Richardson-Lucy (RL) deconvolution]. [26][27][28] Such methodology assumes that the reconstruction of a spherical stimulus is modeled accurately by 3D convolution of a sphere with the local 3D PSF. For example, Robert et al 28 estimated the 3D PSF using 3D RL deconvolution, yielding the post-sampling PSF with resulting MTF characterized up to the Nyquist frequency of the image reconstruction.…”

Section: Introductionmentioning

confidence: 99%

“…[26][27][28] Such methodology assumes that the reconstruction of a spherical stimulus is modeled accurately by 3D convolution of a sphere with the local 3D PSF. For example, Robert et al 28 estimated the 3D PSF using 3D RL deconvolution, yielding the post-sampling PSF with resulting MTF characterized up to the Nyquist frequency of the image reconstruction. Lee et al 26 estimated the projection of the 3D PSF from multiple views using RL deconvolution with Tikhonov-Miller (TM) regularization, giving projections that can be reconstructed via FBP to estimate the 3D PSF.…”

Section: Introductionmentioning

confidence: 99%

“…A second category of methodology aims to estimate the 3D PSF and MTF using a spherical test object and deconvolution [e.g., Richardson–Lucy (RL) deconvolution] 26–28 . Such methodology assumes that the reconstruction of a spherical stimulus is modeled accurately by 3D convolution of a sphere with the local 3D PSF.…”

Section: Introductionmentioning

confidence: 99%

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Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

Wu¹,

Boone

Hernandez

et al. 2021

Medical Physics

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Purpose The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three‐dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone‐beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two‐dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT. Methods Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi‐wire tool for measurement of the axial plane MTF [denoted as MTF(fr;φ=0∘), where φis the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g., φ = 45°, denoted as MTF(fr;φ=45∘)]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C‐arm with CBCT capability, showing that MTF(fr;φ=45∘) yields an informative one‐dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide “isotropic” resolution was evaluated by quantitative comparison of MTF at various φ. Results All three test tools provided consistent measurement of MTF(fr;φ=0∘), and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane (φ>0∘) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C‐arm system exhibited non‐isotropic spatial resolution with conventional non‐isotropic 1D apodization filters (i.e., frequency cutoff filters) — which is common in CBCT — and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non‐isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D MTF(fr;φ=45∘). Conclusion Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Exper...

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“…Of particular interest are the factors that affect the MTF differently in the axial

(x, y)

and longitudinal

(z)

domains and the extent to which a 3D image reconstruction can be considered isotropic [i.e.,

M T F (f_{x}) = M T F (f_{y}) = M T F false(f_{z} false)

Section: Methodsmentioning

confidence: 99%

Section: A5 Interpretation and Implicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

Wu¹,

Boone

Hernandez

et al. 2021

Medical Physics

View full text Add to dashboard Cite

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

2020

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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.

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Chest tomosynthesis deblurring using CNN with deconvolution layer for vertebrae segmentation

2023

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BackgroundLimited scan angles cause severe distortions and artifacts in reconstructed tomosynthesis images when the Feldkamp‐Davis‐Kress (FDK) algorithm is used for the purpose, which degrades clinical diagnostic performance. These blurring artifacts are fatal in chest tomosynthesis images because precise vertebrae segmentation is crucial for various diagnostic analyses, such as early diagnosis, surgical planning, and injury detection. Moreover, because most spinal pathologies are related to vertebral conditions, the development of methods for accurate and objective vertebrae segmentation in medical images is an important and challenging research area.PurposeThe existing point‐spread‐function‐(PSF)‐based deblurring methods use the same PSF in all sub‐volumes without considering the spatially varying property of tomosynthesis images. This increases the PSF estimation error, thus further degrading the deblurring performance. However, the proposed method estimates the PSF more accurately by using sub‐CNNs that contain a deconvolution layer for each sub‐system, which improves the deblurring performance.MethodsTo minimize the effect of the spatially varying property, the proposed deblurring network architecture comprises four modules: (1) block division module, (2) partial PSF module, (3) deblurring block module, and (4) assembling block module. We compared the proposed DL‐based method with the FDK algorithm, total‐variation iterative reconstruction with GP‐BB (TV‐IR), 3D U‐Net, FBPConvNet, and two‐phase deblurring method. To investigate the deblurring performance of the proposed method, we evaluated its vertebrae segmentation performance by comparing the pixel accuracy (PA), intersection‐over‐union (IoU), and F‐score values of reference images to those of the deblurred images. Also, pixel‐based evaluations of the reference and deblurred images were performed by comparing their root mean squared error (RMSE) and visual information fidelity (VIF) values. In addition, 2D analysis of the deblurred images were performed by artifact spread function (ASF) and full width half maximum (FWHM) of the ASF curve.ResultsThe proposed method was able to recover the original structure significantly, thereby further improving the image quality. The proposed method yielded the best deblurring performance in terms of vertebrae segmentation and similarity. The IoU, F‐score, and VIF values of the chest tomosynthesis images reconstructed using the proposed SV method were 53.5%, 28.7%, and 63.2% higher, respectively, than those of the images reconstructed using the FDK method, and the RMSE value was 80.3% lower. These quantitative results indicate that the proposed method can effectively restore both the vertebrae and the surrounding soft tissue.ConclusionsWe proposed a chest tomosynthesis deblurring technique for vertebrae segmentation by considering the spatially varying property of tomosynthesis systems. The results of quantitative evaluations indicated that the vertebrae segmentation performance of the proposed method was better than those of the existing deblurring methods.

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Determination of 3D PSFs from computed tomography reconstructed x‐ray images of spherical objects and the effects of sphere radii

Cited by 3 publications

References 18 publications

Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

Theory, method, and test tools for determination of 3D MTF characteristics in cone‐beam CT

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

Chest tomosynthesis deblurring using CNN with deconvolution layer for vertebrae segmentation

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