Improved C-arm Computed Tomography for the Early Diagnosis ... · Improved C-arm Computed...

Improved C-arm Computed Tomography for the

Early Diagnosis of Osteoarthritis

22.05.2013

Martin Berger

Pattern Recognition Lab, Dept. of Computer Science

Friedrich-Alexander-University Erlangen-Nuremberg

22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis

Osteoarthritis and Imaging Modalities

● Degeneration of knee cartilage

● Symptoms: pain, stiffness

● Causes: trauma, infection, injury

● Current imaging modalities: MRI, Radiography

● Patient in supine position

● Measure narrowing of joint-space

● Insensitive to early changes

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Taken from: http://www.regenexx.com

Images taken from: www.siemens.com


Stress-Test of the Knee Joint

● Measure cartilage deformation under

weight-bearing conditions

● Use C-arm CT with horizontal trajectory

● Patient standing or in squatting position

● Load simulated, e.g. by backpack

● Outcome: deformation vs. load curve

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Reconstruction Challenges

● Limited rotation angle

● Increased patient motion

● Fast scans

low resolution + noise

● Evaluation of the reconstructed

volumes (No ground truth)

Artis Zee MP system

Pros:

• Freely positionable

• Low-priced

Cons:

• Only 160° rotation angle

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Super-Short-Scans

● Iterative methods popular for

reconstructions from few views

● FBP is fast and well known

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𝜆 ≥ 𝜋 + 2𝛿𝑚𝑎𝑥 Short-Scan:

𝜆 < 𝜋 + 2𝛿𝑚𝑎𝑥 Super-Short-Scan: Iterative (TV) New FBP Method

Thanks for your attention


Methods

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Redundancy Weights

● Redundant rays

𝑔 𝛿, 𝜆 = 𝑔 −𝛿, 𝜋 + 𝜆 + 2𝛿

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𝜆 ≥ 𝜋 + 2𝛿𝑚𝑎𝑥 Short-Scan:

𝜆 < 𝜋 + 2𝛿𝑚𝑎𝑥 Super-Short-Scan:


Compensation Weights

● Scan range: 𝜋 + 𝛿𝑥

● Super-short-scan leads to

missing data

● Compensate missing data by

increasing the weight of spatially

close rays

● Redundancy weights still

needed

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Compensation Weights

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Bilateral Filtering

● Compensation weights can remove low-frequency bias

● Reconstruction still produces streaking artifacts and noise

● Solution: Apply bilateral filter after reconstruction

● Geometric distance: 𝑔1 𝑥′, 𝑦′ = 𝑔 𝑥′, 𝑦′ 𝑇 − 𝑥, 𝑦 𝑇 2, 𝜎𝑔

● Photometric distance: 𝑔2 𝑥′, 𝑦′ = 𝑔( 𝑓 𝑥, 𝑦 − 𝑓 𝑥′, 𝑦′ , 𝜎𝑝)

𝑓𝐵𝐹 𝑥, 𝑦 = 𝑔1 𝑥′, 𝑦′ × 𝑔2(𝑥

′, 𝑦′)

(𝑥′,𝑦′)∈𝑁

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Reconstruction Pipeline

1. Precompute “compensation weights” based on geometry

2. Multiply projection data with “compensation weights”

3. Reconstruct using a conventional FBP approach

4. Apply bilateral filter on reconstructed data

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Evaluation and Results

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Evaluation

● Simulations using the Shepp-Logan phantom

● Geometrical setup

● 640 detector elements of size 0.5mm

● Source to detector distance 500mm

● Fan angle 2𝛿𝑚𝑎𝑥 ≈ 35.5°

● 180 projections in a range of 180° (Short-Scan = 215.5°)

● 5 different reconstructions:

● FBP using redundancy weights

● FBP using redundancy weights + BF

● Iterative with TV regularizer

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● FBP using compensation weights

● FBP using compensation weights + BF


Qualitative Results

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Qualitative Results – Line Profiles

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Quantitative Results

● Error metrics:

● Mean-square-error (MSE)

● Relative root mean-square-error (rRMSE)

● Structural similarity index (SSIM)

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rRMSE MSE SSIM

Redundancy 0.1301 0.0286 0.9528

Redundancy BF 0.1271 0.0273 0.9594

Compensation 0.0673 0.0076 0.9594

Compensation BF 0.0569 0.0055 0.9673

Iterative TV 0.0566 0.0054 0.9777


Further Results: 160° scan range / 20° fan-angle

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Summary / Outlook

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Summary / Outlook

● We propose novel projection data weights, that consider:

● redundant data

● missing data

● The weights remove a low-frequency bias caused by missing data

● Bilateral filtering to remove high-frequency artifacts and noise

● Reconstruction results are comparable to iterative, TV regularized

approach

● Future work:

● Extend concept to cone-beam geometry

● Evaluation on real data

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References

Redundancy Weights

● Parker, D. L. (1982). Optimal short scan convolution reconstruction for fan beam CT. Medical Physics, 9(2), 254–257.

● Silver, M. D. (2000). A method for including redundant data in computed tomography. Medical Physics, 27(4), 773–774.

● Wesarg, S., Ebert, M., & Bortfeld, T. (2002). Parker weights revisited. Medical Physics, 29(3), 372–378.

Super-Short Scan

● Noo, F., Defrise, M., Clackdoyle, R., & Kudo, H. (2002). Image reconstruction from fan-beam projections on less than a short

scan. Physics in medicine and biology, 47(14), 2525–2546.

Iterative vs. FBP

● Bruder, H., Raupach, R., Sunnegardh, J., Sedlmair, M., Stierstorfer, K., & Flohr, T. (2011). Adaptive iterative reconstruction.

Proc. SPIE 7961, Medical Imaging 2011: Physics of Medical Imaging (Vol. 7961, p. 79610J–79610J–12).

● Zeng, G. L. (2012). View-based noise modeling in the filtered backprojection MAP algorithm. Proc. 2nd Intl. Mtg. on image

formation in X-ray CT (pp. 103–106).

● Zeng, G. L., & Zamyatin, A. (2013). A filtered backprojection algorithm with ray-by-ray noise weighting. Medical Physics, 40(3),

031113.

● Zeng, G. L., Li, Y., & Zamyatin, A. (2013). Iterative total-variation reconstruction versus weighted filtered-backprojection

reconstruction with edge-preserving filtering. Physics in Medicine and Biology, 58(10), 3413–3431.

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