21 March 2016 Sinogram smoothing and interpolation via alternating projections onto the slope and curvature constraints
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Abstract
Reducing the radiation dose in computed tomography (CT) requires reducing the number or the energy of the photons that pass through the patient's body. An image reconstructed from such noisy or undersampled measurements will contain much noise and artifacts that can significantly reduce the diagnostic value of the image. Effective sinogram denoising or interpolation can reduce these noise and artifacts. In this paper, we present a novel approach to sinogram smoothing and interpolation. The proposed method iteratively estimates the local slope and curvature of the sinogam and forces the sinogram to follow the estimated slope and curvature. This is performed by projection onto the set of constraints that define the slope and the curvature. The constraints on the slope and curvature correspond to very simple convex sets. Projection onto these sets have simple analytical solutions. Moreover, these operations are highly parallelizable because the equations defining the slope and curvature constraints for all the points in a sinogram can be summarized as five convex sets, regardless of the length of the sinogram. We apply the proposed method on simulated and real data and examine its effect on the quality of the reconstructed image. Our results show that the proposed method is highly effective and can lead to a substantial improvement in the quality of the images reconstructed from noisy sinogram measurements. A comparison with the K-SVD denoising algorithm shows that the proposed algorithm achieves better results. We suggest that the proposed method can be a useful tool for low-dose CT.
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Davood Karimi, Davood Karimi, Rabab K. Ward, Rabab K. Ward, } "Sinogram smoothing and interpolation via alternating projections onto the slope and curvature constraints", Proc. SPIE 9784, Medical Imaging 2016: Image Processing, 97840M (21 March 2016); doi: 10.1117/12.2216280; https://doi.org/10.1117/12.2216280
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