Low-Dose Computed Tomography Filtering Using Geodesic Distances
Due to the concerns related to patient exposure to X-ray, the dosage used in computed tomography must be reduced (Low-dose Computed Tomography - LDCT). One of the effects of LDCT is the degradation in the quality of the final reconstructed image. In this work, we propose a method of filtering LDCT sinograms that are subject to signal-dependent Poisson noise. To filter this type of noise, we use a Bayesian approach, changing the Non-local Means (NLM) algorithm to use geodesic stochastic distances for Gamma distribution, the conjugate prior to Poisson, as a similarity metric between each projection point. Among the geodesic distances evaluated, we found a closed solution for the Shannon entropy for Gamma distributions. We compare our method with the following methods based on NLM: PoissonNLM, Stochastic Poisson NLM, Stochastic Gamma NLM and the original NLM after Anscombe transform. We also compare with BM3D after Anscombe transform. Comparisons are made on the final images reconstructed by the Filtered-Back Projection (FBP) and Projection onto Convex Sets (POCS) methods using the metrics PSNR and SSIM.
J. Z. Liang et al., "Guest editorial low-dose ct: What has been done, and what challenges remain?" IEEE Transactions on Medical Imaging, vol. 36, no. 12, pp. 2409–2416, Dec 2017.
I. A. Elbakri and J. A. Fessler, "Efﬁcient and accurate likelihood for iterative image reconstruction in x-ray computed tomography," in Medical Imaging 2003: Image Processing, M. Sonka and J. M. Fitzpatrick, Eds., vol. 5032, May 2003, pp. 1839–1850.
L. F. Granato, P. E. Cruvinel, F. Cassaro, and S. Crestana, "A tech- nique for improvement of linear attenuation coefﬁcient maps obtained by means of x-ray tomography in multiple energies," in Proceedings SIBGRAPI’98. International Symposium on Computer Graphics, Image Processing, and Vision (Cat. No.98EX237), Oct 1998, pp. 62–68.
R. Gu and A. Dogandzi´c, "Blind x-ray ct image reconstruction from polychromatic poisson measurements," IEEE Transactions on Computational Imaging, vol. 2, no. 2, pp. 150–165, June 2016.
A. Webb and K. Copsey, Statistical Pattern Recognition. Wiley, 2011. Smídl, V. Smidl, and A. Quinn, The Variational Bayes Method
V. in Signal Processing, ser. Signals and Communication Technology. Springer, 2006.
C. R. Rao, "Information and accuracy attainable in the estimation of statistical parameters," Bulletin of Calcutta Mathematical Society, vol. 37, no. 3, pp. 81–91, 1945.
M. L. Men´endez, D. Morales, L. Pardo, and M. Salicrú, "(h, Φ)-entropy differential metric," Applications of Mathematics, vol. 42, no. 2, pp. 81– 98, 1997.
M. Salicrú, M. Men´endez, D. Morales, and L. Pardo, "Asymptotic distribution of (h, φ)-entropies," Communications in Statistics - Theory and Methods, vol. 22, no. 7, pp. 2015–2031, 1993.
R. C. Evangelista, "Abordagens bayesianas nao-locais para ﬁltragem de ruído poisson em imagens tomograﬁcas com baixas taxas de contagem utilizando distˆancias estocásticas," Master’s thesis, Centro Universitário de Campo Limpo Paulista - UNIFACCAMP, 2017.
R. J. Geraldo, L. M. V. Cura, P. E. Cruvinel, and N. D. A. Mascarenhas, "Low dose CT ﬁltering in the image domain using MAP algorithms," IEEE Transactions on Radiation and Plasma Medical Sciences, vol. 1, no. 1, pp. 56–67, 2017.
C. Deledalle, F. Tupin, and L. Denis, "Poisson NL means: Unsupervised non local means for Poisson noise," Proceeding of the International Conference on Image Processing, pp. 801 – 804, 2010.
A. A. Bindilatti and N. D. A. Mascarenhas, "A nonlocal Poisson denois- ing algorithm based on stochastic distances," IEEE Signal Processing Letters, vol. 20, no. 11, pp. 1010–1013, Nov 2013.
K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3-d transform-domain collaborative ﬁltering," IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080–2095, 2007.
F. V. Salina and N. D. A. Mascarenhas, "A hybrid estimation theoretic- pocs method for tomographic image reconstruction," in XVIII Brazilian Symposium on Computer Graphics and Image Processing (SIB- GRAPI’05), Oct 2005, pp. 220–224.
Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, April 2004.
D. A. Góes and N. D. Mascarenhas, "Poisson denoising under a ´ Bayesian nonlocal approach using geodesic distances with low-dose CT applications," Digital Signal Processing, vol. 106, p. 102835, Nov 2020.