Abstract
Objective:
The signal-to-noise ratio in computed tomography (CT) data should be improved by using adaptive noise estimation for level-dependent threshold determination in the wavelet domain.
Method:
The projection data measured in CT and, thus, the slices reconstructed from these data are noisy. For a reliable diagnosis and subsequent image processing, like segmentation, the ratio between relevant tissue contrasts and the noise amplitude must be sufficiently large. By separate reconstructions from disjoint subsets of projections, e.g. even and odd numbered projections, two CT volumes can be computed, which only differ with respect to noise. We show that these images allow a position and orientation adaptive noise estimation for level-dependent threshold determination in the wavelet domain. The computed thresholds are applied to the averaged wavelet coefficients of the input data.
Results:
The final result contains data from the complete set of projections, but shows approximately 50% improvement in signal-to-noise ratio.
Conclusions:
The proposed noise reduction method adapts itself to the noise power in the images and allows for the reduction of spatially varying and oriented noise.
Similar content being viewed by others
References
Borsdorf A, Raupach R and Hornegger J (2006). Wavelet based noise reduction by identification of correlation. In: Franke, K, Müller, K, Nickolay, B, and Schäfer, R (eds) Pattern recognition (DAGM 2006), Lecture notes in computer science, vol 4174, pp 21–30. Springer, Berlin,
Borsdorf A, Raupach R and Hornegger J (2007). Separate CT-reconstruction for orientation and position adaptive wavelet denoising. In: Horsch, A, Deserno, T, Handels, H, Meinzer, H, and Tolxdoff, T (eds) Bildverarbeitung fnr die Medizin 2007, pp 232–236. Springer, Berlin,
Bruder H, Stierstorfer K, McCullough C, Raupach R, Petersilka~M, Grasruck M, Suess C, Ohnesorge B, Flohr T (2006) Design considerations in cardiac CT. In: Flynn M, Hsieh J (eds) Medical imaging 2006: physics of medical imaging. Proceedings of the SPIE, vol 6142, pp 151–163
Buzug T (2004). Einführung in die Computertomographie. Springer, Berlin
Coifman RR, Donoho DL (1995) Translation-invariant de-noising. In: Lecture notes in statistics: wavelets and statistics, vol 103, pp 125–150
Cunningham IA and Reid BK (1992). Signal and noise in modulation transfer function determinations using the slit, wire and edge techniques. Medi Phys 19(4): 1037–1044
Daubechies I (1992). Ten lectures on wavelets. Society for Industrial and Applied Mathematics, Philadelphia
Demirkaya O (2001) Reduction of noise and image artifacts in computed tomography by nonlinear filtration of projection images. In: Sonka M, Hanson KM (eds) Proc SPIE, vol 4322. Medical imaging 2001: image processing, pp 917–923
Donoho DL and Johnstone IM (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3): 425–455
Fessler J, Ficaro E, Clinthorne N and Lange K (1997). Grouped- coordinate ascent algorithms for penalized-likelihoodtransmission image reconstruction. IEEE Trans Med Imaging 16(2): 166–175
Hsieh J (1998). Adaptive streak artifact reduction in computed tomography resulting from excessive X-ray photon noise. Medi Phys 25(11): 2139–2147
Kachelrieß M, Watzke O and Kalender WA (2001). Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT. Medi Phys 28(4): 475–490
Kak A, Slanely M (2001) Principles of computerized tomographic imaging. Society for Industrial and Applied Mathematics. http://www.slaney.org/pct/pct-toc.html
Kalender W (2000). Computed tomography. Publics MCD Werbeagentur GmbH, Munich
La Rivire P, Bian J and Vargas P (2006). Penalized-likelihood sinogram restoration for computed tomography. IEEE Trans Med Imaging 25(8): 1022–1036
Li T, Li X, Wang J, Wen J, Lu H, Hsieh J and Liang Z (2004). Nonlinear sinogram smoothing for low-dose X-ray CT. IEEE Trans Nuclear Sci 51(5): 2505–2512
Lu H, Li X, Li L, Chen D, Xing Y, Hsieh J, Liang Z (2003) Adaptive noise reduction toward low-dose computed tomography. In: Yaffe MJ, Antonuk LE (eds) Medical imaging 2003: physics of medical imaging. Presented at the society of photo-optical instrumentation engineers (SPIE) conference, vol 5030, pp 759–766
Mallat SG (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7): 674–693
Mathworks Inc (2006) Wavelet Toolbox. http://www.mathworks.com/products/wavelet/
Rust GF, Aurich V, Reiser M (2002) Noise/dose reduction and image improvements in screening virtual colonoscopy with tube currents of 20 mAs with nonlinear Gaussian filter chains. In: Clough AV, Chen CT (eds) Proc SPIE, vol 4683. Medical imaging 2002: physiology and function from multidimensional images, pp 186–197
Stierstorfer K, Flohr T and Bruder H (2002). Segmented multiple plane reconstruction: a novel approximate reconstruction scheme for multi-slice spiral CT. Phys Med Biol 47(4): 2571–2581
Stierstorfer K, Rauscher A, Boese J, Bruder H, Schaller S and Flohr T (2004). Weighted FBP—a simple approximate 3DFBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch. Phys Med Biol 49(11): 2209–2218
Strang G and Nguyen T (1996). Wavelets and Filter Banks. Cambridge Press, Wellesley
Weisstein EW (2006) Variance. From MathWorld—A Wolfram Web resource. http://mathworld.wolfram.com/Variance.html
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Borsdorf, A., Raupach, R. & Hornegger, J. Multiple CT-reconstructions for locally adaptive anisotropic wavelet denoising. Int J CARS 2, 255–264 (2008). https://doi.org/10.1007/s11548-007-0139-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11548-007-0139-8