Abstract
In this paper, we consider the statistical characteristics of the so-called portal images, which are acquired prior to the radiotherapy treatment, as well as the noise that present the portal imaging systems, in order to analyze whether the well-known noise and image features in other image modalities, such as natural image, can be found in the portal imaging modality. The study is carried out in the spatial image domain, in the Fourier domain, and finally in the wavelet domain. The probability density of the noise in the spatial image domain, the power spectral densities of the image and noise, and the marginal, joint, and conditional statistical distributions of the wavelet coefficients are estimated. Moreover, the statistical dependencies between noise and signal are investigated. The obtained results are compared with practical and useful references, like the characteristics of the natural image and the white noise. Finally, we discuss the implication of the results obtained in several noise reduction methods that operate in the wavelet domain.
Similar content being viewed by others
References
Herman MG, Balter JM, Jaffray DA, McGee KP, Munro P, Shalev S, Van Herk M, Wong JW: Clinical use of electronic portal imaging. Report of AAPM Radiation Therapy Committee Task Group 58. Med Phys 28(5):712–737, 2001
Antonuk LE: Electronic portal imaging devices: a review and historical perspective of contemporary technologies and research. Phys Med Biol 47:R31–R65, 2002
Weaver JB, Xu Y, Healy D, Driscoll J: Filtering noise from images with wavelet transforms. Magn Reson Med 21(2):288–295, 1991
Unser M, Aldroubi A, Laine A: Special issue on wavelets in medical imaging. IEEE Trans Med Imaging, 2003
Donoho DL, Johnstone TM: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3):425–455, 1994
Simoncelli EP, Adelson EH: Noise removal via Bayesian wavelet coring. In Proc. IEEE Internat. Conf. Image Proc. (ICIP): 379–382,1996
Portilla J, Strela V, Wainwright MJ, Simoncelli EP: Image denoising using a scale mixture of Gaussians in the wavelet domain. IEEE Trans Image Process 12(11):1338–1351, 2003
Ferrari RJ, Winsor R: Digital radiographic image denoising via wavelet-based hidden Markov model estimation. J Digit Imaging 18(2):154–167, 2005
González A, Morales J, Verdú R, Larrey J, Sancho JL, Tobarra B: SURE-LET and BLS-GSM wavelet-based denoising algorithms versus linear local Wiener estimator in radiotherapy portal image denoising. In Proc. IFMBE World Congress on Medical Physics and Biomedical Engineering. Springer Berlin Heidelberg, 2009
Bhaudaria H, Dewal M: Efficient denoising technique for CT images to enhance brain hemorrhage segmentation. Journal of Digital Imaging 25:1–10, 2012
Oppenheim AV, Schafer RW, Buck JR: Discrete-time signal processing, 2nd edition. New Jersey: Prentice-Hall, 1999
Simoncelli E, Olshausen B: Natural image statistics and neural representation. Annu Rev Neurosci 24:1193–1216, 2001
Donoho DL, Johnstone TM: Adapting to unknown smoothness via wavelet shrinkage. J Am Stat Assoc 90(432):1200–1224, 1995
Sendur L, Selesnick IW: Bivarite shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans Image Process 50(11):2744–2756, 2002
Stein C: Estimation of the mean of a multivariate normal distribution. Ann Stat 9(6):1135–1151, 1981
Luisier F, Blu T, Unser M: A new SURE approach to image denoising: interscale orthonormal wavelet thresholding. IEEE Trans Image Process 16(3):593–606, 2007
Blu T, Luisier F: The SURE-LET approach to image denoising. IEEE Trans Image Process 16(11):2778–2786, 2007
Delpretti S, Luisier F, Ramani S, Blu T, Unser M: Multiframe sure-let denoising of time lapse fluorescence microscopy images. In Proceedings of ISBI:149–152, 2008
Wainwright MJ, Simoncelli EP, Willsky AS: Random cascades on wavelet trees and their use in modelling and analyzing natural imagery. Appl Comput Harmon Anal 11(1):89–123, 2001
Field DJ: Relations between the statistics of natural images and the response properties of cortical cells. J Opt Soc Am 4:2379–2394, 1987
Ruderman DL, Bialek W: Statistics of natural images: scaling in the woods. Phys Rev Lett 73(6):814–817, 1994
Torralba A, Oliva A: Statistics of natural image categories. Comput Neural Syst 14(3):391–412, 2003
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
González-López, A., Morales-Sánchez, J., Verdú-Monedero, R. et al. Statistical Characterization of Portal Images and Noise from Portal Imaging Systems. J Digit Imaging 26, 457–465 (2013). https://doi.org/10.1007/s10278-012-9516-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10278-012-9516-0