Abstract
Approximate entropy (ApEn) is a computable measure of sequential irregularity that is applicable to sequences of numbers of finite length. As such, it may be used to determine how random a sequence of numbers is. We exploit this property to determine the relevance of image information; to determine whether a spatial signal intensity distribution varies in a regular fashion — and is therefore likely to be an image feature or image texture, or is highly random — and likely to be noise. We present an outline of two possible methodologies for creating an ApEn-based noise filter: a modified median filter and a modified anisotropic diffusion scheme. We show that both approaches lead to effective noise reduction in MR images, with improved information-retaining properties when compared with their conventional counterparts.
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References
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12 (1990) 629–639
Catté, F., Lions, P-L., Morel, J-M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. Siam. J. Numer. Anal. 29 (1992) 182–193
Gerig, G., Kübler, O., Kikinis, R., Jolesz, F.A.: Nonlinear anisotropic filtering of MRI data. IEEE Trans. Med. Imag. 11 (1992) 221–232
Pincus, S.M., Huang, W-M.: Approximate entropy: statistical properties and applications. Commun. Statist. Theory Meth. 21 (1992) 3061–3077
Pincus, S.M., Kalman, R.E.: Not all (possibly) “random” sequences are created equal. Proc. Natl. Acad. Sci. USA. 94 (1997) 3513–3518
Pincus, S.M., Singer, B.H.: Randomness and degrees of irregularity. Proc. Natl. Acad. Sci. USA. 93 (1996) 2083–2088
Canny, J.: A computational approach to edge detection. Pattern Anal. Machine Intell. 8 (1986) 679–698
Niessen, W.J., Ter Har Romeny, B.M., Florack, L.M.J., Viergever, M.A.: A general framework for geometry-driven evolution equations. Int. J. Comput. Vision. 21 (1997) 187–205
Bajla, I., Srámek, M.: Nonlinear filtering and fast ray tracing of 3-D image data. IEEE Engineering in Medicine and Biology March/April (1998) 73–80
Sanchez-Ortiz, G.I., Rueckert, D., Burger, P.: Knowledge-based tensor anisotropic diffusion of cardiac MR images. MedIA 3 (1999)
Gonzalez, R.G., Woods, R.E.: Digital image processing. Addison-Wesley (1993)
Chatfield, C.: The analysis of time series. 4th edn. Chapman and Hall, London New York (1989)
Singer, B.H., Pincus, S.: Irregular arrays and randomization. Proc. Natl. Acad. Sci. USA. 95 (1998) 1363–1386
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© 1999 Springer-Verlag Berlin Heidelberg
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Parker, G.J.M., Schnabel, J.A., Barker, G.J. (1999). Nonlinear Smoothing of MR Images Using Approximate Entropy — A Local Measure of Signal Intensity Irregularity. In: Kuba, A., Šáamal, M., Todd-Pokropek, A. (eds) Information Processing in Medical Imaging. IPMI 1999. Lecture Notes in Computer Science, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48714-X_50
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DOI: https://doi.org/10.1007/3-540-48714-X_50
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