Continuous and discrete wavelet x-ray transform

Robertus A. Zuidwijk

doi:10.1117/12.279696

30 October 1997 Continuous and discrete wavelet x-ray transform

Robertus A. Zuidwijk

Proceedings Volume 3169, Wavelet Applications in Signal and Image Processing V; (1997) https://doi.org/10.1117/12.279696
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Combined use of the X-ray (Radon) transform and the wavelet transform has proved to be useful in application areas such as diagnostic medicine and seismology. In the present paper, the wavelet X-ray transform is introduced. This transform performs 1D wavelet transforms along line in Rⁿ, which are parameterized in the same fashion as for the X-ray transform. It is shown that the transform has the same convenient inversion properties as the wavelet transform. The reconstruction formula receives further attention in order to obtain usable discretizations of the transform. Finally, a connection between the wavelet X-ray transform and the filtered backprojection formula is discussed.

Citation Download Citation

Robertus A. Zuidwijk "Continuous and discrete wavelet x-ray transform", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); https://doi.org/10.1117/12.279696

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