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 one-dimensional wavelet transforms along lines in ${oR^n$, 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.

General harmonic expansions, frames (msc 42C15), Radon transform (msc 44A12), Seismology (msc 86A15)
CWI. Probability, Networks and Algorithms [PNA]

Zuidwijk, R.A. (1997). The wavelet X-ray transform. CWI. Probability, Networks and Algorithms [PNA]. CWI.