Abstract:
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. The wavelet X-ray transform performs one-dimensional wavelet transforms along lines in R n which are parameterized in the same fashion as for the X-ray transform. The reconstruction formula for this transform gives rise to a continuous family of elementary projections. These projections provide the building blocks of a directional wavelet analysis of functions in several variables. Discrete wavelet X-ray transforms are described which make use of wavelet orthonormal bases and, more generally, of biorthogonal systems of wavelet Riesz bases.
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