Abstract: We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These inversion formulas are local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R $GRT 0 about a point x to within error $epsilon $GRT 0, we can find $alpha@($epsilon@) $GRT 0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R $PLU $alpha@($epsilon@) about x. We give explicit a priori estimates on the error in the L$+2$/ and L$+$INF$/ norms.!18
展开▼
