INVERSION-FORMULA AND SINGULARITIES OF THE SOLUTION FOR THE BACKPROJECTION OPERATOR IN TOMOGRAPHY

Let R mu := integral(S2) mu(alpha, alpha . x)d alpha, x is an element of R(n), be the backprojection operator. The range of this operator a s an operator on non-smooth functions R : X := L(0)(infinity) (S-n-1 X R) --> L(loc)(2) (R(n)) is described and formulas for (R)(-1) are d erived. It is proved that the operator R is not injective on X but is injective on the subspace X(e) of X which consists of even functions mu(alpha, p) = mu(-alpha, -p). Singularities of the function (R)(-1) h are studied. Here h is a piecewise-smooth compactly supported functi on. Conditions for mu to have compact support are given. Some applicat ions are considered.