Inversion of TAU-P transform by simultaneous iterative reconstruction techniques

Simultaneous Iterative Reconstruction Techniques (SIRT) have been investigated for the approximate solution of the problem of finding the function f(x,y) from the integrals R{f(x,y)}(p,τ)=∫_R▒〖f(x,τ+px)dx〗 where τ,p ϵ ℝ. R{f(x,y)}(p,τ) transform has important applications in seismology and is called as tau-p transform. By using the relation between tau-p transform and Radon transform, the relationship between the discrete form of these transforms is obtained. The system of equations derived from the discrete models of these problems are often ill-conditioned and large-scaled, and Landweber, SART, Cimmino, CAV and DROP methods are used for approximating the solution of the resulting equation systems. In addition, examples are given for comparing the approximate solution and exact solution, and the effect of noise error to approximate solution and semi-convergence behavior are shown.