A homotopy regularization method for nonlinear ill-posed problems

We report on a new method for nonlinear ill-posed operator equation in Hilbert spaces. Based on the principle of the homotopy method, a new functional is introduced to replace the Tikhonov functional. The minimizer of this replacement functional will constitute a continuous curve connecting the initial value with the approximate solution of the original problem. Following the curve by using the numerical continuation method, with local linearization as the basic iteration, we can Anally obtain the approximate solution. As a practical application, we present numerical results for the reconstruction of activity function in Single Photon Emission Tomography.