Iterative solutions of multilinear ill-posed problems with an application to medical imaging. (English) Zbl 0957.65050
Summary: We report on a new iterative approach for solving a nonlinear operator equation \(F(x)= y\). Assuming that the operator itself can be decomposed into (or approximated by) a sum of a linear and a bilinear operator, we introduce a two-step iteration scheme based on methods for solving linear equations. For the bilinear Landweber method, convergence results in the weak topology are given. Finally, we present numerical results for the reconstruction of the emission function in single photon emission computed tomography.
MSC:
65J15 | Numerical solutions to equations with nonlinear operators |
65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
47J25 | Iterative procedures involving nonlinear operators |
92C55 | Biomedical imaging and signal processing |