Iterative least squares estimators in nonlinear image restoration

摘要

The concept of iterative least squares estimation as applied to nonlinear image restoration is considered. Regarding the convergence analysis of nonlinear iterative algorithms, the potential of the global convergence theorem (GCT) is explored. The theoretical analysis is performed on a general class of nonlinear algorithms, which defines a signal-dependent linear mapping of the residual. The descent properties of two normed functions are considered. Furthermore, a procedure for the selection of the iteration parameter is introduced. The steepest descent (SD) iterative approach for the solution of the least squares optimization problem is introduced. The convergence properties of the particular algorithm are readily derived on the basis of the generalized analysis and the GCT. The factors that affect the convergence rate of the SD algorithm are thoroughly studied. In the case of the SD algorithm, structural modifications are proposed, and two hybrid-SD algorithms attain convergence in a more uniform fashion with respect to their entries. In general, the algorithms achieve larger convergence rates than the conventional SD technique.