Iterative generalized inverse image restoration

Restoration of an image distorted by a linear spatially invariant system can be viewed as a 2-D deconvolution problem. The major difficulties lie in stabilizing the solution of such an ill-posed problem and in the computational burden inherent to the large amount of data involved in realistic image processing. The iterative and recursive Kaczmarz method for solving linear systems of equations is a powerful tool to settle these last ones. But the generalized inverse solution it provides is unstable in presence of noise. A generalization of this method, with a stability and a convergence speed increased, is presented and shown to be an iterative method for computing a regularized solution. This method is applied to images considered as complex functions on IR²to avoid loss of information in problems involving wave equations. Simulated examples of images restoration are given.