An Identification Approach to Image Deblurring

In this paper we present a new method of reconstructing an image that undergoes a spatially invariant blurring process and is corrupted by noise. The methodology is based on a theory of multidimensional moment problems with rationality constraints. This can be seen as generalized spectral estimation with a finiteness condition, which in turn can be considered a problem in system identification. With noise it becomes an ill-posed deconvolution problem and needs regularization. A Newton solver is developed, and the algorithm is tested on two images under different boundary conditions. These preliminary results show that the proposed method could be a viable alternative to regularized least squares for image deblurring, although more work is needed to perfect the method.