Ill-conditioned signal restoration and the conjugate gradient method

The application of the conjugate gradient method, an efficient iterative method for solving positive-definite systems of linear equations, to an ill-conditioned signal restoration problem is considered. The author reexamines the application of the conjugate gradient method to such problems based on a recent interpretation of it as a spectral filtering method. An expression is derived for the mean-square error at each iteration based on spectral filtering analysis. This expression is sued to determine an optimal stopping point for the iteration and to help explain the effect of sampling rate changes on the conjugate gradient method