Regularization by conjugate gradient of nonnegatively constrained least squares

In many image deconvolution applications the nonnegativity of the computed solution is required. Conjugate Gradient (CG), often used as a reliable regularization tool, may give solutions with negative entries, particularly evident when large nearly zero plateaus are present. The active constrains set, detected by projection onto the nonnegative quadrant, turns out to be largely incomplete and poor effects on the accuracy of the reconstructed image may occur. In this paper an inner-outer method based on CG is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constrains set. This method appears to be especially suitable for the deconvolution of images having large nearly zero backgrounds. The numerical experimentation validates the effectiveness of the proposed method with respect to widely used classical algorithms for nonnegative reconstruction.