Projected Barzilai-Borwein Method with Infeasible Iterates for Nonnegative Least-Squares Image Deblurring

We present a non-monotonic gradient descent algorithm with infeasible iterates for the nonnegatively constrained least-squares deblurring of images. The skewness of the intensity values of the deblurred image is used to establish a criterion for when to enforce the nonnegativity constraints. The approach is observed on several test images to either perform comparably to or to outperform a non-monotonic gradient descent approach that does not use infeasible iterates, as well as the gradient projected conjugate gradients algorithm. Our approach is distinguished from the latter by lower memory requirements, making it suitable for use with large, three-dimensional images common in medical imaging.