A Modified Newton Projection Method for ℓ1 -Regularized Least Squares Image Deblurring

In recent years, ℓ1-regularized least squares have become a popular approach to image deblurring due to the edge-preserving property of the ℓ1-norm. In this paper, we consider the nonnegatively constrained quadratic program reformulation of the ℓ1-regularized least squares problem and we propose to solve it by an efficient modified Newton projection method only requiring matrix–vector operations. This approach favors nonnegative solutions without explicitly imposing any constraints in the ℓ1-regularized least squares problem. Experimental results on image deblurring test problems indicate that the developed approach performs well in comparison with state-of-the-art methods.