Parameter Space Reduction Based L2-norm Noise Constrained Estimation for Image Restoration

In this paper, the image restoration is formulated as an l
₂
-norm noise constrained estimation problem. Realizing that the constrained optimization problem is a separable nonlinear least squares problem, we eliminate a part of the parameters from the objective function using the idea of variable projection algorithms. Then, the gradient projection method is used to optimize the reduced parameter space problem. The numerical experiments on image restoration illustrate that the proposed methodology accelerates the convergence rate significantly.