We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.
Benedetta Morini, Margherita Porcelli, Raymond H. Chan (2010). A reduced Newton method for constrained linear least-squares problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 233, 2200-2212 [10.1016/j.cam.2009.10.006].
A reduced Newton method for constrained linear least-squares problems
PORCELLI, MARGHERITA;
2010
Abstract
We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
