F. Mehrdoust - Islamic Azad University. Fouman Branch,
M. Salahi - Department of Mathematics, University of Guilan,
M. Ghamgosar - Environmental research institute. ACECR, Guilan Branch,

Least squares problems frequently arise in image deblurring. SVD and TSVD are the classical methods to solve this problem. However, when the coefficient matrix is ill-conditioned, these methods might lead to meaningless solutions. We show that the robust counterpart of the least squares problem is in the form of second order cone program which is solvable efficiently using interior point methods and leads to better solution. Then we consider a new regularized version of the least squares problem which is in the form of a constrained quadratic problem. We considered an unconstrained version of it using the penalty approach and show that the unconstrained problem result to better solutions comparedto the existing algorithms.

Image deblurring, SVD, TSVD, Robust model, Second order cone, Interior point methods,Penalty method