Image super-resolution restoration and enhancement (SR) based on reconstruction is a typically ill-posed and high-dimensional problem

which needs effective regularization to stable the solution. Lately a parametric and regularized blind SR( RPSR) was proposed by Nguyen et al

which has set up a frame work for the blind SR. Under the frame of RPSR

in this paper

an adaptive RPSR(ARPSR) based on image locale smoothing characteristics is put forward

and for the conveniences of computing

an approximate ARPSR is proposed also

by which at first the ARPSR problem is transformed into a weighted combination of two RPSR problems

then the optical blurring and regularization free parameters are estimated by the standard RPSR frame

and then by exploiting the structures of the reordered system matrices

a preconditioner is constructed for the preconditioned conjugate gradient method(PCG) by which the high-resolution image is solved at last. Computational analyses and experimental results with synthetic low-resolution sequences show the improvements of ARPSR to the RPSR frame.