The Hessian matrix comprises fidelity and regularization terms. Without a special structure

the inverse Hessian matrix is difficult and expensive to compute. To overcome these shortcomings

a Newton projection iterative algorithm with a block diagonal Hessian matrix is proposed. The fidelity term is described by the L norm. The regularization term is established by considering the bounded variation function as a variable of the compound function. The energy function of the regularization model is established. The regularization model is converted into an augmentation energy function by using the potential function. Constructing preconditioned matrix makes the Hessian matrix diagonal and easy to compute. A retrospective linear search algorithm and an improved Barzilai-Borwein step length update criterion are adopted for complete convergence to prevent the Newton projection iterative algorithm from trapping the local optimal solution. For the problem of image deblurring regularization models easily smoothing edges and producing the stair effect

a new image deblurring model and Newton projection iterative algorithm are proposed. The simulation shows that the problem is fairly solved by the proposed method. Compared with other regularization image deblurring models

the proposed model exhibits better image improvement

such as effectively protecting image edges

alleviating the stair effect

and achieving lower relative error and deviation as well as higher peak signal-to-noise ratio and structural similarity index measure.