The traditional techniques of PET image reconstruction such as the least-squares and the penalty weighted least-squares can obtain high quality image

but they can't suppress the noise well under the limited angle situation.The total variation(TV) was used widely as penalty in image reconstruction

which applied the sparsity prior of image and could accurately reconstruct the image from the limited angle (a small quality of measurement).This article combined the advantages of the weighted least squares and total variation and constructed the objective function based on them

and solved the objective function using the alternate methods.The objective function was decomposed into two simple optimization problems for solving quadratic optimization and total variation regularization

the over relaxation method and the gradient descent method were used to solve these two optimization problems.Simulations using Zubal model were utilized to estimate the qualities of the reconstructed images

the evaluation parameters included CORR

VAR and SNR.The experimental results show the proposed algorithm has better performance in noise suppression and good reconstruction effect under limited angle situations.