It is not easy to reconstruct the geometrical characteristics of the distorted images captured by the devices. One of the most popular optimization methods is fast iterative shrinkage/ thresholding algorithm. In this paper, to deal with its approximation error and the turbulence of the decrease process, an adaptive proximal conjugate gradient (APCG) framework is proposed. It contains three stages. At first stage, a series of adaptive penalty matrices are generated iterate-to-iterate. Second, to trade off the reconstruction accuracy and the computational complexity of the resulting sub-problem, a practical solution is presented, which is characterized by solving the variable ellipsoidal-norm based sub-problem through exploiting the structure of the problem. Third, a correction step is introduced to improve the estimated accuracy. The numerical experiments of the proposed algorithm, in comparison to the favorable state-of-the-art methods, demonstrate the advantages of the proposed method and its potential.