Abstract: Euler Lagrange equations with Neumann boundary are generated when the functional of optimization problem is solved by calculus.To solve this problem,the L₂ model is discretized by using maximum likelihood estimation,and a discrete L₂ model that can handle free boundaries is obtained.The optimal linear conditions are solved by conjugate gradient method,and the surface to be reconstructed is obtained.The numerical results show that compared with the fast Fourier transform method and Horn-Brook's method,the image boundary obtained by the conjugate gradient method is smoother and more robust.

Key words: conjugate gradient method, gradient reconstruction, triangulation measurement, L₂ model