<p>Mean curvature regularization can preserve image contrast while producing artifact-free results. However, high nonlinearity and nonconvexity challenge its optimization. In this paper, we propose a novel variable-splitting method based on bilinear decomposition to solve the mean curvature-based image reconstruction model. We first utilize the bilinear decomposition of the image surface to reformulate the mean curvature model as an equivalent constrained optimization problem, mitigating its nonlinearity. Then, we discretize the reformulated model and develop a proximal alternating direction method of multiplier (ADMM). The proposed method introduces two Lagrange multipliers, and each resulting subproblem is either easily solvable or admits a closed-form solution. We also show that the sequence generated by the proposed algorithm converges to the KKT points of the discretized constraint model under verifiable conditions. Finally, numerical experiments show that the proposed method produces comparable image reconstruction results with some state-of-the-art methods.</p>