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This paper considers Weber's law and proposes a new non-convex model for images contaminated by Gaussian noise and Rayleigh noise. The alternating direction method of multipliers (abbreviated as ADMM) is a recent popular method that can handle convex and non-convex problems well. This paper compares denoising effect between ADMM and the Euler-Lagrange equation method applied to the non-convex model. The numerical experimental results show that ADMM performs better and has a higher Peak Signal to Noise Ratio.