Image smoothing techniques are widely used in computer vision and graphics applications, such as detail enhancement, artifact removal, image denoising and high dynamic range (HDR) tone mapping. In this paper, an 𝓵𝓵pnonconvex minimization model is presented to achieve diverse smoothness of edges. To induce sparsity more strongly than the 𝓵𝓵1 norm regularization, we take the nonconvex arctangent penalty function of the image gradient as the regularization term. To make the model more flexible and effective, we use the 𝓵𝓵p norm function as the fidelity term. The majorization-minimization (MM) algorithm is employed for the proposed nonconvex optimization model. We discuss the convergence of the resulting MM algorithm. Comprehensive experiments and comparisons show that the proposed method is effective in a variety of image processing tasks.