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 𝓵p-nonconvex minimization model is presented to achieve diverse smoothness of edges. To induce sparsity more strongly than the 𝓵1 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 𝓵p 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.
Many real-world applications in image processing and computer vision require splitting an input image into a cartoon component and a texture component. We propose a nonconvex variational image decomposition model for simultaneously recovering cartoon and texture images. To induce the sparsity of gradient norms of the cartoon image more strongly than the classical total variation regularization, we applied the nonconvex firm penalty function as a regularizer for the cartoon image. The nonconvex firm penalty regularizer function has a better ability to separate the piecewise constant component with neat edges. The G-norm was used as an oscillating prior for the texture image. Converting the proposed optimization model to a constrained problem by variable splitting, we addressed it with the alternating direction method of multipliers. Experimental results and comparisons were given to verify the superiority of existing state-of-the-art methods in terms of correlation, peak signal-to-noise ratio, structural similarity, and visual quality. Finally, we demonstrated the effectiveness of the proposed model by several applications such as image abstraction and pencil sketching, artifact removal, image denoising, image composition, and detail enhancement.
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