The sparsity-based approaches have demonstrated promising performance in image processing. In this paper, for better preservation of the salient edge structures of images, we propose an ℓ ₀ + ℓ ₂-norm based analysis model， which requires solving a challenging non-separable ℓ ₀-norm related minimization problem, and we also propose an inexact augmented Lagrangian method with proven convergence to a local minimum. Extensive experiments in image smoothing, including texture removal and context smoothing, show that our method achieves better visual results over various sparsity-based models and the CNN method. Also, experiments on sparse view CT reconstruction further validate the advantage of the proposed method.

基于稀疏性的方法已在图像处理中表现出令人鼓舞的性能。在本文中，为了更好地保存图像的边缘突出的结构，我们提出了一个ℓ ₀ + ℓ ₂范数为基础的分析模型，这需要解决一个具有挑战性的不可分离ℓ ₀范数相关的最小化问题，我们也提出了一个经证明可收敛至局部最小值的不精确增强拉格朗日方法。广泛的图像平滑实验（包括纹理去除和上下文平滑）表明，与基于稀疏模型的各种模型和CNN方法相比，我们的方法可获得更好的视觉效果。此外，在稀疏视图CT重建上的实验进一步验证了该方法的优势。