Decomposition of an image into cartoon and texture components is frequently used in many image processing applications. Here, the cartoon component has been characterized by the frequently used total variation norm. However, it becomes very challenging to obtain the texture component due to the varying nature of the texture. In general, the texture component has oscillatory behavior locally or globally. Owing to this oscillatory behavior, the texture component has been characterized via low-rank regularization which is widely used to extract texture component from the image. In the works reported till now, convex nuclear norm has been frequently used as a surrogate of the matrix rank, which is suboptimal because of shrinking each singular value equally, while the non-convex surrogate of the rank treats each singular value adaptively. In this paper, we are introducing a new tightest non-convex surrogate of the rank that assigns different weights to each singular value. The new non-convex image decomposition minimization model provides us cartoon and texture components by minimizing the total variation norm and non-convex function simultaneously. This model can also work best for many image restoration problems such as image deblurring and inpainting. The conventional alternating direction method of multiplier (ADMM) has been exploited as the solver of the non-convex minimization model. The proposed model works well on both globally patterned and natural images. In the experimental section, we demonstrate the outperformance of the proposed model over the state-of-the-art methods.

在许多图像处理应用程序中经常使用将图像分解为卡通和纹理组件。在这里，卡通组件的特点是经常使用的总变异范数。然而，由于纹理的不同性质，获取纹理分量变得非常具有挑战性。通常，纹理分量具有局部或全局的振荡行为。由于这种振荡行为，纹理分量已通过低秩正则化进行表征，该正则化广泛用于从图像中提取纹理分量。在迄今为止报道的工作中，凸核范数经常被用作矩阵秩的代理，由于均等地收缩每个奇异值，这是次优的，而秩的非凸代理自适应地处理每个奇异值。在本文中，我们正在引入一个新的最紧非凸的秩替代物，它为每个奇异值分配不同的权重。新的非凸图像分解最小化模型通过同时最小化总变化范数和非凸函数为我们提供卡通和纹理组件。该模型还可以最有效地解决许多图像恢复问题，例如图像去模糊和修复。传统的交替方向乘法器 (ADMM) 已被用作非凸最小化模型的求解器。所提出的模型适用于全局图案和自然图像。在实验部分，我们展示了所提出的模型优于最先进的方法。