广义齐型Besov范数约束下的图像分解

Image Decomposition Constrained by Generalized Homogeneous Besov Norm

为了将图像分解为分片光滑的结构部分和振荡部分,提出一种新的变分图像分解模型.该模型利用第二代曲波和局部余弦基分别表征含噪图像中的结构分量和纹理分量,并采用全变差半范约束分片光滑部分的结构性;同时利用Meyer所建议的广义齐型Besov范数对噪声分量进行约束;最后利用基追踪去噪算法对新模型进行迭代求解.理论分析和实验结果表明,该算法对噪声具有较强的鲁棒性,并使边缘和细小的纹理信息保持稳定.

To separate oscillating parts such as texture and noise from piecewise smooth parts, a new variational image decomposition model is presented. The second generation curvelets and local cosine bases are used to represent structure and texture respectively. The total variational semi-norm is added for restricting structure parts. The generalized homogeneous Besov norm proposed by Meyer is used to constrain noisy components. Finally, the basis pursuit denoising algorithm is used to solve the new model. Experiments show that the approach is very robust to noise, and able to maintain edges and textures stably.