基于图像局部梯度L0范数正规化的图像分解算法

针对基于梯度L0范数正规化的变分泛函最优化分解图像时误判噪声梯度为边缘梯度的问题,提出一种基于图像局部梯度的L0范数正规化的图像分解算法。该算法构造了一个由保真函数和正则项构成的适用于图像分解的变分泛函,其中正则项用图像的局部梯度的L0范数进行估计,进而通过求解泛函的最小值,以分解出图像的结构信息(即图像的边缘)。与直接基于图像一阶梯度的L0范数的分解算法相比,该算法可以去除噪声梯度的干扰,从而使分解出的图像边缘中不含有噪声。实验结果表明,该算法在分解图像结构和纹理时,既能很好地把边缘保留在图像结构层中,也可把噪声分解到图像结构层外。

Image decomposition with L0-norm regularization from local gradient

An image decomposition based on minimizing the variational function with L0-norm regularization using local gradient was proposed, with regard to the problem that difference between gradient of the noise and gradient of the edge cannot be discriminated by the typical gradient computed from the first-order derivative. It consisted of fidelity term and regular term, and the regular term was estimated by the L0-norm of local gradient from the first-order derivative. Finally, the base layer, only including edges and excluding noises, was obtained by minimizing the proposed variational function. Compared with the decomposition algorithm with the typical L0 gradient regulation, the proposed algorithm can preserve sharp edges and avoid the impact of noises.