基于修正小波阈值的图像变分分解

Image Variational Decomposition Based on Modified Wavelet Threshold

Daubechies等人(2004)首先提出了图像的变分分解和小波软阈值之间的联系。小波软阈值会对图像边缘造成过度光滑,使重构图像在边缘附近产生吉布斯震荡现象,为克服该问题,本文用具有更高正则性的分段n次多项式小波阈值和指数阈值做图像分解,得到图像分解的变分泛函的近似最小值。当n越大时,图像分解的变分问题的近似最小值越逼近精确最小值。这样得到了图像的变分分解和修正小波阈值之间的联系。实验结果表明该模型用于图像分解的有效性。

The relation of variational image decomposition and wavelet soft threshold was discovered recently by Daubechies and Teschke. A major issue is that thresholded coefficients entail oversmoothing of edges, coefficients set to zero yield Gibbs oscillations in the vicinity of edges, while coefficients remain corrupted generate artifacts. To overcome this problem, piecewise n-degree polynomial threshold and exponential threshold are used to decompose images in this paper, both of which have higher regularity. The near-minimizer of the variational function of image decomposition is obtained. Here, n may be chosen as any positive number and the bigger the degree n is, the better the approximation quality is. Thus, the connection of image variational decomposition and the modified wavelet threshold are obtained. Experimental results demonstrate the effectiveness of the model.