变分图像分解，通过极小化能量泛函将图像分解为不同的特征分量，可以被应用到图像的恢复和重建。提出了变分框架下的多尺度图像恢复和重建的思想。基于这种思想，首先提出了一个单参数的（BV ，G ，E ）三元变分分解模型，并且理论分析了参数与不同特征分量的尺度的关系。然后将此模型的参数选为一个二进制序列，得到多尺度的（BV ，G ，E ）变分分解。该多尺度变分分解可以将图像分解为一序列图像结构、纹理和噪声。证明了此多尺度分解的收敛性并且基于对偶理论和交替迭代算法给出了其数值求解方法。最后将提出的多尺度的（BV ，G ，E ）变分分解应用到图像恢复和重建，实验结果证实了理论分析的正确性，显示了将此模型进行图像多尺度恢复和重建的有效性，和与一些其他分解模型相比较的优越性。%By minimizing the energy functional ,we can obtain the variational image decomposition which decomposes image into different characteristic components ,and can be used for image restoration and reconstruction .An idea of multiscale image restoration and reconstruction in the framework of variation is proposed .Based on this idea ,firstly ,a single-parameter (BV ,G ,E ) trituple decomposition model is proposed ,and the relationship between the parameter and the scale of each component is studied the-oretically .And then ,by replacing the parameter with a binary sequence ,we achieve a multiscale (BV ,G ,E) decomposition which can decompose an image into a sequence of image structure ,texture and noise .The convergence of this multiscale decomposition is proved ,and an efficient numerical method based on the duality theory and alternate iteration algorithm is introduced to solve it .At last ,the proposed multiscale (BV ,G ,E ) decomposition is applied for image restoration and reconstruction .Numerical results sup-port the theoretical results and show that the proposed model is efficient for multiscale image restoration and reconstruction ,and is superior to some other decomposition models .
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