有限脊波域受约束的全变差能量泛函

为了减小有限脊波变换在图像处理应用中所出现的“卷绕”伪直线，将此伪直线视为一种振荡，首先对降质图像进行非线性有限脊波变换阈值，然后引入全变差正则化方法来抑制这一振荡，并约束所保留系数与待恢复图像的变换系数相等，以此确定可行域，进而建立了一种带脊波域约束的极小化全变差能量泛函模型，借助投影梯度算法对其进行求解．实验结果表明该方法对噪声具有较强的鲁棒性，在去噪和保留边缘的同时，使“卷绕”伪直线得到有效的抑制．

Total variation energy functional with restrictions on the finite ridgelet domain

To reduce the "wrap around" aliased lines from finite ridgelets transform(FRIT),the aliased lines are regarded as a kind of oscillation.Firstly,the nonlinear thresholding strategy is applied to coefficients of FRIT.And then,the total variational regularization method is introduced to suppress the oscillation.So a minimization total variation energy functional model with restrictions on the FRIT domain is established.By assuming that the coefficients remaining are identical with those of the restoration image,the feasible domain of the model is determined.Finally,the projected gradient algorithm is used to solve the model.Experiments show that the approach is very robust to noise,and that the aliased line are suppressed efficiently,and at the same time,remove noise and maintain the edge.