基于变指数分数阶全变差和整数阶全变差的图像恢复算法

结合变指数全变差(totalvariation, TV)和整数阶TV,提出一种变分图像恢复算法。该变分问题的能量泛函主要分为三个部分:变指数p(x)的分数阶TV正则化项、整数阶TV正则化项和数据保真项。该模型中的指数p(x)是与图像的梯度信息有关的函数。在理论上,由于分数阶导数和整数阶导数的结合,使得所提方法不仅能有效地去除图像噪音,保护图像的边界高频信息,还能更好地保留图像的纹理细节等中低频信息,同时可以极大地消除图像处理中产生的阶梯效应和散斑效应。在模型的求解上,利用变分法可以简单地将极小化泛函的优化问题转化为梯度下降流方程。最后,通过模拟数据和真实数据对本文所提方法进行了验证。试验结果表明,该方法可以去除噪声的同时,有效保持边界和纹理细节,并且对噪声是鲁棒的,具有一定的实际应用价值。

An image restoration algorithm based on variable exponential fractional order total variation and integer order total variation

This paper proposes a new variational image restoration algorithm based on variable exponential total variation(TV)and integer order TV. The energy functional of the variational problem is mainly composed of three parts: a fractional order TV regularization term of variable exponent p(x), an integer order TV regularization term and a data fidelity term. The exponential p(x) in this model is a function which related to the gradient information of the image. As the combination of the fractional order derivative and integral derivative, the proposed method can effectively remove the noise of the image, protect the image boundary, and also better retain the image texture details. At the same time, this method can greatly eliminate the staircase effect and the speckle effect. To solve the model, using the variational method, the optimization problem can be simply transformed into a gradient descent flow. Finally, to validate the effectiveness of our proposed method, we give the experiments with simulated data and real data. The experimental results show that this method can effectively remove noise, keep boundary and texture details and is robust to noise. And it has certain practical application value.