Abstract: 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.

Key words: fractional order total variation, integer order total variation, variable exponent, variational method, gradient descent flow