Denoising of images corrupted by multiplicative noise is an important task in various
applications, such as laser imaging, synthetic aperture radar and ultrasound imaging.
We propose a combined first-order and second-order variational model for removal of
multiplicative noise. Our model substantially reduces the staircase effects while
preserving edges in the restored images, since it combines advantages of the
first-order and second-order total variation. The issues of existence and uniqueness
of a minimizer for this variational model are analysed. Moreover, a gradient descent
method is employed to solve the associated Euler–Lagrange equation, and
several numerical experiments are given to show the efficiency of our model. In
particular, a comparison with an existing model in terms of peak signal-to-noise
ratio and structural similarity index is provided.