A nonstandard higher-order variational model to speckle noise removal and thin-structure detection
This work addresses speckle noise removal and thin-structure detection for image processing, but the improvements are incremental over existing variational methods.
The paper proposes a multiscale PDE-based model for speckle noise removal and thin-structure detection, using a topological gradient to guide adaptive exponent functions. Numerical results show effectiveness compared to TVL and biharmonic models, but no concrete performance numbers are provided.
In this work, we propose a multiscale approach for a nonstandard higher-order PDE based on the $p(\cdot)$-Kirchhoff energy. First, we consider a topological gradient approach for a semilinear case in order to detect important object of image. Then, we consider a fully nonlinear $p(\cdot)$-Kirchhoff equation with variables exponent functions that are chosen adaptively based on the map furnished by the topological gradient in order to preserve important features of the image. Then, we consider the split Bregman method for the numerical implementation of our proposed model. We compare our model with other classical variational approaches such that the TVL and biharmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.