While the graph Laplacian regularizer (GLR) offers several advantages, such as promoting smoothness and leveraging local pixel relationships, it also has potential limitations compared to other signal priors:
Sensitivity to Graph Construction: The performance of the GLR heavily depends on the quality of the graph construction. If the graph does not accurately represent the underlying image structure, the denoising or restoration results may suffer. To address this, one can incorporate adaptive graph construction techniques that dynamically adjust the graph based on the input image characteristics, such as using local pixel statistics or learned features to define edges and weights.
Computational Complexity: The computation of the graph Laplacian and its inverse can be computationally intensive, especially for large images. This can be mitigated by employing efficient algorithms for sparse matrix operations or approximating the graph Laplacian using techniques like low-rank approximations, which can reduce the computational burden while maintaining performance.
Limited Expressiveness: Compared to more complex signal priors, such as deep learning-based methods that can capture intricate patterns, the GLR may be less expressive. To enhance expressiveness, one could combine the GLR with other priors, such as total variation or learned neural network features, creating a hybrid model that benefits from the strengths of multiple approaches.