# Genetic Programming to Remove Impulse Noise in Color Images
## 6 Conclusions and Future Work  
This work presents an adaptive filter designed for the removal of three prevalent types of impulse noise, namely salt and pepper, uniform, and correlated noise, in color digital images. The proposed filter employs a two-step process, leveraging a binary classification model to identify noisy pixels within the image, followed by a correction step tailored to the specific color channels. What sets this proposed filter apart from the majority of filters utilizing classification models for noise removal is its high level of interpretability. This interpretability is a result of the evolutionary approach taken during model training--a process rooted in the principles of the genetic programming paradigm. By evolving the model through an iterative genetic programming framework, the resulting filter not only achieves effective noise reduction but also provides insights into the decision-making process of the classification model. Another distinctive feature of the training is that it only required a single image purposefully contaminated by the impulse noise models. Using a unique training image was particularly useful in reducing the computational complexity. An experimental study was conducted to evaluate the performance of the proposed adaptive filter. A comparison with other filters was performed via the four image quality metrics (PSNR, MAE, SSIM, and FSIM). The experimental results show that most comparison filters present variability in the values of their quality metrics depending on the noise model and the image characteristics. In this vein, the proposed filter, called GP in Tables 4 and 5, consistently obtained good performance values, second only to the ICDNN, which uses a deep learning-based approach. When measuring efficiency as a minimizing/maximizing multi-objective problem, as shown in Figures 7-10, the proposed filter is one of the closest to an equilibrium point across all images and noise models used in the experiment, on par with the ICDNN and GSAPA filters. Future work will focus on the integration of alternative machine learning techniques for the identification and correction of noisy pixels in color digital images. An intriguing avenue of exploration would be predicting the correlation of color channels to facilitate improved pixel replacement strategies within the image. This innovative approach holds promise for further enhancing the robustness and adaptability of the proposed adaptive filter in diverse real-world scenarios. It would also be interesting to explore how the genetic programming algorithm can be fine-tuned or adapted according to user preferences and specific requirements for noise removal in color images. Finally, optimizing the evolutionary settings of the genetic programming algorithm by employing other metaheuristic algorithms or ensemble approaches is also a topic left for future research. Figure 10: Three-dimensional Pareto front for FSIM average values by considering the whole set of test images with noise densities \(p=0.05,0.10,0.15\), and \(0.20\). **Supplementary Materials:** The following supporting information can be downloaded at: [[https://bitbucket.org/dfajardod/impulse_noise_gpfilter/src/](https://bitbucket.org/dfajardod/impulse_noise_gpfilter/src/)]([https://bitbucket.org/dfajardod/impulse_noise_gpfilter/src/](https://bitbucket.org/dfajardod/impulse_noise_gpfilter/src/)). **Author Contributions:** Conceptualization, D.F.-D. and M.G.S.-C.; methodology, D.F.-D., M.G.S.-C. and A.Y.R.-G.; software, D.F.-D. and M.G.S.-C.; validation, A.Y.R.-G., S.S.-P. and J.E.M.-S.; writing--original draft preparation, D.F.-D. and M.G.S.-C.; supervision, A.Y.R.-G., S.S.-P. and J.E.M.-S.; project administration, D.F.-D. and M.G.S.-C. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Tecnologico Nacional de Mexico under grant number 18205.23-P.  
**Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.