# Genetic Programming to Remove Impulse Noise in Color Images
## 2 Related Works
Some comprehensive studies of adaptive filters for impulse noise removal from color images are presented in [15; 26]. Machine learning-based techniques have also been applied to remove impulse noise from color images. For example, a support vector machine (SVM)-based filtering technique was proposed in [27]. Later, fuzzy c-means (FCM) clustering combined with a fuzzy-support vector machine (FSVM) was introduced in [28]. Additionally, multiple neuro-fuzzy filters were trained with an artificial bee colony algorithm and combined with a decision tree algorithm in [29] to denoise corrupted images. Also, neural network-based denoising methods are another popular approach. For instance, a convolutional neural network-based denoising method mainly composed of a sparse block, a feature enhancement block, an attention block, and a reconstruction block was described in [30]. Also, a convolutional autoencoder-based feature map domain was combined with low-rank models to improve denoising quality in [31]. Recently, a novel denoising network called DeQCANet was introduced in [32] for removing color random-valued impulse noise. This work implements a quaternion convolutional neural network, incorporating a novel quaternion map construction strategy to enhance color features across channels. The proposed denoising technique exhibits competitive performance compared to other well-established methods for denoising color images. Another recent development is the impulse detection convolutional neural network (IDCNN) introduced in [33], which utilizes a switching filtering technique consisting of a deep neural network architecture to detect noisy pixels, followed by a restoration stage of these pixels through the fast adaptive mean filter. In [34], a neural network architecture was introduced to recognize images affected by random-valued impulse noise, comprising a preprocessing stage and incorporating a pixel distortion detector, a cleaning mechanism, and a neural network complex for image recognition. An overview of deep learning techniques on image denoising can be found in [35]. While convolutional neural networks and deep learning-based approaches excel in performance, they are complex and opaque. Their intricate architectures and complex hierarchical representations in these techniques make it challenging to decipher the exact decision-making process, limiting the transparency and understanding of how the denoising outcomes are achieved. Achieving transparency is crucial for various reasons, especially in applications where interpretability is essential for user trust, accountability, and ethical considerations. Alternative filtering techniques tackle the challenge of image denoising through an evolutionary computing approach. For instance, in [36], [PERSON] et al. introduced a denoising method employing a genetic algorithm. In their method, an input noisy image is represented as an individual, and the individuals of the initial population are represented as mutated versions of the image. The evolutionary process applied to the population allows for the continuous refinement and adaptation of the original noisy individual until an enhanced image is found. In a similar vein, in [37], we addressed image denoising by merging output images of robust and adaptive filters to integrate them as an evolving population for a genetic algorithm. Genetic algorithms, in this context, are frequently employed to fine-tune specific filter parameters, essentially framing them as an optimization task. On the other hand, genetic programming has emerged as a highly promising field for the creation of adaptive filters aimed at noise reduction; however, no filters use genetic programming to remove impulse noise from color digital images. Nevertheless, there are a few works that have addressed impulse noise removal for grayscale images, the most relevant being [38; 39; 40]. [PERSON] and [PERSON] [38] used genetic programming to produce two binary classification models for identifying noisy pixels in grayscale images following a cascade approach.