# Genetic Programming to Remove Impulse Noise in Color Images
## 2 Related Works  
A large number of filters for impulse noise removal from color images have been proposed in the literature, e.g., [15]. Two types of filters, robust and adaptive, stand out in scenarios where images are degraded by complex noise patterns or variations in lighting and contrast. Robust filters deal with noisy pixels as a violation of the spatial coherence of the image intensities. The most well-known robust filter is the vector median filter (VMF) [16], a non-linear method that is still a reference in the field. The VMF orders the color input vectors based on their relative magnitude differences in a predefined sliding window. However, robust filters apply a correction procedure to every image pixel, even if the pixels are not noisy. Therefore, filtered images commonly present too much smoothing and extensive blurring [9]. Other methods exploit the sparsity of the image in some transform domains, formulating noise removal as an optimization problem. For example, the generalized synthesis and analysis prior algorithm (GSAPA) proposed in [17] uses the split-Bregman technique to break down the optimization problem with multiple regularization parameters into relatively easy-to-solve subproblems. In [18], an extension of the mean-shift technique was introduced to effectively reduce Gaussian and impulsive noise in color digital images; utilizing a novel similarity measure between pixelsand a patch at the block's center, the technique demonstrates efficiency in restoring heavily disturbed images. On the other hand, adaptive filters assume that only some image pixels are perturbed by noise. These filters adapt to various image characteristics and noise statistics using different approaches. One of these approaches is the fuzzy peer-group concept, which associates a set of neighboring pixels whose distance to a central pixel does not exceed a threshold founded on fuzzy logic (see, for example, [19]). Under this approach, the fuzzy modified peer-group filter (FMPGF) [20] stands out due to its efficiency. Other approaches use fuzzy logic tools to measure magnitude differences, providing an adaptive framework to distinguish between noise and data. For example, the adaptive fuzzy filter proposed in [21] uses a noise-detection mechanism to select a small portion of input image pixels and convolves them with a set of weighted kernels to create a layer of convolved feature vectors. The feature vectors are then fed into a fuzzy inference system, where fuzzy membership degrees and a reduced set of fuzzy rules play a crucial role in categorizing pixels as either noise-free, associated with edges, or noisy. Another fuzzy inference rule-based filter for impulse noise is the noise adaptive fuzzy switching median (NAFSM) filter [22]. The NAFSM filter uses two-stage processing specialized for salt-and-pepper noise detection and removal, preserving strong edges through spatial averaging. A recent contribution in a similar vein is the adaptive fuzzy filter based on histogram estimation (AFHE) [23]. The AFHE filter dynamically adjusts the window size based on local noise densities using fuzzy-based criteria. Additionally, it incorporates an iterative procedure based on the Gaussian mean for further processing. Another recent development presented in [24] introduces a spatio-temporal filter designed to eliminate impulse noise from videos through the application of fuzzy logic. The distinctive feature of this filter is its ability to leverage both spatial and temporal correlations and color components in a sequential process, allowing it to effectively handle high impulse noise levels, even up to 70%. Other adaptive approaches are based on more straightforward decisions, such as the decision-based algorithm for the removal of impulse noise (DBAIN) [25]. The DBAIN filter processes a noisy image by first detecting salt-and-pepper noise (as its major decision) and then replacing the noisy pixel values with the median of their neighboring pixels.