An effective weighted vector median filter for impulse noise reduction based on minimizing the degree of aggregation

Impulse noise is regarded as an outlier in the local window of an image. To detect noise, many proposed methods are based on aggregated distance, including spatially weighted aggregated distance, n nearest neighbour distance, local density, and angle‐weighted quaternion aggregated distance. However, these methods ignore the weight of each pixel or have limited adaptability. This study introduces the concept of degree of aggregation and proposes a weighting method to obtain the weight vector of the pixels by minimizing the degree of aggregation. The weight vector obtained gives larger components on the signal pixels than on the noisy pixels. Then it is fused with the aggregated distance to form a weighted aggregated distance that can reasonably characterise the noise and signal. The weighted aggregated distance, along with an adaptive segmentation method, can effectively detect the noise. To further enhance the effect of noise detection and removal, an adaptive selection strategy is incorporated to reduce the noise density in the local window. At last, noisy pixels detected are replaced with the weighted channel combination optimization values. The experimental results exhibit the validity of the proposed method by showing better performance in terms of both objective criteria and visual effects.