Local Attention Neural Network for Median Filtering: Enhancing Nonlinear Local Operations

Recent advancements in large-scale neural networks have achieved performance levels nearly indistinguishable from human capabilities across various domains, such as image recognition, natural language processing, and game playing. Despite their impressive capabilities, it is known that even the most powerful neural networks cannot directly execute basic arithmetic operations without specific architectural design. The median filter is a nonlinear, local processing technique widely used in image processing for noise reduction. Unlike simple arithmetic operations, the median filter involves sorting pixel values within a neighborhood, which requires logical operations in addition to numerical calculations. Surprisingly, research on implementing such nonlinear local operations within neural networks is relatively sparse. Self-attention, a core component of modern transformer models, enables the network to focus on specific parts of the input data. In this paper, we propose a novel neural network architecture that implements the median filtering operation by locally applying self-attention mechanisms. By leveraging self-attention, our approach effectively mimics the sorting and selection process inherent to the median filter. Our experimental results demonstrated that this architecture surpasses the performance of previous convolutional neural networks specifically designed to implement the median filter, achieving 100% accuracy on a subset of random image data. However, the model did not consistently achieve perfect accuracy across all input types. This suggests that while our approach significantly improves performance, it does not yet flawlessly replicate the median filter's functionality.