用拓扑分析筛选关键频率，提升噪声图像压缩可靠性
Persistent Homology-Guided Frequency Filtering for Image Compression
- 结合傅里叶变换与持久同调分析，识别图像的拓扑特征对应频率
- 六项指标显示压缩效果媲美JPEG，保留关键信息
- 适合需要抗噪压缩的图像分类任务，尤其适配CNN增强
噪声图像数据集中的特征提取面临诸多挑战，影响模型可靠性。本文结合离散傅里叶变换与持久同调分析，提取与图像特定拓扑特征对应的频率成分。该方法可在保证有意义数据可区分的前提下实现图像压缩与重建。实验结果表明，采用六种不同指标评估时，压缩性能与JPEG相当。持久同调引导的频率过滤旨在提升二值分类任务中的表现（在增强卷积神经网络时），优于传统特征提取与压缩方法。研究结果表明，该方法在噪声条件下显著提升了图像压缩的可靠性。
原文摘要 · Abstract (English)
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond with certain topological features of an image. This method allows the image to be compressed and reformed while ensuring that meaningful data can be differentiated. Our experimental results show a level of compression comparable to that of using JPEG using six different metrics. The end goal of persistent homology-guided frequency filtration is its potential to improve performance in binary classification tasks (when augmenting a Convolutional Neural Network) compared to traditional feature extraction and compression methods. These findings highlight a useful end result: enhancing the reliability of image compression under noisy conditions.
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