🤖 AI Summary
To address semantic information loss and low feature reliability in noisy image compression, this paper proposes a persistent homology-guided frequency-domain filtering method. First, discrete Fourier transform (DFT) is applied to input images; then, persistent homology analysis identifies topologically significant frequency components critical for classification tasks; finally, structure-preserving filtering is performed in the frequency domain to achieve noise-robust compression and reconstruction. This work is the first to embed topological data analysis into the image frequency-domain compression pipeline, explicitly preserving semantic-relevant topological structures. Evaluated on CNN-based downstream binary classification tasks, the method matches JPEG’s performance across six compression quality metrics—including PSNR and SSIM—while significantly enhancing feature discriminability and classification accuracy on noisy images. The approach establishes a novel paradigm for robust image representation learning.
📝 Abstract
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.