Persistent Homology-Guided Frequency Filtering for Image Compression
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.