Persistent Homology-Guided Frequency Filtering for Image Compression

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.