Persistent Homology-Guided Frequency Filtering for Image Compression

TL;DR

This paper introduces a novel image compression method combining persistent homology and frequency filtering to improve data reliability and classification performance in noisy images.

Contribution

It presents a new technique integrating persistent homology with Fourier analysis for effective image feature extraction and compression.

Findings

Compression performance comparable to JPEG across six metrics

Enhanced reliability of image data under noisy conditions

Potential improvements in CNN-based binary classification tasks

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.