Image Compression

Fourier Analysis · Axiom Academy

REAL WORLD Image Compression with Wavelets How a 10MB photo becomes 200KB without looking different The Magic of Image Compression Your phone's camera captures a stunning photo: 12 megapixels, crystal clear, full of detail. The file size? A whopping 10 megabytes . But when you share it on social media, it's suddenly just 200 kilobytes —that's 50 times smaller—and yet it still looks virtually identical to your eyes. The Question: How is this possible? What mathematical magic allows us to throw away 98% of the data while preserving the visual quality? The answer lies in wavelet transforms —the technology behind JPEG 2000 and modern image compression. In this module, we'll explore how wavelets achieve what seems impossible: massive compression with minimal quality loss. You'll see why JPEG 2000 produces better results than traditional JPEG, and why wavelets are revolutionizing not just image compression, but also video streaming, medical imaging, and digital cinema. While the Fourier Transform decomposes signals into frequencies that extend infinitely, the wavelet transform uses small, localized wave packets that are both time and frequency limited. This makes wavelets perfect for images, where we care about where details occur, not just that they exist. The wavelet transform analyzes an image at multiple scales, separating it into different levels of detail—from coarse approximations to fine details.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.