How SVD Compresses an Image — One Layer at a Time
Last Updated on October 29, 2026 by Editorial Team
Author(s): Arjun Bhasin
Originally published on Towards AI.
Every photo can be rebuilt from simple layers, and the first few carry most of the picture.
Suppose we are allowed to keep only a fifth of the numbers in a photo.
The article introduces how Singular Value Decomposition (SVD) represents an image as a sum of simple rank-1 “layers,” each built from a row pattern multiplied by a column pattern. It shows that the layers with the largest singular values contribute most of the image’s visible structure and “energy,” so truncating to only a few layers can reconstruct recognizable images (while later layers mostly add finer texture). The author explains why this happens—layers don’t interfere because their directions are orthogonal—and discusses the limits of compressibility, including randomness (noise) and structures like diagonal/curved edges that require many layers. The piece also covers how the same idea extends to grayscale-to-color images by decomposing each color channel separately, why this differs from JPEG (which uses fixed cosine patterns), and concludes with practical takeaways about when SVD compression is effective versus when it breaks down.
Read the full blog for free on Medium.
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