How the Discrete Cosine Transform Revolutionized Image and Video Compression

Why DCT matters for JPEG/MPEG

Although many people only know JPEG as a file extension, it is a lossy compression standard that relies on the Discrete Cosine Transform (DCT) to reduce image size while preserving visual quality.

Lossy compression discards information that the human eye is less sensitive to, unlike lossless compression which can be perfectly reconstructed.

What DCT does

DCT is a type of Fourier transform that converts spatial‑domain pixel values into frequency‑domain coefficients. In a 3×3 pixel block, the first coefficient (DC) captures the overall brightness (low‑frequency information) while the remaining eight coefficients (AC) represent fine details (high‑frequency information).

After DCT, most image energy concentrates in the DC coefficient, while many AC coefficients become small or zero after quantization, enabling high compression ratios.

JPEG compression pipeline

Images are divided into 8×8 blocks, converted from RGB to YUV, transformed by DCT, quantized using a table based on human visual thresholds, and finally entropy‑coded (e.g., Huffman coding) to produce the compressed bitstream.

Decompression applies the inverse DCT (IDCT) to reconstruct the image.

Historical background

DCT was invented in the early 1970s by three relatively unknown Indian engineers—Nasir Ahmed, K. R. Rao, and T. Natarajan—who developed the algorithm during a summer without funding. Their 1974 paper "Discrete Cosine Transform" was published in IEEE Transactions on Computers and has been cited over 5,800 times.

The algorithm became the foundation for major standards such as JPEG (1992), MPEG, WebP (2010), HEIF (2013), and AV1 (2018).

The people behind DCT

Nasir Ahmed (born 1940) is a professor emeritus at the University of New Mexico; K. R. Rao is an Indian‑American scholar and IEEE Fellow; T. Natarajan was Ahmed’s Ph.D. student, about whom little information is available.

Despite initial rejection by the NSF—deemed "too simple"—the team persisted, and their work eventually transformed how we share images and videos today.