JPEG compression process steps

JPEG (Joint Photographic Experts Group) is a standard for compressing continuous-tone still images. The baseline (lossy, DCT-based) method has four main stages: preparation, DCT, quantization and entropy coding.

Image -> Preparation -> DCT -> Quantization
      -> Zig-zag + DPCM/RLE -> Huffman -> JPEG file

1. Image preparation

• The image is split into components. An RGB image is usually converted to YCbCr (luminance Y and chrominance Cb, Cr).
• Chroma subsampling: the eye is less sensitive to colour than brightness, so Cb and Cr are reduced, for example 4:2:0 (one chroma sample per 2x2 block of pixels). This alone halves the data.
• Each component is divided into 8 x 8 blocks of pixels, and 128 is subtracted from each value (level shift) so values range from -128 to 127.

2. Discrete Cosine Transform (DCT)

• A 2-D DCT is applied to each 8 x 8 block. It converts spatial pixel values into 64 frequency coefficients.
• The top-left coefficient is the DC coefficient (average of the block); the other 63 are AC coefficients, growing in frequency toward the bottom-right.
• DCT itself is nearly lossless; it only makes the data easier to compress, since most energy gathers in few low-frequency coefficients.

3. Quantization (the lossy step)

• Each coefficient is divided by the matching entry of a quantization table and rounded to the nearest integer.
• High-frequency entries have large divisors, so they become zero. Example: a coefficient 52 divided by 16 gives 3.25, rounded to 3; a high-frequency coefficient 7 divided by 99 rounds to 0.
• A larger divisor means more compression and lower quality. This is the "quality" setting.

4. Entropy coding

• Zig-zag scan: the 8 x 8 matrix is read in zig-zag order, giving a 1-D list with non-zero values first and a long tail of zeros.
• DC coefficients are coded by DPCM: only the difference from the previous block's DC value is stored.
• AC coefficients are coded by run-length encoding as (zeros-run, value) pairs, ending with an end-of-block (EOB) code.
• The result is compressed with Huffman coding (or arithmetic coding), and written with headers to the JPEG file.

Mini example: after quantization a block's zig-zag list is 15, -2, 3, 0, 0, 1, 0, ... 0. It is stored as DC = 15 (as a difference), then (0,-2), (0,3), (2,1), EOB. Sixty-four values reduce to a few symbols.

Decoding reverses the steps: Huffman decode, de-quantize (multiply), inverse DCT, add 128, upsample chroma, convert to RGB. The quantization loss cannot be recovered. Typical compression is 10:1 to 20:1 with good quality.