Discrete Cosine Transform

From iA wiki

See also: Compression | JPEG | Run Length Encoding | Huffman Encoding

A type of lossy compression.

The Discrete Cosine Transform (DCT) tranforms a signal from the spacial domain to the frequency domain. It is often used in JPEG with a quantization table. DCT is lossy to begin with, and using quantization exacerbates this. The lossiness is due (essentially) to the fact that on a computer, if we start with A, let B = cos(A), then let C = arccos(B), C != A (although it is very close). Quantization exacerbates this by removing the precision of B.

DCT was chosen for JPEG because within the 8x8 pixel size the DCT operates on in JPEG, there is usually very little variation in chroma, so the quantized DCT of the region has a few values near the beginning, then many 0's (zeros) following. This property lends itself to Run Length Encoding of the DCT values, which compresses the data.