Transform coding

Transform coding is a method for data compression to compress signals like audio signals (1-D) or images (2-D). In transform coding, a frequency transform or other basis transformation is applied before entropy coding, and the inverse transformation is applied after decoding. This has the advantage that the resulting coefficients have a statistically significant distribution and can be modelled and compressed more easily.

This means: After the transform, some coefficients are predictably greater, others smaller. Thus, some coefficients can be neglected or quantized (lossy compression) and/or entropy encoded (lossless compression).

For instance, JPEG performs a discrete cosine transform on 8-by-8 pixel blocks (in some pictures the chrominance is subsampled, so is transformed in 16-by-16 blocks with 3/4 of the results discarded), then the coefficients are quantized depending on their frequencies.

See also:

• Wavelet transform
• Karhunen-Loève transform