TITLE: Why is $8 \times 8$ matrix chosen for Discrete Cosine Transform?
QUESTION [8 upvotes]: In JPEG and MPEG, why is $8 \times 8$ matrix chosen for Discrete Cosine Transform?
Why not any other, say $64 \times 64$?

REPLY [9 votes]: From the MPEG FAQ:

Q22. Why was the 8x8 DCT size chosen?
A Experiments showed little compaction gains could be acheived with
  larger 
      sizes, especially when considering the increased implementation
      complexity. A fast DCT algorithm will require roughly double the
      arithmetic operations per sample when the linear transform point
      size is doubled. Naturally, the best compaction efficiency has
  been
      demonstrated using locally adaptive block sizes (e.g. 16x16, 16x8,
      8x8, 8x4, and 4x4) (See Gary Sullivan and Rich Baker 'Efficient Quadtree
      Coding of Images and Video,' ICASSP 91, pp 2661-2664.). 
      Inevitably, this introduces additional side information overhead and 
      forces the decoder to implement programmable or hardwired
  recursive 
      DCT algorithms. If the DCT size becomes too large, then more edges
      (local discontinuities) and the like become absorbed into the
      transform block, resulting in wider propagation of Gibbs (ringing)
  and
      other phenomena.  Finally, with larger transform sizes, the DC
  term is
      even more critically sensitive to quantization noise.