Lecture Notes - DCT and JPEG

Question 1

What is the Karhunen Loeve Transform not used in practice? What is used instead?

Answer 1

Not convenient to compute as it depends on the signal statistics. The Discrete Cosine Transform is used instead.

Question 2

When observing R-D curves, does the DCT or Haar transform perform better?

Answer 2

1. The DCT performs better (i.e. DCT 4X4, 8X8, 16X16)
2. Found that 8x8 was optimum DCT

Question 3

What effect is observed when increasing the DCT size?

Answer 3

1. See a shimmering effect.
2. However, due to quantisation as the Qstep loses the coefficients on tails of sinc function.

Question 4

Which colour space does JPEG use and why?

Answer 4

1. JPEG works on YUV images
2. Found that it is the best colour space for entropy.

Question 5

Explain why the DCT is used over the Haar transform

Answer 5

1. The transform matrix is of size n x n.
2. For n > 2, DCT is better.