# How is compression ratio related to number of dct coefficients

Lets say we have a picture with 6bits/pixel and we use discrete cosine transform with 8x8 blocks of pixels and each coefficient is 8 bits. We can use 2 8x8 masks, a zonal mask A and a zonal bit allocation mask B.

A =

[1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...... ]

B =
[8 7 6 4 3 2 1 0 7 6 5 4 3 2 1 0 6 5 4 3 3 1 1 0 4 4 3 3 2 1 0 0 3 3 3 2 1 1 0 0 2 2 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0  ]

Is it correct to say that for A we have 64 : 15 compression namely 4.2 : 1 cause we keep 15 coefficients out of 64? does the same apply for B ?

• your original image is 6 bits but not 8 bits? – lennon310 Mar 6 '14 at 17:47
• yeah its 6bits. if it was 8 bits then if would be like i said above. thanks btw. – hardstudent Mar 6 '14 at 18:03
• you are very welcome! – lennon310 Mar 6 '14 at 18:04

Compression ratio is defined as the amount of bits in the original image divided by the amount of bits in the compressed image. In the original image the number of coefficients is 64, while you choose 15 coefficients after DCT in the compressed image with mask A. The ratio is 64*6/15*8. With mask B it is 64*6/41*8