# Math Help - Discrete Cosine Transform

1. ## Discrete Cosine Transform

Discrete Cosine Transform?
Could someone explain how Discrete Cosine Transform (DCT) in image compression is used as simple as possible?

Thanks

2. Originally Posted by taurus
Discrete Cosine Transform?
Could someone explain how Discrete Cosine Transform (DCT) in image compression is used as simple as possible?

Thanks
It's not a real "simple" explanation.
Best is to use Wikipedia, google etc, to get a synopsis of what DCT does.
For a full explanation, there are hundreds of monographs on the web.

However, the best way to comprehend what it does is 1) use a sheet of graph paper
2) create any image you can on paper
3) follow DCT algorithm to generate a block
&
4) then decompose that block.

You can see that the decomposed block does not exactly match the original, but it is close enough.
It is a "lossy" form of compression and saves a bunch of memory.

3. Originally Posted by taurus
Discrete Cosine Transform?
Could someone explain how Discrete Cosine Transform (DCT) in image compression is used as simple as possible?

Thanks
The image is segmented into blocks of an appropriate size and the algorithm works on those blocks.

You take the 2-D DCT of the block, most of the coefficients are small and discarded, the large coefficients are retained and has a smaller file size than the original data that constituted the image.

When the image is reconstructed from the highest coefficients it will be a good representation of the original if enough coefficients have been retained.

The compression is lossy because information has been discarded.

CB

4. What do you mean by coefficients?

5. Originally Posted by taurus
What do you mean by coefficients?
What the DCT gives, they are coefficients in a (circular) cosine expansion of the image data.

CB

6. ## DCT and JPEG Compression

Have a look at following two links to get an idea of the combination between JPEG compression and DCT

JPEG - JPEG Image Compression Explained

DCT - Discrete Cosine Transformation (DCT)