How does fourier analysis work in the jpeg file?

Question

Can someone explain to me how fourier analysis compresses an image so well in the JPEG file.

Answer 1

JPEG divides up the image into 8 by 8 pixel blocks, and then for each block calculates a Fast-Fourier Transformation called a discrete cosine transform (DCT). A quantizer rounds off the DCT coefficients according to the quantization matrix. This step reduces the numerous pixels to just the coefficients making for a large compression ratio. But the quantization means that you are losing part of the data. This is called a "lossy" compression, meaning that the decompressed image isn't quite the same as the original. JPEG is designed to exploit known limitations of the human eye, notably the fact that small color changes are perceived less accurately than small changes in brightness. Thus, JPEG is intended for compressing images
that will be looked at by humans. If you plan to machine-analyze your images, the small errors introduced by JPEG may be a problem for you, even if they are invisible to the eye.

The "loss" is not usually apparent to someone looking at the picture. The major features and even the details of the picture are all there. It's only if you look at the edges, or in patches of colors that you'll see compression artifacts. And, if you've ever edited a JPEG, then saved, and edited, and saved, you'll definitely notice the generation losses that JPEG compression introduces, but this is all offset by the useful nature of the "lossy" compression.

JPEG's compression technique uses a variable length code on the coefficients, and then writes the compressed data stream to an output file (*.jpg). For decompression, JPEG recovers the quantized DCT coefficients from the compressed data stream, takes the inverse transforms and displays the image.

Answer 2

Hmmm, your asking how analysis compresses an image, but the compression is actually 'filtering' out high frequency information using a digital transform similar to a Fourier one. As stated above, and in more depth in the link. Fourier analysis identifies the various frequencies and scales of the building blocks that make up a 2-d image, then pieces that are not perceived by our vision are filtered.