The quantization table is given on the JPEG Wiki page. How was this table derived? I'm currently doing a project where I have to come up with custom quantization table for an image, but I don't know how to begin. I figure if I learn how the JPEG table was derived, I might come up with a semi-original idea.
The standard JPEG quantization table is a typically 8 x 8 matrix of weights whose elements divide the corresponding elements of the 8 x 8 DCT coefficients of an image block.
The division effectively reduces the value of the DCT coefficients and most of them forced to be zero. The standard table is determined (optimized) to yield minimum distortion with maximum compression (per quality) with respect to the most typical images and average viewer visual charactersitics.
As s result high frequency coefficients are reduced as much as possible.
Note that the JPEG quality parameter already gives the user a means of adjusting the effective quantization table weights, but not over individual, elements. So you can also design an application (or viewer) specific quantization table if you wish according to the rate-distortion criteria you have in your mind.
Note that designing a per block optimized quantization table would most probably outweigh the JPEG compression efficiency due to the necessity of transmitting the specific quantization table weights per block to the decoder side.