Discrete Cosine Transform (DCT)

Definition:Discrete Cosine Transform is a technique applied to image pixels in spatial domain in order to transform them into a frequency domain in which redundancy can be identified.

In JPEG compression [1], image is divided into 8×8 blocks, then the two-dimensional Discrete Cosine Transform (DCT) is applied to each of these 8×8 blocks. In JPEG decompression, the Inverse Discrete Cosine Transform (IDCT) is applied to the 8×8 DCT coefficient blocks. DCT and IDCT are defined as follows: DCT: IDCT: where f(i, j) and F(u, ν) are respectively the pixel value and the DCT coefficient, and

As shown in Figure 1, in an 8×8 DCT coefficient block, F(0,0) is called DC coefficient, while other 63 DCT coefficients are called AC coefficients. The coefficients at the bottom-right corner are of high frequencies, and they are sensitive to distortions such as compression. The coefficients at the upper-left corner are of low frequencies, and they are robust to distortions. Human eyes are less sensitive...