Quantization

Definition: Quantization is a technique used in lossy image and video compression algorithms based on DCT, DFT, or DWT.

Quantization can be modeled as [1]:

((1))

where q is a constant quantization step size, and rounds x to the nearest integer x _q .

Dequantization can be modeled as:

((2))

where x′ is the regenerated integer, which is normally not equal to x. Therefore the quantization process is lossy.

Most common lossy compression algorithms first transform the original signals into a different domain such as Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT), or Discrete Wavelet Transform (DWT) domain. Then, each of the resulting coefficients is independently quantized.

Quantization is being used by many robust or semi-fragile watermarking algorithms. A robust watermarking algorithm need survive the quantization process, while an ideal semi-fragile watermarking algorithm need provide fragility that is proportional to the quantization step size q.

Quantization has the...