ABSTRACT
This chapter introduces the mathematical preliminaries of digital watermarking techniques for different embedding purposes and domains. It presents some commonly used operations in digital watermarking, including least-significant-bit (LSB) substitution, the discrete Fourier transform (DFT), the discrete cosine transform (DCT), the discrete wavelet transform (DWT), random sequence generation, chaotic maps, error correction code (ECC), and set partitioning in hierarchical trees (SPIHT). The LSB method is easy to implement and can possess high embedding capacity and low visual perceptibility because every cover bit contains one bit of the hidden message. The Fourier series was originally motivated by the problem of heat conduction and later found a vast number of applications as well as providing a basis for other transforms, such as the DCT. The DWT is also a simple and fast transformation approach that translates an image from the spatial domain to the frequency domain. SPIHT coding uses a bit allocation strategy to produce a progressively embedded scalable bitstream.
