**4. Conclusion**

The need for digital watermarking on electronic distribution of copyright material is becoming more prevalent. In this paper an overview of the digital watermarking techniques are given and a blind invisible watermarking technique for grayscale images based on DWT and DFT is presented. The algorithm use 512\*512 gray images as a host image and 32\*32 binary image as watermarked image.

Firstly, two level wavelet decomposition is implemented on the host image. Then, the middle frequency components are extracted and divided in to several blocks of size 4\*4 and DFT is implemented on them. Finally, two pseudo random sequences are created and embedded to blocks which have implemented DFT according to whether the corresponding position is 0 or 1 in the watermark matrix which has been implemented.

The original image is not required while extracting the watermark Instead, correlations among each block and two sequences are respectively calculated. Watermark is recovered on foundation of the relative magnitude of correlation between the corresponding block and one sequence or the other. The idea of applying two transform is based on the fact that

K=30

524 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Original Gray Image

The experimental results are represented in the following, respectively for watermarked image and extracted watermark image as shown in Fig. 9 (i), and Fig. 9 (ii), while taking the different values of gain factor *K*. And various observations for experiment are depicted in

Fig. 7. Original image of pepper

Fig. 8. Watermark image

Table I. K=10

**3.1 Experimental result and analysis** 

K=20

**0**

**23**

**The Wavelet Transform as a Classification**

**Hyperspectral Images**

Daniel Acevedo and Ana Ruedin

*Facultad de Ciencias Exactas y Naturales*

*Departamento de Computación*

*Universidad de Buenos Aires*

*Argentina*

**Criterion Applied to Improve Compression of**

Satellites continually feeding images to their base, pose a challenge as to the design of compression techniques to store these huge data volumes. We aim at lossless compression of hyperspectral images having around 200 bands, such as AVIRIS images. These images consist of several images (or bands) obtained by filtering radiation from the earth at different wavelengths. Compression is generally achieved through reduction of spatial as well as

Most of the hyperspectral compressors are prediction–based. Since spectral correlation is usually high (much more higher than spatial correlation) pixels are predicted with other pixels in an adjacent band (rather than other pixels surrounding the one to be predicted). SLSQ (Rizzo et al., 2005), a low-complexity method designed for hyperspectral image compression, performs a simple prediction for each pixel, by taking a constant times the same pixel in the previous band. The constant is calculated by least squares over 4 previously encoded neighboring pixels. SLSQ–OPT version of SLSQ performs one band look–ahead to determine if the whole band is better compressed this way or with intraband prediction, while in the SLSQ–HEU version this decision is taken by an offline heuristic. CCAP (Wang et al., 2005) predicts a pixel with the conditional expected value of a pixel given the context. The expected value is calculated over coded pixels having matching (highly correlated) contexts. Slyz and Zhang (Slyz & Zhang, 2005) propose 2 compressors (BH and LM) for hyperspectral images. BH predicts a block as a scalar times the same block in the previous band. Coding contexts are defined by the quantized average error. LM predicts a pixel by choosing among different intraband predictions the one that works best for several pixels at the same position

Mielikainen and Toivanen proposed C-DPCM (Mielikainen & Toivanen, 2003), a method that classifies the pixels at the same location and through all the bands, with vector quantization. Interband prediction is performed using the pixels at the same position in 20 previous bands. Weights, calculated for each class/ band, are sent into the code, as well as the 2D template with the classes. Aiazzi et al. (Aiazzi et al., 1999) classify the prediction context of every

**1. Introduction**

spectral correlations.

in previous bands.

combined transforms could compensate for the drawbacks of each other, resulting in effective watermarking.

#### **5. References**

