**5. References**

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

*Lena Zelda Goldhill Peppers* Average

0.37/ 48.25

48.25

0.33/ 48.81

0.43/ 49.37

*s*

0.23/ 43.60

43.15

0.55/ 43.84

0.60/ 43.75

0.23/ 47.95

0.20/ 48.25

0.33/ 48.81

0.45/ 49.45

Average

0.29/ 43.60

0.46/ 43.15

0.54/ 43.84

0.61/ 43.87

0.15/ 48.25

48.25 - 0.17/

48.81

0.40/ 50.27

*Lena Zelda Goldhill Pepper*

0.28/ 43.60

43.15 - 0.41/

43.84

0.55/ 44.24

Methods Images

0.19/ 47.75

0.18/

48.81 - 0.26/

0.49/ 49.02

Methods Images

0.24/ 43.60

0.53/ 43.15

0.62/

0.64/ 43.94

Table 3. Embedding rate and PSNR performance comparison between various methods

0.40/ 43.60

0.42/

43.84 - 0.45/

0.66/ 43.56

Table 4. Embedding rate and PSNR performance comparison between various methods

In this chapter, we first propose a robust lossless data hiding via the feature-based bit embedding (FBBE) algorithm based on integer wavelet transform (IWT). Data bits can be effectively carried by the IWT blocks via the FBBE algorithm and the hidden message can be successfully identified later at the receiver. Moreover, the FBBE algorithm can completely recover the host media if the marked image remains intact, and extract (most part of) the hidden message if manipulations were intentionally (or unintentionally) altered to the marked images. In addition, we employ a smart arrangement of the IWT coefficients so as to provide a high-capacity lossless data hiding scheme. Simulations validate that the marked images generated by the proposed FBBE algorithm are robust to a variety of attacks such as JPEG2000, JPEG, cropping, noise additions, (colour) quantization, bits truncation,

0.20/ 47.55

0.23/ 48.25

0.38/

0.48/ 49.14

Wu et al.'s scheme

Lee et al.'s algorithm

Proposed method

Yang & Tsai's technique

when PSNR value was approximately 48 dB.

Wu et al.'s scheme

Lee et al.'s algorithm

Proposed method

**4. Conclusion** 

Yang & Tsai's technique

when PSNR value was approximately 43 dB.


**0**

**25**

*China*

**Time-Varying Discrete-Time**

Guangyu Wang, Qianbin Chen and Zufan Zhang

*Chongqing Key Lab of Mobile Communications, Chongqing University of Posts and*

Discrete-time wavelet transform (DWT) is found to be better than other transforms in the time-varying system analysis, e.g. for time-varying parametric modelling [16], time-varying systems identification [17], time-varying parameter estimation [18] and time domain signal analysis [19]. In the literature the common method to analyze the time-varying system using discrete-time wavelet transform is to model the time-varying system with a time-invariant system firstly, because a general analysis of time-varying discrete-time wavelet transform (TV-DWT) is still missing. To analyze the time-varying system directly using the time-varying discrete-time wavelet transform, we need the theory for the time-varying discrete-time

The theory of time-invariant discrete-time wavelet transform (DWT) are quite complete [1,2,3]. For time-varying discrete-time wavelet transform, in literature there are some papers related with this topic by studying the changes of two different filter banks [10,11,12]. In [10] the authors analyzed the time-varying wavelet transform through changing the two-band filter banks used in the tree-structured implementation of DWTs with an simple example. In [11] the time-varying wavelet packets built with time-varying cosine-modulated filter banks were investigated. Similar with [10], in [12] the authors studied time-varying wavelet packets more theoretically with changing the two orthogonal two-band filter banks used in tree-structure of DWTs. Generally, in the existed theory of time-varying discrete-time wavelet transform it lacks a basic definition and description of the time-varying discrete-time wavelet transform. A basic analysis of time-varying discrete-time wavelet transform is also missing. The author has studied TV-DWT since some years and has published a series of papers about

In our method the time-varying discrete-time wavelet transform is studied using a time-varying octave-band filter bank with tree structure. With this implementation the analysis of the time-varying discrete-time wavelet transform is equal to the analysis of the time-varying discrete-time octave-band filter bank. Then, the time-varying filter bank theory can be used in TV-DWT analysis. In this chapter we provide some theorems for the

this topic. In this Chapter we summarize the author's main research results.

time-varying discrete-time wavelet transform with proofs.

**1. Introduction**

wavelet transform.

**Wavelet Transforms**

*Telecommunications (CQUPT)*

