Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 670535, 12 pages

http://dx.doi.org/10.1155/2015/670535

## Reversible Watermarking Using Prediction-Error Expansion and Extreme Learning Machine

^{1}School of Information Science & Technology, Jiujiang University, Jiujiang 332005, China^{2}Institute of Network & Information Security, Jiujiang University, Jiujiang 332005, China

Received 3 May 2015; Revised 29 June 2015; Accepted 30 July 2015

Academic Editor: Roque J. Saltarén

Copyright © 2015 Guangyong Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Currently, the research for reversible watermarking focuses on the decreasing of image distortion. Aiming at this issue, this paper presents an improvement method to lower the embedding distortion based on the prediction-error expansion (PE) technique. Firstly, the extreme learning machine (ELM) with good generalization ability is utilized to enhance the prediction accuracy for image pixel value during the watermarking embedding, and the lower prediction error results in the reduction of image distortion. Moreover, an optimization operation for strengthening the performance of ELM is taken to further lessen the embedding distortion. With two popular predictors, that is, median edge detector (MED) predictor and gradient-adjusted predictor (GAP), the experimental results for the classical images and Kodak image set indicate that the proposed scheme achieves improvement for the lowering of image distortion compared with the classical PE scheme proposed by Thodi et al. and outperforms the improvement method presented by Coltuc and other existing approaches.

#### 1. Introduction

Digital watermarking has been extensively applied to the fields of digital library, fingerprinting, and secret communication. The conventional watermarking algorithms [1–3] can introduce irreversible distortion of digital works, which do not apply to military and medical domains. However, the reversible watermarking, known as lossless technology, can restore the original signal and has become a hot area of research since the last ten years.

Currently, the reversible watermarking schemes mainly focus on the spatial domain and are divided into three categories including difference expansion-based method [4–7], histogram shifting-based method [8–12], and prediction error-based method [13–17]. The difference expansion-based method was firstly proposed by Tian [4], which used the difference and average values of neighbor pixels to embed watermarking bits. Alattar [5] embedded the watermarking information by calculating the difference expansion of the integer transformation. Chen and Tsai [6] presented an adaptive block sized reversible image watermarking scheme with difference expansion, which had higher capacity than conventional fixed block sized method. Gu and Gao [7] used chaotic logistic map to randomly select the position for watermarking embedding and also to search the threshold space of reversibility. The proposed method achieved balance between the reversibility and the robustness with the help of chaotic system.

In [8], a breakthrough idea for histogram shifting was proposed by Ni et al. The watermarking bits were embedded by the shifting of zero-peak pairs of the image histogram. Ni’s method is nonblind, requiring the encoder to transmit the extra side information to the decoder. To solve this issue, some blind watermarking schemes based on histogram shifting are presented. Wang et al. [9] presented a multilevel embedding method using histogram shifting without the side information, in which the synchronization mechanism is adopted to ensure the selection of optimal zero-peak pairs in each level. Coatrieux et al. [10] contributed a modulation method of dynamic histogram shifting, adaptively taking care of the local specificities of the image content and inserting data in textured areas. Moreover, some reversible watermarking algorithms, combining histogram shifting with prediction technique, are presented to satisfy both high embedding capacity and good visual quality [11, 12].

The prediction-error expansion (PE) algorithm was developed by Thodi and Rodríguez [13, 14], which is essentially a particular form of difference expansion. Thodi and Rodríguez employed a pixel’s three-neighbor context to predict the pixel value and used the expansion of prediction-error between the original pixel value and the estimated one to embed message. The PE algorithm achieved a maximal embedding rate of 1 bit per pixel (bpp). Aiming at reducing the embedding distortion in the PE algorithm, Coltuc [15] proposed an improvement scheme. Instead of embedding the entire expanded difference into the current pixel, the expanded difference is split between the current pixel and its prediction context with global optimization, and Coltuc’s scheme achieved the improvement with popular predictors. Sachnev et al. firstly proposed to utilize the rhombus-context predictor (RCP) to predict the centered pixel [16], and the rhombus-context is composed of the four horizontal/vertical close neighbors. Later, some improvement schemes based on RCP are proposed by Ou et al. [17], Dragoi and Coltuc [18], and Li et al. [19].

Recently, some reversible watermarking schemes on frequency domain are presented [20–22]. Lei et al. [20] applied two-level wavelet transform to each subblock of an image and then performed singular value decomposition (SVD) on the low frequency wavelet coefficients of each block to generate the singular values. The watermark bits were embedded by quantizing the first singular values using the recursive dither modulation (RDM) approach. In [21], an intelligent reversible watermarking approach* GA-RevWM* for medical images is proposed.* GA-RevWM* adopted block-based embedding strategy using integer wavelet transform (IWT), and an intelligent method for threshold selection with genetic algorithm (GA) was applied to increase the imperceptibility of the marked image.

In order to improve the performance of reversible watermarking, this paper proposes a scheme to lower the embedding distortion based on PE. The main idea of the presented method is to enhance the accuracy of prediction value of image pixel by the extreme learning machine (ELM) [23, 24] with good generalization ability. Moreover, an optimized method of ELM is utilized to further diminish the prediction error. In this paper, the improved PE scheme is tested using two popular predictors, that is, median edge detector (MED) predictor [25] and gradient-adjusted predictor (GAP) [26]. The experimental results demonstrate that the proposed scheme achieves improvement for the image distortion compared with the classical PE scheme proposed by Thodi and Rodríguez [13, 14]. In addition, through the experimental contrast and theoretical analysis between the proposed approach and the noted improvement embedding scheme proposed by Coltuc [15], it is observed that the proposed approach outperforms Coltuc’s one.

The outline of the paper is organized as follows. The basic principle of PE scheme is presented in Section 2. Section 3 describes the improvement method of PE-based reversible watermarking using the optimized ELM. The improvement schemes with MED and GAP predictors are given in Section 4, respectively. Experimental results and analyses are shown in Section 5. Finally, Section 6 draws the conclusion.

#### 2. Basic Principle of PE

In the PE algorithm [13], the prediction-error between the original image pixel value and the estimated value is utilized to embed the watermarking. The concrete procedure of embedding watermarking of the PE algorithm is shown as follows.

*Step 1. *Scan the image according to certain sequence; then starting with the first pixel of the image, the prediction value of pixel is computed with , a neighborhood of , by a mathematical equation (e.g., (14) of Section 4).

*Step 2. *With the prediction error (), the prediction-error expansion is defined as follows:where is watermarking bit, , and then the watermarked pixel is given byIf , then the pixel is considered as extensible one.

*Step 3. *Select a threshold ; if the prediction error satisfies and the pixel is extensible, then we mark the pixel with “1”; otherwise, we mark it with “0.” Thus a matrix called the location map (LM) is composed of a set of “0” and “1,” which has same size with the original image. Then LM is compressed by arithmetic encoding (AE) or run-length encoding (RLE), generating a bit stream with a length of .

*Step 4. *The least significant bits (LSBs) of first pixels of the image form a sequence noted as , which is utilized for the lossless image restoration, and then in terms of (2), we embed the watermarking information and into the extensible image pixels except for first ones.

*Step 5. *Embed into the LSBs of first pixels, and generate the final watermarked image.

The watermarking extracting procedure of PE algorithm is shown as follows.

*Step 1. *Scan the image according to same sequence as the embedding procedure; then extract the LSBs of first pixels, decompressed by AE or RLE to obtain LM.

*Step 2. *Start with final pixel of LM; if the pixel value is “1,” then the prediction error is calculated by , and the watermarking information and are extracted by

*Step 3. *The LSBs of first pixels of the image are replaced with .

*Step 4. *Compute using , and generate the restored pixel value by

#### 3. Proposed Scheme

In this section, the basic principle of ELM is firstly introduced. Then the optimized ELM is provided with better prediction performance than ELM. Finally, a PE-based improvement scheme using optimized ELM is presented.

##### 3.1. Extreme Learning Machine

The extreme learning machine (ELM) is proposed by Huang et al. [23, 24] in terms of the generalized inverse theory, by which the output weight of the learning network can be achieved only with a step calculation. Compared with neural network (NN) [27, 28] and support vector machine (SVM) [29–31], ELM greatly improves the generalization ability and learning speed of the network [23]. The network training model of ELM uses the structure of a single layer feed-forward neural network, shown in Figure 1, where , , and are the node number of network input layer, hidden layer, and output layer, respectively. is the activation function, and is the hidden node threshold. is the training sample, where and , .