Improving SVD-based image watermarking via block-by-block optimization on singular values

Huang-Nan Huang,Wei-Che Hsu,Der-Fa Chen,Chiu-Chun Lin,Shuo-Tsung Chen

doi:10.1186/s13640-015-0073-6

Abstract

The purpose of this paper is to improve the robustness of traditional image watermarking based on singular value decomposition (SVD) by using optimization-based quantization on multiple singular values in the wavelet domain. In this work, we divide the middle-frequency parts of discrete-time wavelet transform (DWT) into several square blocks and then use multiple singular value quantizations to embed a watermark bit. To minimize the difference between original and watermarked singular values, an optimized-quality formula is proposed. First, the peak signal-to-noise ratio (PSNR) is defined as a performance index in a matrix form. Then, an optimized-quality functional that relates the performance index to the quantization technique is obtained. Finally, the Lagrange Principle is utilized to obtain the optimized-quality formula and then the formula is applied to watermarking. Experimental results show that the watermarked image can keep a high PSNR and achieve better bit-error rate (BER) even when the number of coefficients for embedding a watermark bit increases.

Highlights

With the rapid development of activity on the internet, much digital information is widely spread
Due to the fact that discrete-time wavelet transform (DWT) provides a useful platform, numerous DWT-based algorithms for digital watermarking have been proposed in recent years
Experimental results show that the watermarked image can keep a high peak signal-to-noise ratio (PSNR) and achieve a better biterror rate (BER) even when the number of coefficients for embedding a watermark bit increases

Summary

Introduction

With the rapid development of activity on the internet, much digital information is widely spread. The authors used a spread-spectrum technique to embed a watermark by modifying the singular values of the host image in the spatial domain. Unlike the traditional spread-spectrum technique on single singular values [24, 25], we use multiple singular value quantizations to embed a watermark bit. We use a Haar scaling function and wavelet to transform the host image into the orthogonal DWT domain by three-level decomposition. In order to guarantee both image quality and robustness, this study embeds the watermark into the middlefrequency parts LH3 and HL3 in DWT level-three.

Watermark extraction

Method

CA ð23Þ

Method and parameter