Digital Image Processing

B. D. Venkatramana Reddy ¹, T. Jayachandra Prasad ²

Affiliations
1 Department of Electronics and Communication Engineering, Madanapalle Institute of Technology & Science, Madanapalle-517325, Andhra Pradesh, IN
2 Department of Electronics and Communication Engineering, RGM College of Engineering & Technology, Nandyal-518501, Andhra Pradesh, IN

Abstract

A new algorithm for color image de-noising based on quaternion singular value decomposition (QSVD) and quaternion Fourier transform (QFT) is proposed in this paper. The proposed approach is based on the quaternion representation of color image pixels. De-noising is performed in the domain of singular values and singular vectors of a quaternion matrix representing the color image. The de-noising is based on eliminating changes in quaternion singular values and singular vectors caused by additive Gaussian white noise. The experimental results prove the effectiveness of the proposed method.

Keywords

Quaternions, Quaternion Matrix, Quaternion Singular Value Decomposition, Quaternion Fourier Transform.

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B. D. Venkatramana Reddy ¹, T. Jayachandra Prasad ²

Affiliations
1 Department of Electronics and Communication Engineering, Madanapalle Institute of Technology & Science, Madanapalle-517325, A.P, IN
2 Department of Electronics and Communication Engineering, RGM College of Engineering & Technology, Nandyal-518501, A.P, IN

Abstract

In this paper, we first introduce a new tool for color image decomposition based on quaternion representation of a colour image and quaternion matrix algebra. To perform the decomposition of such an image, we introduce the singular value decomposition of a quaternion matrix. Based on this mathematical technique of quaternion singular value decomposition (QSVD) this paper presents a block based digital colour image watermarking scheme. In the proposed approach, the original colour image is divided into blocks, and then the watermark is embedded in the singular values of each block separately. This segmentation and watermarking process makes the watermark much more robust to many image attacks like rotation, scaling, noise, compression, cropping, and lowpass filtering Watermark detection is implemented by extracting the watermark from the singular values of the watermarked blocks. Experimental results show that extracting the watermark from one block at least is enough to ensure the existence of the watermark.

Keywords

Quaternions, Singular Value Decomposition, Watermarking, Watermark Detection.

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