Matrix analysis
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
IBM Systems Journal
SVD-Based Approach to Transparent Embedding Data into Digital Images
MMM-ACNS '01 Proceedings of the International Workshop on Information Assurance in Computer Networks: Methods, Models, and Architectures for Network Security
Robust DWT-SVD domain image watermarking: embedding data in all frequencies
Proceedings of the 2004 workshop on Multimedia and security
Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing
Foundations of Computational Mathematics
Nonlinear Harten's multiresolution on the quincunx pyramid
Journal of Computational and Applied Mathematics
A fully adaptive multiresolution scheme for image processing
Mathematical and Computer Modelling: An International Journal
On the limits of steganography
IEEE Journal on Selected Areas in Communications
Signal analysis using a multiresolution form of the singular value decomposition
IEEE Transactions on Image Processing
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We explore the use of the singular value decomposition (SVD) in image compression. We link the SVD and the multiresolution algorithms. In [22] it is derived a multiresolution representation of the SVD decomposition, and in [15] the SVD algorithm and Wavelets are linked, proposing a mixed algorithm which roughly consist on applying firstly a discrete Wavelet transform and secondly the SVD algorithm to each subband. We propose a new algorithm, which is carried out in two main steps. Firstly we decompose the data matrix corresponding to the image following a singular value decomposition. Secondly we apply a Harten's multiresolution decomposition to the singular vectors which are considered significant. We study the compression capabilities of this new algorithm. We also propose a variant of the implementation, where the multiresolution transformation is carried out by blocks. We apply on each block, depending on a selection process, either the algorithm presented or the 2D multiresolution algorithm based on biorthogonal wavelets.