Several mathematical methods are discussed in this paper, which are applied in image compression and restoration. Singular value decomposition (SVD) is used in compressing image. Conjugate gradients (CG) method and truncated Singular value decomposition (TSVD) regularization method are applied in image restoration. From the experience results we can see that those methods are effective in image...

The Singular Value Decomposition (SVD) is an important tool for linear algebra and can be used to invert or approximate matrices. Although many authors use "SVD" synonymously with "Eigenvector Decomposition" or "Principal Components Transform", it is important to realize that these other methods apply only to symmetric matrices, while the SVD can be applied to arbitrary nonsquare matrices. This...

An approach for three robust and semi-blind digital video watermarking algorithms has been proposed in this paper. These algorithms are based on hybrid transforms using the combination of Discrete Cosine Transform and Singular Value Decomposition (DCTSVD), Discrete Wavelet Transform and Singular Value Decomposition (DWT-SVD) and Discrete Wavelet Transform, Discrete Cosine Transform and Singular...

A new method for detecting shot boundaries in video sequences using singular value decomposition (SVD) is proposed. The method relies on performing singular value decomposition on the matrix A created from 3D histograms of single frames. We have used SVD for its capabilities to derive a low dimensional refined feature space from a high dimensional raw feature space, where pattern similarity can...

We consider the improvement in accuracy of latent semantic analysis when a part of speech tagger is used to augment a term/document matrix. We first construct an augmented term/document matrix as input into singular value decomposition (SVD). The singular values then serve as principal components for a cosine projection. The results show that the addition of POS tags can decrease ambiguities si...

In this paper, we analyze the behaviour of Singular Value Decomposition in a number of word similarity extraction tasks, namely acquisition of translation equivalents from comparable corpora. Special attention is paid to two different aspects: computational efficiency and extraction quality. The main objective of the paper is to describe several experiments comparing methods based on Singular V...

The present paper considers singular value decomposition (SVD) for a class of linear time-varying systems. The class considered herein describes timedriven switched linear systems. Based on an appropriate input-output description, the calculation method of singular values and singular vectors is derived. The SVD enables us to characterize the dominant input–output signals using singular vectors...

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order....

This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t)T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain di erentiability the diagonal entries of S(t) are allowed to be either positive or negative and to appear in any order....

The purpose of this paper is to present a largely self-contained proof of the singular value decomposition (SVD), and to explore its application to the low rank approximation problem. We begin by proving background concepts used throughout the paper. We then develop the SVD by way of the polar decomposition. Finally, we show that the SVD can be used to achieve the best low rank approximation of...