Topic
QR decomposition
About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.
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TL;DR: A new algorithm is presented for the stable computation of sample partial correlation coefficients for symmetric positive-definite matrices B by generalizing Bareiss' algorithm for the solution of linear systems of equations with (non-symmetric) Toeplitz coefficient matrix to matrices that are not ToEplitz, and showing that it computes their LU and UL factorizations.
12 citations
TL;DR: Better imperceptibility, large capacity, and poor detection accuracy compared to existing work validate the efficacy of the proposed image steganography algorithm.
Abstract: This paper presents the transform domain image steganography schemes using three popular matrix factorization techniques and contourlet transform. It is known that security of image steganography is mainly evaluated using undetectability of stego image when steganalyzer examines it in order to detect the presence of hidden secret information. Good imperceptibility only suggests eavesdropper’s inability to suspect about the hidden information; however stego image may be analyzed by applying certain statistical checks when it is being transmit- ted through the channel. This work focusses on improving undetectability by employing ma- trix decomposition techniques along with transform domain image steganography. Singular value decomposition (SVD), QR factorization, Nonnegative matrix factorization (NMF) are employed to decompose contourlet coefficients of cover image and secret is embedded into its matrix factorized coefficients. The variety of investigations include the effect of matrix decomposition techniques on major attributes of image steganography like imperceptibility, robustness to a variety of image processing operations, and universal steganalysis perfor- mance. Better imperceptibility, large capacity, and poor detection accuracy compared to existing work validate the efficacy of the proposed image steganography algorithm. Compa- rative analysis amongst three matrix factorization methods is also presented and analyzed.
12 citations
TL;DR: A hybrid method of adaptively modified characteristic basis function method (AM CBFM) and QR factorization with a dual modified Gram‐Schmidt (Dual‐MGS) algorithm, which is called QR‐AMCBFM, is presented.
Abstract: In this article, a hybrid method of adaptively modified characteristic basis function method (AMCBFM) and QR factorization with a dual modified Gram-Schmidt (Dual-MGS) algorithm, which is called QR-AMCBFM, is presented. The first step is to derive the primary basis functions by using AMCBFM. To get the high-level basis functions, QR factorization algorithm with Dual-MGS is used to decompose the mutual coupling matrices. Different threshold values for the near and far field domains are set in the QR scheme. When the numerical rank gotten in the upper program is down to a set threshold, the rest interaction between farther blocks would be ignored. Subsequently, the high-level characteristic basis functions and the coefficient of current are calculated. Once the adjacent currents precision arrives at a certain criterion, the higher-level basis functions are thought of unnecessary. The hybrid algorithm estimates adaptively in the entire process. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2879–2883, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22830
12 citations
TL;DR: Parallel strategies are proposed for updating the QR decomposition of an mxn matrix after adding k rows and are found to complete the updating in fewer steps by comparison to a recently published algorithm.
Abstract: Parallel strategies are proposed for updating the QR decomposition of an mxn matrix after adding k rows (k ≫ n). These strategies are based on Givens rotations and are found to complete the updating in fewer steps by comparison to a recently published algorithm. An efficient adaptation of the first parallel strategy to compute the QR decomposition of structured banded matrices is also discussed in detail.
12 citations
Patent•
04 Oct 2001TL;DR: In this article, an improved symbol decision is generated of a desired subchannel of the signal vector by first generating a baseline decision for the sub-channel, which is then multiplied by a unitary matrix generated from a QR decomposition of another channel matrix.
Abstract: A system and method for performing extended space-time processing. An improved symbol decision is generated of a desired sub-channel of the signal vector by first generating a baseline decision for the sub-channel. A contribution of a strongest sub-channel is subtracted from the signal vector to generate a modified signal vector. The modified signal vector is multiplied by a unitary matrix generated from a QR decomposition of another channel matrix. Channel interference of the remaining sub-channels of the modified signal vector is cancelled from a remaining sub-channel.
12 citations