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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Patent•
20 Apr 2011
TL;DR: In this paper, a linear precoding method in a multiuser multi-input and multi-output (MIMO) system is proposed, which comprises the following steps: determining the interference channel transmission matrix in the system of each user according to the channel estimation results, wherein, k is user index and k is in the range from 1 to K, and K is the user number served by the system base station simultaneously in the same band range.
Abstract: The invention discloses a linear precoding method in a multiuser multi-input and multi-output (MIMO) system, which comprises the following steps: determining the interference channel transmission matrix HK in the system of each user according to the channel estimation results, wherein, k is user index, k is in the range from 1 to K, and K is the user number served by the system base station simultaneously in the same band range; carrying out the QR decomposition to the conjugate transposed matrix HK of a random user's interference channel transmission matrix HK, and forming the user's linear precoding matrix Tk according to the QR decomposition result; and carrying out the linear precoding to each user's emission signal sk respectively by utilizing the formed linear precoding matrix Tk.
21 citations
TL;DR: This work introduces symplectic Householder transformations and shows their main features and constructs a new algorithm, the analogous of the classical QR factorization, via Householders transformations, which involves free parameters.
21 citations
DOI•
01 Jan 2017TL;DR: Experimental results show that the proposed color image scheme has stronger robustness against most common attacks such as image compression, filtering, cropping, noise adding etc.
Abstract: A novel color image watermarking scheme based on DWT (Discrete Wavelet Transform) and QR decomposition is proposed to embed color watermark image into color host image. Firstly, the each component of the color host image is transformed by one-level DWT, and further divided to 44 non-overlapping pixel blocks. Then, each selected pixel block is decomposed by QR decomposition and the first row elements in the matrix R is quantified for embedding the watermark information. In the extraction procedure, the watermark can be extracted from the watermarked image without the requirement of the original host image or the original watermark image. Experimental results, compared with the related existing methods, show that the proposed color image scheme has stronger robustness against most common attacks such as image compression, filtering, cropping, noise adding etc.
21 citations
09 May 1995
TL;DR: Simulation results demonstrate the efficiency of this new combined structure for acoustic echo cancellation, and a fixed-point implementation of the proposed scheme confirms the expected numerical robustness of the fast QR-RLS algorithm.
Abstract: High quality acoustic echo cancellation is now required by hands-free systems used in mobile radio and teleconference communications. The demand for fast convergence, good tracking capabilities, and reduced complexity cannot be met by classical adaptive filtering algorithms. In this paper, a new echo canceller using multirate systems and a fast QR-decomposition based RLS algorithm is investigated. Simulation results demonstrate the efficiency of this new combined structure for acoustic echo cancellation, and a fixed-point implementation of the proposed scheme confirms the expected numerical robustness of the fast QR-RLS algorithm.
21 citations
Proceedings Article•
01 Aug 2010TL;DR: An algorithm is presented for computing the singular value decomposition (SVD) of a polynomial matrix that avoids “squaring” the matrix to be factorised, uses only unitary and paraunitary operations, and therefore exhibits a high degree of numerical stability.
Abstract: An algorithm is presented for computing the singular value decomposition (SVD) of a polynomial matrix. It takes the form of a sequential best rotation (SBR) algorithm and constitutes a generalisation of the Kogbetliantz technique for computing the SVD of conventional scalar matrices. It avoids “squaring” the matrix to be factorised, uses only unitary and paraunitary operations, and therefore exhibits a high degree of numerical stability.
21 citations