l(1)-K-SVD: A robust dictionary learning algorithm with simultaneous update

We develop a new dictionary learning algorithm called the l(1)-K-svp, by minimizing the l(1) distortion on the data term. The proposed formulation corresponds to maximum a posteriori estimation assuming a Laplacian prior on the coefficient matrix and additive noise, and is, in general, robust to non-Gaussian noise. The l(1) distortion is minimized by employing the iteratively reweighted least-squares algorithm. The dictionary atoms and the corresponding sparse coefficients are simultaneously estimated in the dictionary update step. Experimental results show that l(1)-K-SVD results in noise-robustness, faster convergence, and higher atom recovery rate than the method of optimal directions, K-SVD, and the robust dictionary learning algorithm (RDL), in Gaussian as well as non-Gaussian noise. For a fixed value of sparsity, number of dictionary atoms, and data dimension, l(1)-K-SVD outperforms K-SVD and RDL on small training sets. We also consider the generalized l(p), 0 < p < 1, data metric to tackle heavy-tailed/impulsive noise. In an image denoising application, l(1)-K-SVD was found to result in higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise. The structural similarity index increases by 0.1 for low input PSNR, which is significant and demonstrates the efficacy of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

Adaptive Scalable SVD Unit for Fast Processing of Large LSE Problems

Singular Value Decomposition (SVD) is a key linear algebraic operation in many scientific and engineering applications. In particular, many computational intelligence systems rely on machine learning methods involving high dimensionality datasets that have to be fast processed for real-time adaptability. In this paper we describe a practical FPGA (Field Programmable Gate Array) implementation of a SVD processor for accelerating the solution of large LSE problems. The design approach has been comprehensive, from the algorithmic refinement to the numerical analysis to the customization for an efficient hardware realization. The processing scheme rests on an adaptive vector rotation evaluator for error regularization that enhances convergence speed with no penalty on the solution accuracy. The proposed architecture, which follows a data transfer scheme, is scalable and based on the interconnection of simple rotations units, which allows for a trade-off between occupied area and processing acceleration in the final implementation. This permits the SVD processor to be implemented both on low-cost and highend FPGAs, according to the final application requirements.

On the use of a decimative spectral estimation method based on eigenanalysis and SVD for formant and bandwidth tracking of speech signals

In this paper, a Decimative Spectral estimation method based on Eigenanalysis and SVD (Singular Value Decomposition) is presented and applied to speech signals in order to estimate Formant/Bandwidth values. The underlying model decomposes a signal into complex damped sinusoids. The algorithm is applied not only on speech samples but on a small amount of the autocorrelation coefficients of a speech frame as well, for finer estimation. Correct estimation of Formant/Bandwidth values depend on the model order thus, the requested number of poles. Overall, experimentation results indicate that the proposed methodology successfully estimates formant trajectories and their respective bandwidths.

基于SVD和能量最小原则的图像自适应降噪算法

基于奇异值分解和能量最小原则,提出了一种自适应图像降噪算法,并给出了基于有界变差的能量降噪模型的代数形式。通过在矩阵范数意义下求能量最小,自适应确定去噪图像重构的奇异值个数。该算法的特点是将能量最小法则和奇异值分解结合起来,在代数空间中建立了一种自适应的图像降噪算法。与基于压缩比和奇异值分解的降噪方法相比,由于该算法避免了图像压缩比函数及其拐点的计算,因此具有快速去噪和简单可行的优点。实验结果证明,该算法是有效的。

A note on stopping rules for iterative regularisation methods and filtered SVD

"This volume contains the proceedings of a meeting held at Montpellier from December 1st to December 5th 1986 .sponsored by the Centre national de la recherche scientifique ."--Preface.

SVD for linear inverse problems

info:eu-repo/semantics/published

CORDIC based application-specific instruction set processor for QRD/SVD

An application specific programmable processor (ASIP) suitable for the real-time implementation of matrix computations such as Singular Value and QR Decomposition is presented. The processor incorporates facilities for the issue of parallel instructions and a dual-bus architecture that are designed to achieve high performance. Internally, it uses a CORDIC module to perform arithmetic operations, with pipelining of the internal recursive loop exploited to multiplex the two independent micro-rotations onto a single piece of hardware. The net result is a flexible processing element whose functionality can be changed under program control, which combines high performance with efficient silicon implementation. This is illustrated through the results of a detailed silicon design study and the applications of the techniques to a combined SVD/QRD system.

SVD-Based Universal Spatial Domain Image Steganalysis

This paper is concerned with the universal (blind) image steganalysis problem and introduces a novel method to detect especially spatial domain steganographic methods. The proposed steganalyzer models linear dependencies of image rows/columns in local neighborhoods using singular value decomposition transform and employs content independency provided by a Wiener filtering process. Experimental results show that the novel method has superior performance when compared with its counterparts in terms of spatial domain steganography. Experiments also demonstrate the reasonable ability of the method to detect discrete cosine transform-based steganography as well as the perturbation quantization method.

QRD and SVD processor design based on an approximate rotations algorithm

A silicon implementation of the Approximate Rotations algorithm capable of carrying the computational load of algorithms such as QRD and SVD, within the real-time realisation of applications such as Adaptive Beamforming, is described. A modification to the original Approximate Rotations algorithm to simplify the method of optimal angle selection is proposed. Analysis shows that fewer iterations of the Approximate Rotations algorithm are required compared with the conventional CORDIC algorithm to achieve similar degrees of accuracy. The silicon design studies undertaken provide direct practical evidence of superior performance with the Approximate Rotations algorithm, requiring approximately 40% of the total computation time of the conventional CORDIC algorithm, for a similar silicon area cost. © 2004 IEEE.

A floating point CORDIC based SVD processor

An SVD processor system is presented in which each processing element is implemented using a simple CORDIC unit. The internal recursive loop within the CORDIC module is exploited, with pipelining being used to multiplex the two independent micro-rotations onto a single CORDIC processor. This leads to a high performance and efficient hardware architecture. In addition, a novel method for scale factor correction is presented which only need be applied once at the end of the computation. This also reduces the computation time. The net result is an SVD architecture based on a conventional CORDIC approach, which combines high performance with high silicon area efficiency.

Modulation-Mode Assignment in SVD-Aided Downlink Multiuser MIMO-OFDM Systems

Multicarrier transmission such as OFDM (orthogonal frequency division multiplexing) is an established technique for radio transmission systems and it can be considered as a promising approach for next generation wireless systems. However, in order to comply with the demand on increasing available data rates in particular in wireless technologies, systems with multiple transmit and receive antennas, also called MIMO (multiple-input multiple-output) systems, have become indispensable for future generations of wireless systems. Due to the strongly increasing demand in high-data rate transmission systems, frequency non-selective MIMO links have reached a state of maturity and frequency selective MIMO links are in the focus of interest. In this field, the combination of MIMO transmission and OFDM can be considered as an essential part of fulfilling the requirements of future generations of wireless systems. However, single-user scenarios have reached a state of maturity. By contrast multiple users' scenarios require substantial further research, where in comparison to ZF (zero-forcing) multiuser transmission techniques, the individual user's channel characteristics are taken into consideration in this contribution. The performed joint optimization of the number of activated MIMO layers and the number of transmitted bits per subcarrier shows that not necessarily all user-specific MIMO layers per subcarrier have to be activated in order to minimize the overall BER under the constraint of a given fixed data throughput.

Modulation-mode assignment in SVD-assisted multiuser MIMO-OFDM systems

In order to comply with the demand on increasing available data rates in particular in wireless technologies, systems with multiple transmit and receive antennas, also called MIMO (multiple-input multiple-output) systems, have become indispensable for future generations of wireless systems. Due to the strongly increasing demand in high-data rate transmission systems, frequency non-selective MIMO links have reached a state of maturity and frequency selective MIMO links are in the focus of interest. In this field, the combination of MIMO transmission and OFDM (orthogonal frequency division multiplexing) can be considered as an essential part of fulfilling the requirements of future generations of wireless systems. However, single-user scenarios have reached a state of maturity. By contrast multiple users’ scenarios require substantial further research, where in comparison to ZF (zero-forcing) multiuser transmission techniques, the individual user’s channel characteristics are taken into consideration in this contribution. The performed joint optimization of the number of activated MIMO layers and the number of transmitted bits per subcarrier along with the appropriate allocation of the transmit power shows that not necessarily all user-specific MIMO layers per subcarrier have to be activated in order to minimize the overall BER under the constraint of a given fixed data throughput.