Scalability and Communication in Parallel Low-Complexity Lossless Compression

Approximation schemes for optimal compression with static and sliding dictionaries which can run on a simple array of processors with distributed memory and no interconnections are presented. These approximation algorithms can be implemented on both small and large scale parallel systems. The sliding dictionary method requires large size files on large scale systems. As far as lossless image compression is concerned, arithmetic encoders enable the best lossless compressors but they are often ruled out because they are too complex. Storer extended dictionary text compression to bi-level images to avoid arithmetic encoders (BLOCK MATCHING). We were able to partition an image into up to a hundred areas and to apply the BLOCK MATCHING heuristic independently to each area with no loss of compression effectiveness. Therefore, the approach is suitable for a small scale parallel system at no communication cost. On the other hand, bi-level image compression seems to require communication on large scale systems. With regard to grey scale and color images, parallelizable lossless image compression (PALIC) is a highly parallelizable and scalable lossless compressor since it is applied independently to blocks of 8 × 8 pixels. We experimented the BLOCK MATCHING and PALIC heuristics with up to 32 processors of a 256 Intel Xeon 3.06 GHz processors machine () on a test set of large topographic bi-level images and color images in RGB format. We obtained the expected speed-up of the compression and decompression times, achieving parallel running times about 25 times faster than the sequential ones. Finally, scalable algorithms computing static and sliding dictionary optimal text compression on an exclusive read, exclusive write shared memory parallel machine are presented. On the same model, compression by block matching of bi-level images is shown which can be implemented on a full binary tree architecture under some realistic assumptions with no scalability issues.     

Greedy Algorithms with Regard to Multivariate Systems with Special Structure

The question of finding an optimal dictionary for nonlinear m -term approximation is studied in this paper. We consider this problem in the periodic multivariate (d variables) case for classes of functions with mixed smoothness. We prove that the well-known dictionary U ^d which consists of trigonometric polynomials (shifts of the Dirichlet kernels) is nearly optimal among orthonormal dictionaries. Next, it is established that for these classes near-best m -term approximation, with regard to U ^d , can be achieved by simple greedy-type (thresholding-type) algorithms. The univariate dictionary U is used to construct a dictionary which is optimal among dictionaries with the tensor product structure. June 22, 1998. Date revised: March 26, 1999. Date accepted: March 22, 1999.     

Approximate Galerkin method applied to an analysis of vibration of continuous mechanical systems

Paper presents fundamental assumptions of the approximate Galerkin method application in order to vibration analysis of continuous mechanical systems with different form of vibration and different boundary conditions. Flexural vibration of beams, longitudinal vibration of rods and torsional vibration of shafts with all possible ways of fixing were considered. Analyzed mechanical systems were treated as subsystems of mechatronic systems with piezoelectric transducers. This work was done as an introduction to the analysis of mechatronic systems with piezoelectric transducers used as actuators or passive vibration dampers [1–3]. It is impossible to use an exact Fourier method in this case. This is the reason why the approximate Galerkin method was chosen and analysis of its exactness was done as a first step of this work. Dynamic flexibilities of considered mechanical systems were calculated twice, using exact and approximate methods. Obtained results were juxtaposed and it was proved that in some cases the approximate method should be corrected while in the other it is precise enough. A correction method was proposed and it was assumed that the approximate method can be used in mechatronic systems analysis. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and system identification of active magnetic bearing systems

Active magnetic bearing (AMB) systems have recently attracted much attention in the rotating machinery industry due to their advantages over traditional bearings such as fluid film and rolling element bearings. The AMB control system must provide robust performance over a wide range of machine operating conditions and over the machine lifetime in order to make this technology commercially viable. An accurate plant model for AMB systems is essential for the aggressive design of control systems. In this paper, we propose two approaches to obtain accurate AMB plant models for the purpose of control design: physical modelling and system identification. The former derives a model based upon the underlying physical principles. The latter uses input – output data without explicitly resorting to physical principles. For each problem, a brief summary of the theoretical derivation and assumptions is given. Experimental results based on data collected from an AMB test facility at the United Technologies Research Center provide a vehicle for a comparison of the two approaches.     

Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries

Many signal processing problems—such as analysis, compression, denoising, and reconstruction—can be facilitated by expressing the signal as a linear combination of atoms from a well-chosen dictionary. In this paper, we study possible dictionaries for representing the discrete vector one obtains when collecting a finite set of uniform samples from a multiband analog signal. By analyzing the spectrum of combined time- and multiband-limiting operations in the discrete-time domain, we conclude that the information level of the sampled multiband vectors is essentially equal to the time–frequency area. For representing these vectors, we consider a dictionary formed by concatenating a collection of modulated discrete prolate spheroidal sequences (DPSS’s). We study the angle between the subspaces spanned by this dictionary and an optimal dictionary, and we conclude that the multiband modulated DPSS dictionary—which is simple to construct and more flexible than the optimal dictionary in practical applications—is nearly optimal for representing multiband sample vectors. We also show that the multiband modulated DPSS dictionary not only provides a very high degree of approximation accuracy in an MSE sense for multiband sample vectors (using a number of atoms comparable to the information level), but also that it can provide high-quality approximations of all sampled sinusoids within the bands of interest.     

Unitary invariants of spectral measures with the CGS-property

A «CGS-property» for the spectral measures is introduced and the classical results of determining complete systems of unitary invariants for self-adjoint and bounded normal operators on separable Hilbert spaces are extended to the class of spectral measures with this property. As a consequence, the above mentioned results are extended to unbounded normal operators on separable Hilbert spaces. Moreover, three different kinds of multiplicity are defined and it is shown that for the measures with the «CGS-property» they all coincide. In the last section some analogues of the multiplicity functions defined by Stone [14] are related to the total multiplicity.     

A simplified pivoting strategy for symmetric tridiagonal matrices

The pivoting strategy of Bunch and Marcia for solving systems involving symmetric indefinite tridiagonal matrices uses two different methods for solving 2 × 2 systems when a 2 × 2 pivot is chosen. In this paper, we eliminate this need for two methods by adding another criterion for choosing a 1 × 1 pivot. We demonstrate that all the results from the Bunch and Marcia pivoting strategy still hold. Copyright © 2006 John Wiley & Sons, Ltd.     

Preservation of reliability classes under the formation of coherent systems

The preservation of reliability aging classes under the formation of coherent systems is a relevant topic in reliability theory. Thus, it is well known that the new better than used class is preserved under the formation of coherent systems with independent components. However, surprisingly, the increasing failure rate class is not preserved in the independent and identically distributed case, that is, the components may have the (negative) aging increasing failure rate property, but the system does not have this property. In this paper, we study conditions for the preservation of the main reliability classes under the formation of general coherent systems. These results can be applied both for systems with independent or dependent components. We consider both the case of systems with identically distributed components and the case of systems with components having different distributions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field

We compute a local linearization for the nonlinear, inverse problem of identifying the stored energy function of a hyperelastic material from the full knowledge of the displacement field. The displacement field is described as a solution of the nonlinear, dynamic, elastic wave equation, where the first Piola–Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that we have a dictionary at hand such that the energy function is given as a conic combination of the dictionary's elements. In that sense, the mathematical model of the direct problem is the nonlinear operator that maps the vector of expansion coefficients to the solution of the hyperelastic wave equation. In this article, we summarize some continuity results for this operator and deduce its Fréchet derivative as well as the adjoint of this derivative. Because the stored energy function encodes mechanical properties of the underlying, hyperelastic material, the considered inverse problem is of highest interest for structural health monitoring systems where defects are detected from boundary measurements of the displacement field. For solving the inverse problem iteratively by the Landweber method or Newton‐type methods, the knowledge of the Fréchet derivative and its adjoint is of utmost importance. Copyright © 2016 John Wiley & Sons, Ltd.     

The $$ \ell _1 $$-Analysis in Phase Retrieval with Redundant Dictionary

This article presents new results concerning the recovery of a signal from the magnitude only measurements where the signal is not sparse in an orthonormal basis but in a redundant dictionary, which we call it phase retrieval with redundant dictionary for short. To solve this phaseless problem, we analyze the \( \ell _1 \)-analysis model. Firstly we investigate the noiseless case with presenting a null space property of the measurement matrix under which the \( \ell _1 \)-analysis model provides an exact recovery. Secondly we introduce a new property (S-DRIP) of the measurement matrix. By solving the \( \ell _1 \)-analysis model, we prove that this property can guarantee a stable recovery of real signals that are nearly sparse in overcomplete dictionaries.     

Denoising deep extreme learning machine for sparse representation

In recent years, a great deal of research has focused on the sparse representation for signal. Particularly, a dictionary learning algorithm, K-SVD, is introduced to efficiently learn an redundant dictionary from a set of training signals. Indeed, much progress has been made in different aspects. In addition, there is an interesting technique named extreme learning machine (ELM), which is an single-layer feed-forward neural networks (SLFNs) with a fast learning speed, good generalization and universal classification capability. In this paper, we propose an optimization method about K-SVD, which is an denoising deep extreme learning machines based on autoencoder (DDELM-AE) for sparse representation. In other words, we gain a new learned representation through the DDELM-AE and as the new “input”, it makes the conventional K-SVD algorithm perform better. To verify the classification performance of the new method, we conduct extensive experiments on real-world data sets. The performance of the deep models (i.e., Stacked Autoencoder) is comparable. The experimental results indicate the fact that our proposed method is very efficient in the sight of speed and accuracy.     

Identification of the relaxation kernel in diffusion processes and viscoelasticity with memory via deconvolution

We present an algorithm for the identification of the relaxation kernel in the theory of diffusion systems with memory (or of viscoelasticity), which is linear, in the sense that we propose a linear Volterra integral equation of convolution type whose solution is the relaxation kernel. The algorithm is based on the observation of the flux through a part of the boundary of a body. The identification of the relaxation kernel is ill posed, as we should expect from an inverse problem. In fact, we shall see that it is mildly ill posed, precisely as the deconvolution problem which has to be solved in the algorithm we propose. Copyright © 2016 John Wiley & Sons, Ltd.     

A tensor-based dictionary learning approach to tomographic image reconstruction

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images and the reconstructions due to the ability of representing repeated features compactly in the dictionary.     

Consistent learning by composite proximal thresholding

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consistent in a statistical sense, and we design an error-tolerant composite proximal thresholding algorithm for computing such estimators. New results on the asymptotic behavior of the proximal forward–backward splitting method are derived and exploited to establish the convergence properties of the proposed algorithm. In particular, our method features a o(1 / m) convergence rate in objective values.     

ESS,NIS and GIS for matrix games in n‐species systems

In this paper, we discuss the concepts of evolutionarily stable strategy (ESS), neighborhood invader strategy (NIS) and global invader strategy (GIS) in n‐species systems. We give their definitions both on system level and species level. Although the definition on system level and that on species level are apparently different, it is found that they are equivalent to one another. About the relationships among an ESS, an NIS and a GIS for n‐species systems, we obtain the results similar to the ones for single species models: a GIS must be an NIS; an NIS must be an ESS; an ESS may not be a GIS; a GIS must be unique. The stability in the frequency dynamics with two phenotypes is also considered and the global stability of a GIS is shown. Copyright © 2010 John Wiley & Sons, Ltd.     

On evaluating the performance of GSS: Furthering the debate

Following criticism from proponents of workstation group support systems about the lack of validity of ‘wide-band’ group support systems (GSS), a recent article argued that it was inappropriate to attempt to establish the level of experimental validity for such GSS that is demanded by researchers working with 'narrow-band' GSS. It was argued that ‘wide-band’ and workstation GSS are very different and this means that it is unlikely that the same measures of success would be appropriate. This paper agrees with this view but not with its extension, that the overall validation requirement is different; theoretical validity is a necessary feature of a full evaluation but it is not sufficient by itself - experimental validity must also be sought. This paper argues against the view that since experimental validity cannot be obtained, theoretical validity will suffice. A twin-track research approach involving theoretical and experimental validity is proposed that can unite researchers investigating (almost) all forms of GSS, modelled on the PIMS programme and supported by one of the research frameworks that already exist.     

基于字典学习方法的CT不完全投影图像重建算法

对于不完全投影角度的重建研究是CT图像重建中一个重要的问题.将压缩感知中字典学习的方法与CT重建算法ART迭代算法相结合.字典学习方法中字典更新采用K-SVD(K-奇异值分解)算法,稀疏编码采用OMP(正交匹配追踪)算法.最后通过对标准Head头部模型进行仿真实验,验证了字典学习方法在CT图像重建中对于提高图像的重建质量和提高信噪比的可行性与有效性.另外还研究了字典学习中图像块大小和滑动距离对重建图像的影响