Recently four non-iterative algorithms for simultaneous low rank approximations of matrices (SLRAM) have been presented by several researchers. In this paper, we show that those algorithms are equivalent to each other...
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Recently four non-iterative algorithms for simultaneous low rank approximations of matrices (SLRAM) have been presented by several researchers. In this paper, we show that those algorithms are equivalent to each other because they are reduced to the eigenvalue problems of row-row and column-column covariance matrices of given matrices. Also, we show a relationship between the non-iterative algorithms and another algorithm which is claimed to be an analytical algorithm for the SLRAM. Experimental results show that the analytical algorithm does not necessarily give the optimal solution of the SLRAM.
A common problem is verifying the correctness of robotic computer programs based on iterative methods. This work presents a number of principles that the authors have found to be useful in testing such programs.
A common problem is verifying the correctness of robotic computer programs based on iterative methods. This work presents a number of principles that the authors have found to be useful in testing such programs.
iterative algorithms are of interest for both positron-emission tomography (PET) and single-photon-emission computed tomography (SPECT) because they permit accurate modeling of the imaging system, and they can be deri...
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iterative algorithms are of interest for both positron-emission tomography (PET) and single-photon-emission computed tomography (SPECT) because they permit accurate modeling of the imaging system, and they can be derived to satisfy certain statistical performance criteria. The convergence process, however, is influenced by the object distribution and noise level, so that different algorithms demonstrate a wide range of convergence phenomena. This object dependence is described for two widely accepted image-reconstruction algorithms; ART and maximum-likelihood estimation.< >
Concurrent iterative Reconstruction algorithms use projection data in the iterative process as the data become available during the SPECT acquisition process and continue iterations in the post-acquisition period as c...
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Concurrent iterative Reconstruction algorithms use projection data in the iterative process as the data become available during the SPECT acquisition process and continue iterations in the post-acquisition period as conventional iterative algorithms. Because projections acquired early are processed more than later projections, regional inhomogeneities may exist in the initial image estimates but decrease with further post-acquisition iteration. Regularization done either during the acquisition or post-acquisition iterations further reduces regional inhomogeneities. We tested statistical differences in regions throughout the reconstructed image to determine the minimal number of post-acquisition iterations and type of regularization needed to reach an image that is inter-regionally consistent. The algorithms provide images free of reconstruction inhomogeneities and can offer a reduction in post-acquisition reconstruction time when compared to conventional iterative algorithms.
This paper evaluates various iterative deconvolution algorithms that are commonly used to restore degraded chromatographic or spectroscopic peak data. The evaluation criteria include rms errors, relative errors in pea...
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This paper evaluates various iterative deconvolution algorithms that are commonly used to restore degraded chromatographic or spectroscopic peak data. The evaluation criteria include rms errors, relative errors in peak areas, peak area variances and rate of convergence. The iterative algorithms to be evaluated include Van Cittert's method, Van Cittert's method with constraint operators, relaxation based methods, and Gold's ratio method. The discussion also includes some enhancements that will improve the algorithms' convergence properties.
Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the...
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Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are temporally correlated. With signal's temporal correlation in mind, we provide a framework of iterative MMV algorithms based on thresholding, functional feedback and null space tuning. Convergence analysis for exact recovery is established. Unlike most of iterative greedy algorithms that select indices in a measurement/solution space, we determine indices based on an orthogonal subspace spanned by the iterative sequence. In addition, a functional feedback that controls the amount of energy relocation from the "tails" is implemented and analyzed. It is seen that the principle of functional feedback is capable to lower the number of iteration and speed up the convergence of the algorithm. Numerical experiments demonstrate that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity and accuracy compared with other state-of-the-art algorithms.
This paper describes a rather broad class of iterative signal restoration techniques which can be applied to remove the effects of many different types of distortions. These techniques also allow for the incorporation...
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This paper describes a rather broad class of iterative signal restoration techniques which can be applied to remove the effects of many different types of distortions. These techniques also allow for the incorporation of prior knowledge of the signal in terms of the specification of a constraint operator. Conditions for convergence of the iteration under various combinations of distortions and constraints are explored. Particular attention is given to the use of iterative restoration techniques for constrained deconvolution, when the distortion band-limits the signal and spectral extrapolation must be performed. It is shown that by predistorting the signal (and later removing this predistortion) it is possible to achieve spectral extrapolation, to broaden the class of signals for which these algorithms achieve convergence, and to improve their performance in the presence of broad-band noise.
This paper describes two new iterative algorithms for determining absolute value equations. The algorithms are based on a splitting of the coefficient matrix. Moreover, we analyze the convergence effects of the presen...
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This paper describes two new iterative algorithms for determining absolute value equations. The algorithms are based on a splitting of the coefficient matrix. Moreover, we analyze the convergence effects of the presented algorithms via some theorems. Eventually, numerical tests are provided to confirm the credibility of our procedures.
Construction of an ontological metamodel of iterative algorithms is proposed to structure knowledge about these algorithms and their implementation. The metamodel will automate the design and use of specialized softwa...
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ISBN:
(纸本)9798350334319
Construction of an ontological metamodel of iterative algorithms is proposed to structure knowledge about these algorithms and their implementation. The metamodel will automate the design and use of specialized software for solving specific applied modeling problems. The advantage of iterative GMDH algorithms over combinatorial ones is that they allow the big datasets processing. The known generalized iterative algorithm, allows you to create typical architectures of previously developed modifications of these algorithms when setting up various modes of operation of this algorithm. The authors have developed an ontological metamodel of iterative GMDH algorithms using the Protege environment.
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