A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints

Lantéri, H.; Roche, Muriel; Cuevas, O.; Aime, Claude

doi:10.1016/s0165-1684(00)00275-9

Cited by 92 publications

(110 citation statements)

References 32 publications

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“…Projected gradient methods [6], [7] are based on successive projections on the feasible region. Multiplicative algorithms are very popular to solve NMF problems [8]. All these algorithms are however based on batch processing, which is not suitable for online system identification problems.…”

Section: Introductionmentioning

confidence: 99%

A modified non-negative LMS algorithm and its stochastic behavior analysis

Chen¹,

Richard²,

Bermudez³

et al. 2011

2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

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Abstract-Non-negativity is a constraint that can sometimes be imposed on parameters to estimate. Non-negative least-meansquare (NN-LMS) algorithm is an efficient online methods that finds adaptively solutions of a Wiener problem subject to such constraints over the filter weights. However, during the convergence of this algorithm, it has been observed that the weights may have unbalanced convergence rates. Small weights have much slower convergence rates compared with larger ones, which is usually an undesired phenomenon. In this paper, we present a modified NN-LMS algorithm in order to compensate this unbalanced rates. We also propose two models to characterize the first-order and the second-order behavior of this algorithm. Experiments are conducted to validate the algorithm and the models.

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Section: Introductionmentioning

confidence: 99%

A modified non-negative LMS algorithm and its stochastic behavior analysis

Chen¹,

Richard²,

Bermudez³

et al. 2011

2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

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“…5.1. About this second step, in a series of recent papers Lanteri et al [Lan01,Lan02] proposed a general approach, denoted as split gradient method (SGM), to the design of iterative methods for the minimization of a wide class of convex (and also non-convex) functionals of the following type:…”

Section: Split Gradient Methods (Sgm)mentioning

confidence: 99%

“…The applicability of the method requires explicit expressions for the dependence of these arrays on f. Then the general structure of the iterative algorithm, as described in Lanteri et al [Lan01], is as follows:…”

Section: Split Gradient Methods (Sgm)mentioning

confidence: 99%

“…We will call it the acceleration factor. Indeed, as discussed by Lanteri et al [Lan01], an integer value of ω > 1 can speed-up the convergence of the iterations and we will focus on this parameter in the Chapter 6. At the very first iterations ω modifies the descent direction; but, when the iterations are close to convergence, the algorithm with ω > 1 is approximately equivalent to the algorithm with ω = 1 and step-size α ω.…”

Section: Split Gradient Methods (Sgm)mentioning

confidence: 99%

“…Then, according to the split gradient method (SGM), proposed by Lanteri et al ([Lan01], [Lan02]), we write also the gradient of the regularization functional in a similar way:…”

Section: Regularized Rlm and Osemmentioning

confidence: 99%

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Large Binocular Telescope

Salinari¹

The Encyclopedia of Astronomy and Astrophysics

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Some of the new giant ground-bases telescopes will be equipped with interferometric systems, so that multiple images of the same target, corresponding to different orientations of the baseline, will be available. These interferometric images will need specific processing to provide a unique high resolution image of the target.In this thesis we consider the case of the Large Binocular Telescope (LBT) which is currently under construction on the top of Mount Graham in Arizona and will be equipped with a Fizeau interferometer with a baseline of 22.8m. From the point of view of image reconstruction, the interesting feature is that LINC/NIRVANA (the Fizeau interferometer for LBT) will require routinely the use of multiple image deconvolution methods to produce a unique image with the resolution of a 22.8m telescope.The aim of the thesis is to investigate the extension of existing reconstruction methods to the problem of multiple image deconvolution, to optimize their use and to propose and develop new methods in order to face problems not yet solved.In this sense we find out that two classes of deconvolution methods with different characteristics may be needed:-quick-look methods, computationally efficient even if not always very accurate, to be routinely used for a preliminary view of the target just after data acquisition; -ad hoc methods, designed for specific classes of astronomical objects, which can be computationally expensive but must be accurate as far as possible for all the objects in a given class.Therefore the processing of LINC/NIRVANA images will in general require two steps: the first, based on a quick-look method, is intended to identify the specific features of the particular object the astronomer is observing; the second consists in the use of the ad hoc method which has been designed for the objects with those specific features.In the case of quick-look methods we develop acceleration techniques of the OS-EM (Ordered Subsets Expectation Maximization) algorithm, allowing a reduction of the number of iterations without a significant increase of the computational cost per iteration. Moreover we investigate and implement the combination of the multi-images provided by LN into a single one to use single image deconvolution methods.For the second class of methods we propose and develop a method which is able to superresolve compact stellar objects such as a binary system with an angular separation smaller than the angular resolution of the telescope. Moreover we extend to the multiple image case a general approach, denoted as SGM (Split Gradient Method), and we use it for introducing a new method for the reconstruction of objects with a high dynamic range.All these methods are validated by means of extensive numerical simulations.Two general problems of image reconstruction are also investigated and solved. Indeed we propose a method for the reduction of the boundary effects (ripples) in the deconvolution of astronomical images. Moreover we develop a blind deconvolution method to be used when po...

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Introduction Toimage Reconstruction and Inverse Problems

Thiébaut

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints

Cited by 92 publications

References 32 publications

A modified non-negative LMS algorithm and its stochastic behavior analysis

A modified non-negative LMS algorithm and its stochastic behavior analysis

Large Binocular Telescope

Introduction Toimage Reconstruction and Inverse Problems

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