Efficient computation of high-order Meixner moments for large-size signals and images analysis

In this paper, we present an in-depth study on the computational aspects of high-order discrete orthogonal Meixner polynomials (MPs) and Meixner moments (MMs). This study highlights two major problems related to the computation of MPs. The first problem is the overflow and the underflow of MPs values (“Nan” and “infinity”). To overcome this problem, we propose two new recursive Algorithms for MPs computation with respect to the polynomial order n and with respect to the variable x. These Algorithms are independent of all functions that are the origin the numerical overflow and underflow problem. The second problem is the propagation of rounding errors that lead to the loss of the orthogonality property of high-order MPs. To fix this problem, we implement MPs based on the following orthogonalization methods: modified Gram-Schmidt process (MGS), Householder method, and Givens rotation method. The proposed Algorithms for the stable computation of MPs are efficiently applied for the reconstruction and localization of the region of interest (ROI) of large-sized 1D signals and 2D/3D images. We also propose a new fast method for the reconstruction of large-size 1D signal. This method involves the conversion of 1D signal into 2D matrix, then the reconstruction is performed in the 2D domain, and a 2D to 1D conversion is performed to recover the reconstructed 1D signal. The results of the performed simulations and comparisons clearly justify the efficiency of the proposed Algorithms for the stable analysis of large-size signals and 2D/3D images.

     

2D and 3D image localization,compression and reconstruction using new hybrid moments

In this article, we will present a new set of hybrid polynomials and their corresponding moments, with a view to using them for the localization, compression and reconstruction of 2D and 3D images. These polynomials are formed from the Hahn and Krawtchouk polynomials. The process of calculating these is successfully stabilized using the modified recurrence relations with respect to the n order, the variable x and the symmetry property. The hybrid polynomial generation process is carried out in two forms: the first form contains the separable discrete orthogonal polynomials of Krawtchouk–Hahn (DKHP) and Hahn–Krawtchouk (DHKP). The latter are generated as the product of the discrete orthogonal Hahn and Krawtchouk polynomials, while the second form is the square equivalent of the first form, it consists of discrete squared Krawtchouk–Hahn polynomials (SKHP) and discrete polynomials of Hahn–Krawtchouk squared (SHKP). The experimental results clearly show the efficiency of hybrid moments based on hybrid polynomials in terms of localization property and computation time of 2D and 3D images compared to other types of moments; on the other hand, encouraging results have also been shown in terms of reconstruction quality and compression despite the superiority of classical polynomials.

     

NARP-HPLC/MS and silver cationization fingerprinting of triacylglycerols in wild and cultivar Tunisian peanut kernels

A simple strategy to identify triacylglycerols (TAGs) in wild and cultivar peanuts was performed using on line coupling of non-aqueous reversed phase chromatography-electrospray ionization–mass spectrometry (NARP-LC-ESI–MS) with silver nitrate (AgNO₃) as a post-column additive. The combination of the structural information given by MS with chromatographic retention laws led to the determination of the structure of TAGs in wild and cultivar peanut oil. In addition, by using the MS⁵ method, the regio-specificity of the TAGs was determined. It was also demonstrated that in Tunisian peanut oil, the saturates have a preference for the sn-1/sn-3 position for the arachidonic and behenic acids. In the wild variety fatty acids with odd numbers of carbons were found and more TAGs were identified in comparison to the cultivar peanut oil.     

Kernelized relative entropy for direct fault detection in industrial rotary kilns

The objective of this work is to use a 1‐dimensional signal that reflects the dissimilarity between multidimensional probability densities for detection. With the modified Kullback‐Leibler divergence, faults can be directly detected without any normality assumption or joint monitoring of related test statistics in different subspaces such as the T² and SPE in principal component analysis–based methods. To relieve the difficulty associated with asymptotic high‐dimensional density estimates, we have estimated the density ratio rather than the densities themselves. This can be done by approximating the density ratio with kernel basis functions and learn the weights from the available data. The developed algorithm is generic and can be applied to any industrial system as long as process historical data is available. As a case study, we apply this algorithm to a real rotary kiln in operation, which is an integral part of the cement manufacturing plant of Ain El Kebira, Algeria.     

Enhanced collective detection for GNSS weak signals acquisition in Rayleigh channel

Global navigation satellite system applications based on high sensitivity and weak‐signal acquisition is a difficult task and has become an important research area. Algorithms and techniques are proposed, principally those associated to cases of limited global navigation satellite system signal availability. Collective detection is a new technique that seems to offer better solutions in a such situation. This paper presents a performance analysis of GPS L₁ noncoherent acquisition via collective detection based on the systematic and efficient collective acquisition algorithm in the Rayleigh fading channel, firstly in the case of a fixed threshold detection and secondly in the case of adaptive threshold detection based on a constant false alarm rate. To compare these methods with traditional acquisition schemes, we develop detection and false alarm probability analytic expressions.     

New formulation of GNSS acquisition with CFAR detection

This paper deals with the analysis of the acquisition process performed by a global navigation satellite system (GNSS) receiver with a pilot and data channel or in case of GNSS hybrid receiver. Signal acquisition decides the presence or absence of GNSS signal by comparing signal under test with a fixed threshold and provides a code delay and a Doppler frequency estimation, but in low signal conditions or in a noisy environment; acquisition systems are vulnerable and can give a high false alarm and low detection probability. Firstly, we introduce a cell‐averaging‐constant false alarm rate (CFAR) then a data‐pilot cell‐averaging‐CFAR detector fusion based to deal with these situations. In this context, we use a new mathematical derivation to develop a closed‐form analytic expressions for the probabilities of detection and false alarm. The performances of the proposed detector are evaluated and compared with a non‐CFAR case through an analytical and numerical results validated by Mont Carlo simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Correction to: 2D and 3D image localization,compression and reconstruction using new hybrid moments

Multidimensional Systems and Signal Processing -     

A robust auto‐adaptive approach for serial acquisition of generalized multi‐carrier spread spectrum in multipath fading mobile channels

In this paper, a new robust auto‐adaptive approach for pseudo‐noise (PN) code acquisition is proposed. It is applied to the generalized multi‐carrier direct‐sequence code‐division multiple‐access (MC DS‐CDMA) systems communicating over frequency‐selective multipath Rayleigh fading channels. This new approach is based on the constant false alarm rate (CFAR) detection algorithm, referred here as automatic selection partial sum ordered statistics (ASPSOS)‐CFAR. The proposed approach does not require any prior information about the background environment and uses maximum likelihood estimation (MLE) method to detect the interfering signals group in the ranked cells for the full reference window. Once this group is identified and censored, the remaining smaller ranked cells are combined to form an estimate of the background noise level to compute the adaptive threshold. Through simulations, the performance of the proposed detector is analyzed and compared with traditional CFAR detectors based on fixed or automatic censoring algorithms. The obtained results show that the proposed detector eliminates the drawbacks of the previously related detectors and offers a robust detection performance to enhance the acquisition process in heterogeneous background environments.     

Direct Arylation of Thiophenes via Palladium‐Catalysed C?H Functionalisation at Low Catalyst Loadings

Palladium associated with cis,cis,cis‐1,2,3,4‐tetrakis(diphenylphosphinomethyl)cyclopentane (Tedicyp) was found to promote the direct 2‐arylation of a variety of thiophene derivatives via C H functionalisation in good yields using very low catalyst loadings. Electron‐deficient, electron‐excessive or sterically‐congested aryl bromides are tolerated. Moreover, several substituents on the aryl bromide or thiophene derivatives such as acetyl, formyl, nitrile, nitro, ester, methoxy, fluoro or trifluoromethyl are tolerated. The most reactive aryl bromides were coupled with thiophenes derivatives using as little as 0.1–0.01 mol % catalyst.