Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios. © 2011 Elsevier Inc.

An aggregate measure of financial ratios using a multiplicative DEA model

This paper examines the problems in the definition of the General Non-Parametric Corporate Performance (GNCP) and introduces a multiplicative linear programming as an alternative model for corporate performance. We verified and tested a statistically significant difference between the two models based on the application of 27 UK industries using six performance ratios. Our new model is found to be a more robust performance model than the previous standard Data Envelopment Analysis (DEA) model.

Noise modelling and outlier detection in satellite scatterometer data

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Investigation of noise and vibration within an oil flooded sliding vane rotary air compressor

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Experimental demonstration of data-dependent pilot-aided phase noise estimation for CO-OFDM

We demonstrate a novel phase noise estimation scheme for CO-OFDM, in which pilot subcarriers are deliberately correlated to the data subcarriers. This technique reduces the overhead by a factor of 2. © OSA 2014.

Noise and gain optimisation in bi-directionally pumped dispersion compensating amplifier modules

We perform optimisation of bi-directionally pumped dispersion compensating Raman amplifier modules. Optimal forward and backward pump powers for basic configurations using different commercially available fibers are presented for both single- and multi-channel systems. Optical signal-to-noise ratio improvement of up to 8 dB is achieved as a result of optimisation. © 2003 Published by Elsevier B.V.

Statistics of a noise-driven Manakov soliton

We investigate the statistics of a vector Manakov soliton in the presence of additive Gaussian white noise. The adiabatic perturbation theory for a Manakov soliton yields a stochastic Langevin system which we analyse via the corresponding Fokker-Planck equation for the probability density function (PDF) for the soliton parameters. We obtain marginal PDFs for the soliton frequency and amplitude as well as soliton amplitude and polarization angle. We also derive formulae for the variances of all soliton parameters and analyse their dependence on the initial values of polarization angle and phase. © 2006 IOP Publishing Ltd.

Bit-error probability for direct detection of optical RZ signal degraded by ASE noise and timing jitter

We analyze theoretically the interplay between optical return-to-zero signal degradation due to timing jitter and additive amplified-spontaneous-emission noise. The impact of these two factors on the performance of a square-law direct detection receiver is also investigated. We derive an analytical expression for the bit-error probability and quantitatively determine the conditions when the contributions of the effects of timing jitter and additive noise to the bit error rate can be treated separately. The analysis of patterning effects is also presented. © 2007 IEEE.

Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.

Span design for reduced noise and nonlinear impairments in a dispersion-managed Raman amplified system

We study a periodic Raman amplified dispersion-managed system with backward-pumping configuration, considering noise and nonlinear impairments. A general optimization method based on nonlinearity management is applied in order to find the configuration that maximizes the system performance. The system is later tested using a full numerical implementation of the nonlinear Schrödinger equation and shown to effectively deliver its longest propagation distance in the same optimal region.

Quasi-pilot aided phase noise estimation for coherent optical OFDM systems

In this letter, a novel phase noise estimation scheme has been proposed for coherent optical orthogonal frequency division multiplexing systems, the quasi-pilot-aided method. In this method, the phases of transmitted pilot subcarriers are deliberately correlated to the phases of data subcarriers. Accounting for this correlation in the receiver allows the required number of pilots needed for a sufficient estimation and compensation of phase noise to be reduced by a factor of 2 in comparison with the traditional pilot-aided phase noise estimation method. We carried out numerical simulation of a 40 Gb/s single polarization transmission system, and the outcome of the investigation indicates that by applying quasi-pilot-aided phase estimation, only four pilot subcarriers are needed for effective phase noise compensation. © 2014 IEEE.