Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

The visually evoked magnetic response (VEMR) to a pattern onset/offset stimulus

This study characterizes the visually evoked magnetic response (VEMR) to pattern onset/offset stimuli, using a single channel BTi magnetometer. The influence of stimulus parameters and recording protocols on the VEMR is studied with inferences drawn about the nature of cortical processing, its origins and optimal recording strategies. Fundamental characteristics are examined, such as the behaviour of successive averaged and unaveraged responses; the effects of environmental shielding; averaging; inter- and intrasubject variability and equipment specificity. The effects of varying check size, field size, contrast and refractive error on latency, amplitude and topographic distribution are also presented. Latency and amplitude trends are consistent with previous VEP findings and known anatomical properties of the visual system. Topographic results are consistent with the activity of sources organised according to the cruciform model of striate cortex. A striate origin for the VEMR is also suggested by the results to quarter, octant and annulus field stimuli. Similarities in the behaviour and origins of the sources contributing to the CIIm and CIIIm onset peaks are presented for a number of stimulus conditions. This would be consistent with differing processing event in the same, or similar neuronal populations. Focal field stimuli produce less predictable responses than full or half fields, attributable to a reduced signal to noise ratio and an increased sensitivity to variations in cortical morphology. Problems with waveform peak identification are encountered for full field stimuli that can only be resolved by the careful choice of stimulus parameters, comparisons with half field responses or with reference to the topographic distribution of each waveform peak. An anatomical study of occipital lobe morphology revealed large inter- and intrasubject variation in calcarine fissure shape and striate cortex distribution. An appreciation of such variability is important for VEMR interpretation, due to the technique's sensitivity to source depth and orientation, and it is used to explain the experimental results obtained.

Visual evoked magnetic responses (VEMR) to flash and pattern reversal stimulation

The problems of using a single channel magnetometer (BTi, Model 601) in an unshielded clinical environment to measure visual evoked magnetic responses (VEMR) were studied. VEMR to flash and pattern reversal stimuli were measured in 100 normal subjects. Two components, the P100M to pattern reversal and P2M to flash, were measured successfully in the majority of patients. The mean latencies of these components in different decades of life were more variable than the visual evoked potentials (VEP) that have been recorded to these stimuli. The latency of the P100M appeared to increase significantly after about 55 years of age whereas little change occurred for the flash P2M. The effects of blur, check size, stimulus size and luminance intensity on the latency and amplitude of the VEMR were studied. Blurring a small (32') check significantly increased latency whereas blurring a large (70') check had little effect on latency. Increasing check size significantly reduced latency of the P100M but had little effect on amplitude. Increasing the field size decreases the latency and increases the amplitude of the P100M. Within a normal subject, most of the temporal variability of the P100M appeared to be associated with run to run variation rather than between recording sessions on the same day or between days. Reproducibility of the P100M was improved to a degree by employing a magnetically shielded room. Increasing flash intensity decreases the latency and increases the amplitude of the P2M component. The magnitude of the effects of varying stimulus parameters on the VEMR were frequently greater than is normally seen in the VEP. The topography of the P100M and P2M varied over the scalp in normal subjects. Full field responses to a large check could be explained as approximately the sum of the half field responses and were consistent with the cruciform model of the visual cortex. Preliminary source localisation data suggested a shallower source in the visual cortex for the flash P2M compared with the P100M. The data suggest that suitable protocols could be devised to obtain normative data of sufficient quality to use the VEMR to flash and pattern clinically.

Watermarking biomedical time series data

This thesis addresses the problem of information hiding in low dimensional digital data focussing on issues of privacy and security in Electronic Patient Health Records (EPHRs). The thesis proposes a new security protocol based on data hiding techniques for EPHRs. This thesis contends that embedding of sensitive patient information inside the EPHR is the most appropriate solution currently available to resolve the issues of security in EPHRs. Watermarking techniques are applied to one-dimensional time series data such as the electroencephalogram (EEG) to show that they add a level of confidence (in terms of privacy and security) in an individual’s diverse bio-profile (the digital fingerprint of an individual’s medical history), ensure belief that the data being analysed does indeed belong to the correct person, and also that it is not being accessed by unauthorised personnel. Embedding information inside single channel biomedical time series data is more difficult than the standard application for images due to the reduced redundancy. A data hiding approach which has an in built capability to protect against illegal data snooping is developed. The capability of this secure method is enhanced by embedding not just a single message but multiple messages into an example one-dimensional EEG signal. Embedding multiple messages of similar characteristics, for example identities of clinicians accessing the medical record helps in creating a log of access while embedding multiple messages of dissimilar characteristics into an EPHR enhances confidence in the use of the EPHR. The novel method of embedding multiple messages of both similar and dissimilar characteristics into a single channel EEG demonstrated in this thesis shows how this embedding of data boosts the implementation and use of the EPHR securely.

Application of SOA-NOLM in all-optical processing

This thesis presents experimental investigations of the use of semiconductor optical amplifiers in a nonlinear loop mirror (SOA-NOLM) and its application in all-optical processing. The techniques used are mainly experimental and are divided into three major applications. Initially the semiconductor optical amplifier, SOA, is experimentally characterised and the optimum operating condition is identified. An interferometric switch based on a Sagnac loop with the SOA as the nonlinear element is employed to realise all-optical switching. All-optical switching is a very attractive alternative to optoelectronic conversion because it avoids the conversion from the optical to the electronic domain and back again. The first major investigation involves a carrier suppressed return to zero, CSRZ, format conversion and transmission. This study is divided into single channel and four channel WDM respectively. The optical bandwidth which limits the conversion is investigated. The improvement of the nonlinear tolerance in the CSRZ transmission is shown which shows the suitability of this format for enhancing system performance. Second, a symmetrical switching window is studied in the SOA-NOLM where two similar control pulses are injected into the SOA from opposite directions. The switching window is symmetric when these two control pulses have the same power and arrive at the same time in the SOA. Finally, I study an all-optical circulating shift register with an inverter. The detailed behaviour of the blocks of zeros and ones has been analysed in terms of their transient measurement. Good agreement with a simple model of the shift register is obtained. The transient can be reduced but it will affect the extinction ratio of the pulses.

Nonlinear and ROADM induced penalties in 28 Gbaud dynamic optical mesh networks employing electronic signal processing

We report the impact of cascaded reconfigurable optical add-drop multiplexer induced penalties on coherently-detected 28 Gbaud polarization multiplexed m-ary quadrature amplitude modulation (PM m-ary QAM) WDM channels. We investigate the interplay between different higher-order modulation channels and the effect of filter shapes and bandwidth of (de)multiplexers on the transmission performance, in a segment of pan-European optical network with a maximum optical path of 4,560 km (80km x 57 spans). We verify that if the link capacities are assigned assuming that digital back propagation is available, 25% of the network connections fail using electronic dispersion compensation alone. However, majority of such links can indeed be restored by employing single-channel digital back-propagation employing less than 15 steps for the whole link, facilitating practical application of DBP. We report that higher-order channels are most sensitive to nonlinear fiber impairments and filtering effects, however these formats are less prone to ROADM induced penalties due to the reduced maximum number of hops. Furthermore, it has been demonstrated that a minimum filter Gaussian order of 3 and bandwidth of 35 GHz enable negligible excess penalty for any modulation order.

Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations

Digital back-propagation (DBP) has recently been proposed for the comprehensive compensation of channel nonlinearities in optical communication systems. While DBP is attractive for its flexibility and performance, it poses significant challenges in terms of computational complexity. Alternatively, phase conjugation or spectral inversion has previously been employed to mitigate nonlinear fibre impairments. Though spectral inversion is relatively straightforward to implement in optical or electrical domain, it requires precise positioning and symmetrised link power profile in order to avail the full benefit. In this paper, we directly compare ideal and low-precision single-channel DBP with single-channel spectral-inversion both with and without symmetry correction via dispersive chirping. We demonstrate that for all the dispersion maps studied, spectral inversion approaches the performance of ideal DBP with 40 steps per span and exceeds the performance of electronic dispersion compensation by ~3.5 dB in Q-factor, enabling up to 96% reduction in complexity in terms of required DBP stages, relative to low precision one step per span based DBP. For maps where quasi-phase matching is a significant issue, spectral inversion significantly outperforms ideal DBP by ~3 dB.

Compensation of nonlinear fibre impairments in coherent systems employing spectrally efficient modulation formats

We investigate electronic mitigation of linear and non-linear fibre impairments and compare various digital signal processing techniques, including electronic dispersion compensation (EDC), single-channel back-propagation (SC-BP) and back-propagation with multiple channel processing (MC-BP) in a nine-channel 112 Gb/s PM-mQAM (m=4,16) WDM system, for reaches up to 6,320 km. We show that, for a sufficiently high local dispersion, SC-BP is sufficient to provide a significant performance enhancement when compared to EDC, and is adequate to achieve BER below FEC threshold. For these conditions we report that a sampling rate of two samples per symbol is sufficient for practical SC-BP, without significant penalties.

Power pre-emphasis for suppression of FWM in coherent optical OFDM transmission

Four-wave-mixing (FWM) due to the fiber nonlinearity is a major limiting factor in coherent optical OFDM transmission. We propose to apply power pre-emphasis, i.e. to allocate the transmitted power nonuniformly among subcarriers in order to suppress the FWM impairment. The proposed technique was numerically investigated for both single channel 15.6 Gbs CO-OFDM transmissions and 7-channel WDM transmissions, showing that up to 1 dB improvement in the system's Qfactor can be achieved without considering sophisticated power loading algorithms developed for wireless communications. © 2014 Optical Society of America.

Optical 2R regeneration at 40 Gbit/s using saturable absorber in long-haul dispersion-managed fiber links

The optical regeneration is an attractive method to improve the performance of long-distance data transmission, though its application in high-speed fiber systems requires careful design consideration/optimization. In this letter we investigate 40 Gbit/s dispersion-managed fiber transmission with optical 2R regeneration based on quantum well saturable absorber and highly non-linear fiber. We demonstrate through numerical modeling a feasibility of a single channel transmission over 10,000 km using optimized system design. © 2003 Elsevier B.V. All rights reserved.

Unrepeatered DPSK transmission over 360 km SMF-28 fibre using URFL based amplification

Unrepeatered 42.7 Gb/s per channel RZ-DPSK transmission over standard SMF-28 fibre with novel URFL based amplification using fibre Bragg gratings is investigated. OSNR and gain performance are studied experimentally and through simulations. Error free transmission for 16 channels across the full C-band with direct detection was experimentally demonstrated for 280 km span length, as well as 6-channel transmission at 340 km and single-channel transmission up to 360 km (75 dB) without employing ROPA or specialty fibres.©2013 Optical Society of America.

Optimization of discrete Raman amplifiers for different kinds of fibers

We present an analysis of the performance of backward-pumped discrete Raman amplifier modules designed for simultaneous amplification and dispersion and/or dispersion slope compensation, both in single-channel and in multichannel systems. Optimal module parameters are determined within a realistic range of pump and signal powers.

Bit error rate estimation methods for QPSK CO-OFDM transmission

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) is an attractive transmission technique to virtually eliminate intersymbol interference caused by chromatic dispersion and polarization-mode dispersion. Design, development, and operation of CO-OFDM systems require simple, efficient, and reliable methods of their performance evaluation. In this paper, we demonstrate an accurate bit error rate estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. By comparing with other known approaches, including data-aided and nondata-aided error vector magnitude, we show that the proposed method offers the most accurate estimate of the system performance for both single channel and wavelength division multiplexing QPSK CO-OFDM transmission systems. © 2014 IEEE.

Phase noise influence in long-range coherent optical OFDM systems with delay detection, IFFT multiplexing and FFT demodulation

We present a study of the influence of dispersion induced phase noise for CO-OFDM systems using FFT multiplexing/IFFT demultiplexing techniques (software based). The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) including - for the first time to our knowledge - in explicit form the effect of equalization enhanced phase noise (EEPN). This, in turns, leads to an analytic BER specification. Numerical results focus on a CO-OFDM system with 10-25 GS/s QPSK channel modulation. A worst case constellation configuration is identified for the phase noise influence and the resulting BER is compared to the BER of a conventional single channel QPSK system with the same capacity as the CO-OFDM implementation. Results are evaluated as a function of transmission distance. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. For a total capacity of 400 (1000) Gbit/s, the transmission distance to have the BER < 10-2 for the worst case CO-OFDM design is less than 800 and 460 km, respectively, whereas for a single channel QPSK system it is less than 1400 and 560 km.

Optimized hybrid QPSK/8QAM for CO-OFDM transmissions

In optical communications, a high spectral efficiency can be realized by applying high order modulation formats such as 8QAM, 16QAM and 64QAM. However, depending on the system's requirements (bandwidth, performance and transmission distance), the maximum spectral efficiency may not be achievable with the regular 2m-array QAM formats. In this case, a hybrid modulation format, such as QPSK/8QAM, can provide an effective solution. In this work, we deliver the optimum design for single channel coherent optical orthogonal frequency division multiplexing systems with hybrid QPSK/8QAM modulation format. We also discuss a simple but effective strategy for applying hybrid QAMs for long-haul optical communications without considering sophisticated bit and power loading algorithms developed for wireless communications.