Reservoir computing using networks of memristors: effects of topology and heterogeneity.

Reservoir computing (RC) has attracted significant interest as a framework for the implementation of novel neuromorphic computing architectures. Previously attention has been focussed on software-based reservoirs, where it has been demonstrated that reservoir topology plays a role in task performance, and functional advantage has been attributed to small-world and scale-free connectivity. However in hardware systems, such as electronic memristor networks, the mechanisms responsible for the reservoir dynamics are very different and the role of reservoir topology is largely unknown. Here we compare the performance of a range of memristive reservoirs in several RC tasks that are chosen to highlight different system requirements. We focus on percolating networks of nanoparticles (PNNs) which are novel self-assembled nanoscale systems that exhibit scale-free and small-world properties. We find that the performance of regular arrays of uniform memristive elements is limited by their symmetry but that this symmetry can be broken either by a heterogeneous distribution of memristor properties or a scale-free topology. The best perfomance across all tasks is observed for a scale-free network with uniform memistor properties. These results provide insight into the role of topology in neuromorphic reservoirs as well as an overview of the computational performance of scale-free networks of memristors in a range of benchmark tasks.

Reservoir computing with 3D nanowire networks.

Networks of nanowires are currently being explored for a range of applications in brain-like (or neuromorphic) computing, and especially in reservoir computing (RC). Fabrication of real-world computing devices requires that the nanowires are deposited sequentially, leading to stacking of the wires on top of each other. However, most simulations of computational tasks using these systems treat the nanowires as 1D objects lying in a perfectly 2D plane - the effect of stacking on RC performance has not yet been established. Here we use detailed simulations to compare the performance of perfectly 2D and quasi-3D (stacked) networks of nanowires in two tasks: memory capacity and nonlinear transformation. We also show that our model of the junctions between nanowires is general enough to describe a wide range of memristive networks, and consider the impact of physically realistic electrode configurations on performance. We show that the various networks and configurations have a strikingly similar performance in RC tasks, which is surprising given their radically different topologies. Our results show that networks with an experimentally achievable number of electrodes perform close to the upper bounds achievable when using the information from every wire. However, we also show important differences, in particular that the quasi-3D networks are more resilient to changes in the input parameters, generalizing better to noisy training data. Since previous literature suggests that topology plays an important role in computing performance, these results may have important implications for future applications of nanowire networks in neuromorphic computing.

Wavefront prediction with reservoir computing for minimizing the effects of angular anisoplanatism.

Supervised learning with recurrent neural networks has been used to estimate perturbations that adversely affect image quality of natural guide stars due to atmospheric turbulence. While this method has been shown to be effective for generating spatially variant point spread functions (PSFs) for image reconstruction using low-turbulence models, recent extensions to these methods, facilitated by enhancements to optimize network parameters, show potential to extend this method to moderate-turbulence multilayer models. In this paper, spatio-temporal learning using reservoir computing, a discriminative learning method known as an echo state network, is proposed to estimate the spatially variant PSF, thus allowing for improved image restoration of point-source exo-atmospheric objects outside the isoplanatic patch. The forward problem is modelled by training a reservoir computer with time-series perturbations from three or more natural guide stars. Known site profile data is incorporated to optimize the model for training, where perturbations under similar conditions are used to test estimated aberrations over a wide, anisoplanatic field.

Identification of vigilance lapses using EEG/EOG by expert human raters.

It is critically important for certain occupational groups to remain highly alert throughout their working day. For safety reasons, it would be useful to automatically detect lapses in performance using EEG/EOG. Automating the detection process could be simplified considerably if we could mimic human experts. Surprisingly, it is unclear to what extent human EEG raters are able to detect lapses. Consequently, we undertook a study in which 4 expert EEG raters assessed the level of alertness of 10 air traffic controllers by observing a combination of their EEG and EOG while they performed a 10 min psychomotor vigilance task (PVT). They were specifically required to identify lapses or sleep episodes that might lead to a lapse in PVT performance. A reaction time .. 500 ms was defined as a PVT lapse. There was a total of 101 lapses (mean duration = 1.00 s). Of these, only 6 lapses were detected by one or more raters and all of these were marked as ;sleep'. Overall the human expert raters were unable to reliably identify lapses based only on EEG and EOG. This poor performance suggests an automated system would need to identify subtle features not overtly visible in the EEG.

Fractal dimension of the EEG for detection of behavioural microsleeps.

The fractal dimension (FD) of EEG has been shown to be of value in the detection of epileptic seizures. In this paper, we assess its usefulness in detecting behavioural microsleeps. Fifteen non-sleep-deprived normal subjects performed two 1-hour sessions of a continuous tracking task while EEG, EOG and facial video were recorded. Higuchi's algorithm was used to calculate the FD of the EEG. Video lapses were scored independently from tracking performance by a human rater. A subset of data was rated independently by three human raters observing both tracking performance and the video rating to identify behavioural microsleep events. The mean point-biserial correlation between FD and the mean human rating was -0.213 indicating modest agreement. Crossvalidated detection performance of the FD was poor with a mean correlation (.. = -0.099). This suggests that, on its own, FD of the EEG is unlikely to be useful for detecting microsleeps.

Efficient frequency-domain sample selection for recovering limited-support images.

An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.

Recovery of limited-extent images aliased because of spectral undersampling.

In imaging situations where observations are made in spatial-frequency space, it is often desirable to lower the number of observations to fewer than that imposed by the Nyquist criterion. It is shown that patterns of regular spectral undersampling lead to aliasing that can be partially eliminated from some regions of a limited-extent image. An algorithm is presented for determining which regions are recoverable and which are not for a given pattern. Noniterative recovery, analogous to that proposed by Walsh and Nielsen-Delaney [J. Opt. Soc. Am. A 11, 572 (1994)], is shown to be feasible in cases of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy.

Wavelet analysis of transient biomedical signals and its application to detection of epileptiform activity in the EEG.

Wavelet based signal analysis provides a powerful new means for the analysis of nonstationary signals such as the human EEG. The properties of the discrete wavelet transform are reviewed in illustrated application examples. The continuous wavelet transform is shown to provide better detection and representation of isolated transients. An approach to extract features of edges and transients from the continuous wavelet transform is outlined. Matching pursuit is presented as a more general transform method that covers both transients and oscillation spindles. A statistical model for the continuous wavelet transform of background EEG is found. A spike detection system based on this background model is presented. The performance of this detection system has been assessed in a preliminary clinical study of 11 EEG recordings containing epileptiform activity and shown to have a sensitivity of 84% and a selectivity of 12%. The spatial context of epileptiform activity will be incorporated to improve system performance.

Enhancement of deep epileptiform activity in the EEG via 3-D adaptive spatial filtering.

The detection of epileptiform discharges (ED's) in the electroencephalogram (EEG) is an important component in the diagnosis of epilepsy. However, when the epileptogenic source is located deep in the brain, the ED's at the scalp are often masked by more superficial, higher-amplitude EEG activity. A noninvasive technique which uses an adaptive "beamformer" spatial filter has been investigated for the enhancement of signals from deep sources in the brain suspected of containing ED's. A forward three-layer spherical model was used to relate a dipolar source to recorded signals to determine the beamformer's spatial response constraints. The beamformer adapts, using the least-mean-squares (LMS) algorithm, to reduce signals from sources distant to some arbitrarily defined location in the brain. The beamformer produces three outputs, being the orthogonal components of the signal estimated to have arisen at or near the assumed location. Simulations were performed by using the same forward model to superimpose realistic ED's on normal EEG recordings. The simulations show the beamformer's ability to enhance signals emanating from deep foci by way of an enhancement ratio (ER), being the improvement in signal-to-noise ratio (SNR) to that observed at any of the scalp electrodes. The performance of the beamformer has been evaluated for 1) the number of scalp electrodes, 2) the recording montage, 3) dependence on the background EEG, 4) dependence on magnitude, depth, and orientation of epileptogenic focus, and 5) sensitivity to inaccuracies in the estimated location of the focus. Results from the simulations show the beamformer's performance to be dependent on the number of electrodes and moderately sensitive to variations in the EEG background. Conversely, its performance appears to be largely independent of the amplitude and morphology of the ED. The dependence studies indicated that the beamformer's performance was moderately dependent on eccentricity with the ER increasing as the dipolar source and the beamformer were moved from the center to the surface of the brain (1.51-2.26 for radial dipoles and 1.17-2.69 for tangential dipoles). The beamformer was also moderately dependent on variations in polar or azimuthal angle for radial and tangential dipoles. Higher ER's tended to be seen for locations between electrode sites. The beamformer was more sensitive to inaccuracies in both polar and azimuthal location than depth of the dipolar source. For polar locations, an ER > 1.0 was achieved when the beamformer was located within +/- 25 degrees of a radial dipole and +/- 35 degrees of a tangential dipole. Similarly, angular ranges of +/- 37.5 degrees and +/- 45 degrees, respectively, for inaccuracies in azimuthal locations. Preliminary results from real EEG records, comprising 12 definite or questionable epileptiform events, from four patients, demonstrated the beamformer's ability to enhance these events by a mean 100% (52%-215%) for referential data and a mean 104% (50%-145%) for bipolar data.

Detection of epileptiform discharges in the EEG by a hybrid system comprising mimetic, self-organized artificial neural network, and fuzzy logic stages.

OBJECTIVE: A multi-stage system for automated detection of epileptiform activity in the EEG has been developed and tested on pre-recorded data from 43 patients. METHODS: The system is centred on the use of an artificial neural network, known as the self-organising feature map (SOFM), as a novel pattern classifier. The role of the SOFM is to assign a probability value to incoming candidate epileptiform discharges (on a single channel basis). The multi-stage detection system consists of three major stages: mimetic, SOFM, and fuzzy logic. Fuzzy logic is introduced in order to incorporate spatial contextual information in the detection process. Through fuzzy logic it has been possible to develop an approximate model of the spatial reasoning performed by the electroencephalographer. RESULTS: The system was trained on 35 epileptiform EEGs containing over 3000 epileptiform events and tested on a different set of eight EEGs containing 190 epileptiform events (including one normal EEG). Results show that the system has a sensitivity of 55.3% and a selectivity of 82% with a false detection rate of just over seven per hour. CONCLUSIONS: Based on these initial results the overall performance is favourable when compared with other leading systems in the literature. This encourages us to further test the system on a larger population base with the ultimate aim of introducing it into routine clinical use.

Multireference adaptive noise canceling applied to the EEG.

The technique of multireference adaptive noise canceling (MRANC) is applied to enhance transient nonstationarities in the electroeancephalogram (EEG), with the adaptation implemented by means of a multilayer-perception artificial neural network (ANN). The method was applied to recorded EEG segments and the performance on documented nonstationarities recorded. The results show that the neural network (nonlinear) gives an improvement in performance (i.e., signal-to-noise ratio (SNR) of the nonstationarities) compared to a linear implementation of MRANC. In both cases an improvement in the SNR was obtained. The advantage of the spatial filtering aspect of MRANC is highlighted when the performance of MRANC is compared to that of the inverse auto-regressive filtering of the EEG, a purely temporal filter.

EEG spectral topography in neurology: II. A new system and a theoretical comparison of interpolation techniques.

An EEG spectral topography system has been developed to produce maps of the time-averaged spectra of a 16-channel EEG. The design of this system is based upon the discussions of the contentious issues of topography presented in Part I and a theoretical study of two-dimensional interpolation techniques. The comparison of techniques is based upon simulated electric fields on a three-layer spherical head model. Four two-dimensional interpolation techniques are investigated: bilinear, nearest neighbour, bicubic splines, and thin-plate splines. The most accurate method, a 2nd degree thin-plate spline, is employed in the new topography system. The EEG spectral topography system adopts the following procedures: the EEG is recorded using the 16 channel ipsilateral-ears montage; spectral analysis is applied to several overlapping epochs, relatively free of artifacts, of length 5.12 s; the averaged frequency spectrum is divided into specified frequency bands; for each channel, the average spectral component of each band is mapped onto a plane representing the head; and the maps are completed using 2nd degree thin-plate spline interpolation. A particular aim of the development was to produce a topography system compatible with the present EEG recording system at Christchurch Hospital. This has been achieved and, consequently, the topography system is of immediate clinical use. The system is currently part of a major clinical study.

EEG spectral topography in neurology: I. A review of techniques.

As researchers investigate methods of automated interpretation of the electroencephalogram (EEG), spectral topography is emerging as an important and popular technique in applied clinical neurophysiology. Several computer-based EEG topography systems have been developed to produce topographic maps showing the spatial distributions of pre-defined frequency bands in the EEG. However, there is ongoing debate as to which technical approaches to EEG topography generate maps that can be most accurately interpreted by clinicians. This paper reviews existing topographic techniques, particularly as they apply to diagnostic neurology, and discusses some of the technical choices that must be addressed by topography users. These choices include the selection of montage, epoch length, interpolation scheme, graphical display method, and artifact removal technique. The points summarised here highlight the general opinion that although EEG topography has many benefits, it should be invoked with care and the user should possess an indepth understanding of the procedures used to produce the topographic maps.

Towards direct reconstruction from a gamma camera based on Compton scattering.

The Compton scattering camera (sometimes called the electronically collimated camera) has been shown by others to have the potential to better the photon counting statistics and the energy resolution of the Anger camera for imaging in SPECT. By using coincident detection of Compton scattering events on two detecting planes, a photon can be localized to having been sourced on the surface of a cone. New algorithms are needed to achieve fully three-dimensional reconstruction of the source distribution from such a camera. If a complete set of cone-surface projections are collected over an infinitely extending plane, it is shown that the reconstruction problem is not only analytically solvable, but also overspecified in the absence of measurement uncertainties. Two approaches to direct reconstruction are proposed, both based on the photons which travel perpendicularly between the detector planes. Results of computer simulations are presented which demonstrate the ability of the algorithms to achieve useful reconstructions in the absence of measurement uncertainties (other than those caused by quantization). The modifications likely to be required in the presence of realistic measurement uncertainties are discussed.

Zero tracks for blind deconvolution of blurred ensembles.

The analytically continued Fourier transform of a two-dimensional image vanishes to zero on a two-dimensional surface embedded in a four-dimensional space. This surface uniquely characterizes the image and is known as a zero sheet. An algorithm is described that employs the zero-sheet concept to blindly deconvolve an ensemble of differently blurred images. To overcome the difficulty of operating within a four-dimensional space, we calculate projections of the zero sheets, known as zero tracks. The zero tracks of each member of the ensemble are superimposed on a plane. The zero tracks that pertain to the original image are similar for every blurred and contaminated image. By contrast those associated with the blurring vary widely across the ensemble. A method of selecting the appropriate zero tracks in order to reconstruct an estimate of the original image is presented. Preliminary results for small positive images suggest that this deconvolution technique may be successful even when the level of contamination is significant.

The sorcerer and his apprentices: contributions of Professor R.H.T. Bates to the physical sciences and engineering in medicine.

The late Professor R. H.T. Bates (Richard) left an enormous legacy of published research and launched many young researchers and engineers into their careers. In doing so he established an international network of information engineering/scientists that is in itself a laudable contribution to the global multidisciplinary scientific community. In this paper are reviewed the contributions that Professor Bates and his students made over the last two decades in the physical sciences applied to medicine. Where appropriate (i.e. where it doesn't overlap with other contributions to this issue) brief descriptions are given of current research projects in the Department of Electrical and Electronic Engineering at Canterbury, (where Professor Bates carried out most of his research, and where the authors are now ensconced) which in some way relate to the work of "the sorcerer" and his former "apprentices" (as Professor Bates liked to refer to the group).

A low cost ECG central station for intensive care.

A electrocardiogram (ECG) central station has been developed for the Intensive Care Unit at Christchurch Hospital. The system allows the selection and display of four ECGs selected from seven bedside monitors in the Unit. It also provides for automatic display, hard copy and audio alarm of ECG from any monitor which has detected an alarm condition--irrespective of whether that channel was being displayed prior to alarm detection. The system comprises a control unit (based on an 8085 microprocessor) and a mobile ECG station (4-channel ECG monitor, ECG recorder and computer terminal). Over the three years since its installation, the central station has been used 24 hours a day by medical and nursing staff and has proven to be a valued and reliable instrument in an intensive care environment.

From living being to medical image--bridging the dimensionality gap.

The human body is viewed, in the context of medical imaging, as a multiplicity of three-dimensional time-varying images, coinciding in time and space. Medical imaging modalities that are well established, or are undergoing clinical trials, or are at the tentative proposal stage, are tabulated. Also listed are the types of radiation and other physical processes employed to gather the image data, the physical parameters which can be imaged, and the physiological attributes represented by these parameters. Image reconstruction algorithms are reviewed and possible improvements are assessed. The processing of multidimensional information is emphasised as of primary concern for future progress in medical imaging. Such processing is seen to be developing along two converging paths: the processing of information from coincident images of different parameter distributions, and the processing of time-sequential images of a single parameter distribution. The images referred to have three spatial dimensions, implying that a challenge for future medical imaging systems is conjectured to be the efficient distillation of useful information (which must include the most effective means of image display) from multiple sets of time-varying volume data. Medical diagnosis can always profit from improved interpretation of information provided by the multifarious types of radiation and other physical processes which are employed in established and tentative medical imaging techniques. There is a premium on parameter sets that provide independent information and on processes, such as magnetic fields, ultrasound, and low frequency electric currents, which are free of the stigma associated with ionising radiations. Promising avenues of exploration are identified.

Translational motion compensation for coronary angiogram sequences.

A method of compensating for the lag of the video cameras typically used in angiographic systems is presented for use in sequences of digitized X-ray images. The lag effect is reduced by a straightforward weighted subtraction, which has the undesirable side effect of increasing noise. By superimposing several lag-corrected and appropriately shifted images, however, the signal-to-noise ratio can be restored. The algorithm uses the phase-correlation method to measure the two-dimensional shift of a mobile coronary arterial structure. Processing is confined to a rectangular area of interest (AOI), which encloses a feature of clinical significance. The differences of the phases of the Fourier transforms of two frames is computed, combined with an appropriate filter, and inverse Fourier-transformed to produce a phase-correlation image. The vector separation from the origin of image space of the peak of the phase-correlation image is the estimate of the shift of the artery's position in the second frame as compared to the first. The isolation of the AOI from the surrounding image is achieved by the application of a window and correction for any linear trend in the background intensity.