Effects of Noise Correlations on Information Encoding and Decoding

This paper considers a Fractional Sampling (FS) technique to enhance the Spectrum Sensing (SS) efficiency of a Cognitive Radio (CR) using a decision statistic based on asymptotic Random Matrix Theory (RMT). Firstly, the effect of noise correlation on eigenvalue based SS is studied analytically and by numerical evaluation. Secondly, new bounds for the Standard Condition Number (SCN) are proposed to enhance the SS efficiency in correlated noise scenarios. It is shown that proposed FS method can enhance SS efficiency up to certain FS rates at the expense of receiver complexity and no performance advantage is obtained if the FS rate is increased beyond this limit. As a result, a method for determining the operating point for the FS rate in terms of sensing performance and complexity is suggested.

New results are given for the bit error probability for binary DPSK modulation over both terrestrial and satellite channels taking into account noise correlation and power imbalance. The new expressions are remarkably simpler than their previously published counterparts. For the terrestrial channel, the results are in closed form in terms of tabulated functions and, for the hard-limiting satellite channel, both in terms of integrals readily evaluated by quadrature and in terms of infinite series. Using the results, it is shown that the error rate does not depend on the noise correlation (down-link in the satellite case) so long as the a priori symbol probabilities are equal, thereby solving an "open problem" posed by Lee, French, and Hong. Also, the satellite case in which each of the up-link and down-link channels contains nonzero noise correlations is briefly treated.

The magnetic recording channel is often equalised to the PR4 partial response. Viterbi detection is used to detect the recorded data, but suffers a loss owing to the effects of noise correlation. The use of coding on the PR4 magnetic recording channel to reduce the effects of noise correlation is proposed. This is shown to achieve a gain in effective SNR over an uncoded channel. Parity codes are shown to be one method of achieving this. The read data is decoded with a soft decision Viterbi detector. The performance of the method is verified through simulations.

The problem of tracking a manoeuvring target with sequentially correlated measurement noise is considered in the paper. Using Singer's method to model the manoeuvring target, the correlated measurement noise can be decorrelated by reformulating the measurement equation such that the conventional Kalman filter can be directly applied in this tracking problem. An analytical error analysis for this processing is derived. If some of the parameters are unknown, the conventional innovation correlation method can usually be employed to estimate these parameters adaptively. This method assumes that the measurement noise is white. If the measurement noise is sequentially correlated, this technique is not valid and the parameters can not be estimated with sufficient accuracy to obtain the desired tracking performance. By considering the effect of noise correlation, a modified computationally efficient method known as a multiple-level estimator is presented to improve the performance in estimating the unknown parameters in the presence of correlated measurement noise. >

Effect of noise correlation in channels of a digital X-ray detector—converter on evaluation of detection quantum efficiency

The influence is considered of two additive correlated noise effects on a two-dimensional quadratic-nonlinear system describing the behavior of two hydrodynamic modes. Using the method of Gaussian approximation, local characteristics of the distribution function are calculated, which are used to construct the global distribution function with the aid of the method of fraction-rational approximations. It is shown that for a system at whose bifurcation point the asymptotic stability is lost, in an expanded space of parameters (bifurcation parameter in the absence of noise plus noise parameters) there appears an instability zone within which the stationary distribution function does not exist. The effect of noise correlation on the stationary characteristics of the system is studied.

Sensory information is represented in the brain through the activity of populations of neurons. How this information is encoded and how it is processed and read out are crucial questions in neuroscience. The work presented here examines these issues using an insect brain model system. Specifically, this work addresses how odor information is represented across a population of neurons in this relatively simple nervous system. It asks how the dynamics of a population of neurons contribute to the encoding of information. To address these questions, simultaneous multi-unit extracellular recordings were made in vivo in the locust brain. The first part of the dissertation describes several advances in spike-sorting methods that were necessary for analyzing such recordings. These advances include quantitative tests of sorting quality, and they allow for automated spike-sorting. Using these techniques, data sampled from tens of neurons over hours of recording can be analyzed with relative ease. The remainder of the dissertation examines the encoding of olfactory information by a population of neurons called projection neurons (PNs), located in the first olfactory relay of the brain. Odor information is shown to be represented by a subpopulation of responsive PNs. The composition of this population changes over time in an odor-specific manner, thus forming a distributed, dynamical representation. The statistics of this response and its dynamics are quantified. Furthermore, the mechanism by which odor information is extracted from the PN population response is examined. A second set of recordings were made from Kenyon cells (KCs), which receive direct excitatory synaptic input from PNs. The dynamic response of the PN population appears to be decoded by KCs through a mechanism based on several underlying components, including oscillatory dynamics, feed-forward inhibition, and intrinsic properties of the KCs. This decoding process is shown to drastically change the odor representations, from dense to sparse. Taken together, the results presented in this dissertation establish that the complex spatial and temporal dynamics of the PN population do encode odor information, and that this information is decoded by other neurons (KCs) in a very precise way, resulting in a drastic transformation of representation. The basic mechanisms underlying this transformation exist in many brain areas and across phyla, suggesting that many of the principles described here could be of general relevance.

Natural stimuli display spatiotemporal characteristics that typically vary over orders of magnitude, and their encoding by sensory neurons remains poorly understood. We investigated population coding of highly heterogeneous natural electrocommunication stimuli in Apteronotus leptorhynchus of either sex. Neuronal activities were positively correlated with one another in the absence of stimulation, and correlation magnitude decayed with increasing distance between recording sites. Under stimulation, we found that correlations between trial-averaged neuronal responses (i.e., signal correlations) were positive and higher in magnitude for neurons located close to another, but that correlations between the trial-to-trial variability (i.e., noise correlations) were independent of physical distance. Overall, signal and noise correlations were independent of stimulus waveform as well as of one another. To investigate how neuronal populations encoded natural electrocommunication stimuli, we considered a nonlinear decoder for which the activities were combined. Decoding performance was best for a timescale of 6 ms, indicating that midbrain neurons transmit information via precise spike timing. A simple summation of neuronal activities (equally weighted sum) revealed that noise correlations limited decoding performance by introducing redundancy. Using an evolution algorithm to optimize performance when considering instead unequally weighted sums of neuronal activities revealed much greater performance values, indicating that midbrain neuron populations transmit information that reliably enable discrimination between different stimulus waveforms. Interestingly, we found that different weight combinations gave rise to similar discriminability, suggesting robustness. Our results have important implications for understanding how natural stimuli are integrated by downstream brain areas to give rise to behavioral responses.SIGNIFICANCE STATEMENT We show that midbrain electrosensory neurons display correlations between their activities and that these can significantly impact performance of decoders. While noise correlations limited discrimination performance by introducing redundancy, considering unequally weighted sums of neuronal activities gave rise to much improved performance and mitigated the deleterious effects of noise correlations. Further analysis revealed that increased discriminability was achieved by making trial-averaged responses more separable, as well as by reducing trial-to-trial variability by eliminating noise correlations. We further found that multiple combinations of weights could give rise to similar discrimination performances, which suggests that such combinatorial codes could be achieved in the brain. We conclude that the activities of midbrain neuronal populations can be used to reliably discriminate between highly heterogeneous stimulus waveforms.

Climbing fiber input produces complex spike synchrony across populations of cerebellar Purkinje cells oriented in the parasagittal axis. Elucidating the fine spatial structure of this synchrony is crucial for understanding its role in the encoding and processing of sensory information within the olivocerebellar cortical circuit. We investigated these issues using in vivo multineuron two-photon calcium imaging in combination with information theoretic analysis. Spontaneous dendritic calcium transients linked to climbing fiber input were observed in multiple neighboring Purkinje cells. Spontaneous synchrony of calcium transients between individual Purkinje cells falls off over approximately 200 microm mediolaterally, consistent with the presence of cerebellar microzones organized by climbing fiber input. Synchrony was increased after administration of harmaline, consistent with an olivary origin. Periodic sensory stimulation also resulted in a transient increase of synchrony after stimulus onset. To examine how synchrony affects the neural population code provided by the spatial pattern of complex spikes, we analyzed its information content. We found that spatial patterns of calcium events from small ensembles of cells provided substantially more stimulus information (59% more for seven-cell ensembles) than available by counting events across the pool without taking into account spatial origin. Information theoretic analysis indicated that, rather than contributing significantly to sensory coding via stimulus dependence, correlational effects on sensory coding are dominated by redundancy attributable to the prevalent spontaneous synchrony. The olivocerebellar circuit thus uses a labeled line code to report sensory signals, leaving open a role for synchrony in flexible selection of signals for output to deep cerebellar nuclei.

We consider the impact of receiver correlation, antenna coupling, matching, and noise on the performance of coordinated beamforming systems. We present a new coordinated beamforming technique for two receivers that is suitable for MIMO broadcast channels with signal and noise correlation at the receiver. We then apply this technique to the specific type of signal and noise correlation that occurs in the presence of receiver mutual coupling. Numerical results suggest that, even in the presence of strong coupling, most of the benefits of coordinated beamforming can be preserved by using appropriate matching networks and linear beamforming. Moreover, these benefits can be achieved even when feedback is limited.

BackgroundPositron Emission Tomography (PET), Computed Tomography (CT), PET/CT and Single Photon Emission Tomography (SPECT) are non-invasive imaging tools used for creating two dimensional (2D) cross section images of three dimensional (3D) objects. PET and SPECT have the potential of providing functional or biochemical information by measuring distribution and kinetics of radiolabelled molecules, whereas CT visualizes X-ray density in tissues in the body. PET/CT provides fused images representing both functional and anatomical information with better precision in localization than PET alone.Images generated by these types of techniques are generally noisy, thereby impairing the imaging potential and affecting the precision in quantitative values derived from the images. It is crucial to explore and understand the properties of noise in these imaging techniques. Here we used autocorrelation function (ACF) specifically to describe noise correlation and its non-isotropic behaviour in experimentally generated images of PET, CT, PET/CT and SPECT.MethodsExperiments were performed using phantoms with different shapes. In PET and PET/CT studies, data were acquired in 2D acquisition mode and reconstructed by both analytical filter back projection (FBP) and iterative, ordered subsets expectation maximisation (OSEM) methods. In the PET/CT studies, different magnitudes of X-ray dose in the transmission were employed by using different mA settings for the X-ray tube. In the CT studies, data were acquired using different slice thickness with and without applied dose reduction function and the images were reconstructed by FBP. SPECT studies were performed in 2D, reconstructed using FBP and OSEM, using post 3D filtering. ACF images were generated from the primary images, and profiles across the ACF images were used to describe the noise correlation in different directions. The variance of noise across the images was visualised as images and with profiles across these images.ResultsThe most important finding was that the pattern of noise correlation is rotation symmetric or isotropic, independent of object shape in PET and PET/CT images reconstructed using the iterative method. This is, however, not the case in FBP images when the shape of phantom is not circular. Also CT images reconstructed using FBP show the same non-isotropic pattern independent of slice thickness and utilization of care dose function. SPECT images show an isotropic correlation of the noise independent of object shape or applied reconstruction algorithm. Noise in PET/CT images was identical independent of the applied X-ray dose in the transmission part (CT), indicating that the noise from transmission with the applied doses does not propagate into the PET images showing that the noise from the emission part is dominant. The results indicate that in human studies it is possible to utilize a low dose in transmission part while maintaining the noise behaviour and the quality of the images.ConclusionThe combined effect of noise correlation for asymmetric objects and a varying noise variance across the image field significantly complicates the interpretation of the images when statistical methods are used, such as with statistical estimates of precision in average values, use of statistical parametric mapping methods and principal component analysis. Hence it is recommended that iterative reconstruction methods are used for such applications. However, it is possible to calculate the noise analytically in images reconstructed by FBP, while it is not possible to do the same calculation in images reconstructed by iterative methods. Therefore for performing statistical methods of analysis which depend on knowing the noise, FBP would be preferred.

In the brain, fast oscillations of local field potentials, which are thought to arise from the coherent and rhythmic activity of large numbers of neurons, were observed first in the olfactory system and have since been described in many neocortical areas. The importance of these oscillations in information coding, however, is controversial. Here, local field potential and intracellular recordings were obtained from the antennal lobe and mushroom body of the locust Schistocerca americana. Different odors evoked coherent oscillations in different, but usually overlapping, ensembles of neurons. The phase of firing of individual neurons relative to the population was not dependent on the odor. The components of a coherently oscillating ensemble of neurons changed over the duration of a single exposure to an odor. It is thus proposed that odors are encoded by specific but dynamic assemblies of coherently oscillating neurons. Such distributed and temporal representation of complex sensory signals may facilitate combinatorial coding and associative learning in these, and possibly other, sensory networks.

Correlated activity between neurons can cause variability in behavior across trials, as trial-by-trial cofluctuations can propagate downstream through the motor system. The extent to which correlated activity affects behavior depends on the properties of the translation of the population activity into movement. A major hurdle in studying the effects of noise correlations on behavior is that in many cases this translation is unknown. Previous research has overcome this by using models that make strong assumptions about the coding of motor variables. We developed a novel method that estimates the contribution of correlations to behavior with minimal assumptions. Our method partitions noise correlations into correlations that are expressed in a specific behavior, termed behavior-related correlations, and correlations that are not. We applied this method to study the relationship between noise correlations in the frontal eye field (FEF) and pursuit eye movements. We defined a distance metric between the pursuit behavior on different trials. Based on this metric, we used a shuffling approach to estimate pursuit-related correlations. Although the correlations were partially linked to variability in the eye movements, even the most constrained shuffle strongly attenuated the correlations. Thus, only a small fraction of FEF correlations is expressed in behavior. We used simulations to validate our approach, show that it captures behavior-related correlations, and demonstrate its generalizability in different models. We show that the attenuation of correlated activity through the motor pathway could stem from the interplay between the structure of the correlations and the decoder of FEF activity.NEW & NOTEWORTHY The effect of noise correlations on neural computations has been studied extensively. However, the degree to which correlations affect downstream areas remains unknown. Here, we take advantage of precise measurement of eye movement behavior to estimate the degree to which correlated variability between neurons in the frontal eye field (FEF) affects subsequent behavior. To achieve this, we developed a novel shuffling-based method and verified it using different models of the FEF.

Cortical neuropil modulations recorded by calcium imaging reflect the activity of large aggregates of axo-dendritic processes and synaptic compartments from a large number of neurons. The organization of this activity impacts neuronal firing but is not well understood. Here we used in vivo 2-photon imaging with Oregon Green Bapta (OGB) and GCaMP6s to study neuropil visual responses to moving gratings in layer 2/3 of mouse area V1. We found neuropil responses to be strongly modulated and more reliable than neighboring somatic activity. Furthermore, stimulus independent modulations in neuropil activity, i.e., noise correlations, were highly coherent across the cortical surface, up to distances of at least 200 μm. Pairwise neuropil-to-neuropil-patch noise correlation strength was much higher than cell-to-cell noise correlation strength and depended strongly on brain state, decreasing in quiet wakefulness relative to light anesthesia. The profile of neuropil noise correlation strength decreased gently with distance, dropping by ~11% at a distance of 200 μm. This was comparatively slower than the profile of cell-to-cell noise correlations, which dropped by ~23% at 200 μm. Interestingly, in spite of the “salt & pepper” organization of orientation and direction encoding across mouse V1 neurons, populations of neuropil patches, even of moderately large size (radius ~100 μm), showed high accuracy for discriminating perpendicularly moving gratings. This was commensurate to the accuracy of corresponding cell populations. The dynamic, stimulus dependent, nature of neuropil activity further underscores the need to carefully separate neuropil from cell soma activity in contemporary imaging studies.

Effect of correlations on signal transmission in a population of spiking neurons