Multiunit normalized cross correlation differs from the average single-unit normalized correlation.

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Neuronal Spike Trains and Stochastic Point Processes: I. The Single Spike Train

Activity-Dependent Control of Neuronal Output by Local and Global Dendritic Spike Attenuation

Prior research studies have shown that the peak signal to noise ratio (PSNR) is the most frequent watermarked image quality metric that is used for determining the levels of strength and weakness of watermarking algorithms. Conversely, normalised cross correlation (NCC) is the most common metric used after attacks were applied to a watermarked image to verify the strength of the algorithm used. Many researchers have used these approaches to evaluate their algorithms. These strategies have been used for a long time, however, which unfortunately limits the value of PSNR and NCC in reflecting the strength and weakness of the watermarking algorithms. This paper considers this issue to determine the threshold values of these two parameters in reflecting the amount of strength and weakness of the watermarking algorithms. We used our novel watermarking technique for embedding four watermarks in intermediate significant bits (ISB) of six image files one-by-one through replacing the image pixels with new pixels and, at the same time, keeping the new pixels very close to the original pixels. This approach gains an improved robustness based on the PSNR and NCC values that were gathered. A neural network model was built that uses the image quality metrics (PSNR and NCC) values obtained from the watermarking of six grey-scale images that use ISB as the desired output and that are trained for each watermarked image’s PSNR and NCC. The neural network predicts the watermarked image’s PSNR together with NCC after the attacks when a portion of the output of the same or different types of image quality metrics (PSNR and NCC) are obtained. The results indicate that the NCC metric fluctuates before the PSNR values deteriorate.

Spiking Irregularity and Frequency Modulate the Behavioral Report of Single-Neuron Stimulation

Summary form only given. Our work over the last 20 years has shown that populations of cortical neurons are active during natural arm movements. Furthermore, enough details of these movements can be easily extracted from the single unit spike trains of these neurons to yield high-fidelity, 3D trajectories of reaching and drawing. Over the last nine years, we have developed a technique to chronically implant microwires in the frontal cortices of rhesus monkeys to record 30-90 single units simultaneously for more than three years in the same animal. The recorded signal is processed in real-time and used to control a 3D cursor or robot arm. The animals are able to learn to control these devices while their own arms are restrained and to produce movements that approximate their natural arm movements. These movements are fast, accurate and repeatable over many trials. A key factor in this success is to provide visual feedback to the subject and to have an adaptive decoding algorithm that recognizes learned changes in the animals' recorded neural output. This 'coadaptation' (the animal learns by changing the tuning properties of individual neurons and the extraction algorithm learns by recognizing these changes) shows that high performance can be achieved with small populations of units, easily attained with present electrode technology.

Motor cortical points are linked by intrinsic horizontal connections having a recurrent network topology. However, it is not known whether neural activity can propagate over the area covered by these intrinsic connections and whether there are spatial anisotropies of synaptic strength, as opposed to synaptic density. Moreover, the mechanisms by which activity spreads have yet to be determined. To address these issues, an 8 × 8 microelectrode array was inserted in the forelimb area of the cat motor cortex (MCx). The centre of the array had a laser etched hole ∼500 μm in diameter. A microiontophoretic pipette, with a tip diameter of 2-3 μm, containing bicuculline methiodide (BIC) was inserted in the hole and driven to a depth of 1200-1400 μm from the cortical surface. BIC was ejected for ∼2min from the tip of the micropipette with positive direct current ranging between 20 and 40 nA in different experiments. This produced spontaneous nearly periodic bursts (0.2-1.0 Hz) of multi-unit activity in a radius of about 400 μm from the tip of the micropipette. The bursts of neural activity spread at a velocity of 0.11-0.24 ms⁻¹ (mean=0.14 mm ms⁻¹, SD=0.05)with decreasing amplitude.The area activated was on average 7.22 mm² (SD=0.91 mm²), or ∼92% of the area covered by the recording array. The mode of propagation was determined to occur by progressive recruitment of cortical territory, driven by a central locus of activity of some 400 μm in radius. Thus, activity did not propagate as a wave. Transection of the connections between the thalamus and MCx did not significantly alter the propagation velocity or the size of the recruited area, demonstrating that the bursts spread along the routes of intrinsic cortical connectivity. These experiments demonstrate that neural activity initiated within a small motor cortical locus (≤ 400 μm in radius) can recruit a relatively large neighbourhood in which a variety of muscles acting at several forelimb joints are represented. These results support the hypothesis that the MCx controls the forelimb musculature in an integrated and anticipatory manner based on a recurrent network topology

1. Bitufted interneurons in layer 2/3 of the rat (P14) somatosensory cortex have elongated apical and basal dendritic arbors that can span the entire depth of the cortex. Simultaneous dendritic and somatic whole-cell voltage recordings combined with Ca2+ fluorescence measurements were made to quantify voltage and Ca2+ signalling in dendritic arbors of bitufted neurons. 2. Action potentials (APs) initiated close to the soma by brief current injection back-propagated into the apical and basal dendritic arbors and evoked a transient increase in volume-averaged dendritic Ca2+ concentration (Delta[Ca(2+)](i)) of about 140 nM peak amplitude per AP. The AP evoked Ca2+ signal decayed with a time constant of about 200 ms. 3. A relatively high endogenous Ca(2+) binding ratio of approximately 285 determines the comparatively small rise in [Ca(2+)](i) of bitufted cell dendrites evoked by a back-propagating AP. 4. The [Ca(2+)](i) transient evoked by back-propagating dendritic APs decreased with distance (< or = 50 microm) from the soma in some neurons. At distances greater than 50 microm transients did not show a spatial gradient between the proximal and distal dendritic branches. 5. During trains of APs the mean amplitude of the steady-state increase in dendritic [Ca(2+)](i) encoded the AP frequency linearly up to 40 Hz with a slope of 20 nM Hz(-1). 6. The results suggest that APs initiated in the axon of bitufted neurons back-propagate and 'copy' the pattern of the axon's electrical activity also to the dendritic arbor. The AP pattern is transduced into a transient rise of dendritic [Ca(2+)](i) which, presumably, can regulate the receptive properties of the dendritic arbor for synaptic input. 7. Bitufted interneurons in layer 2/3 of the rat (P14) somatosensory cortex have elongated apical and basal dendritic arbors that can span the entire depth of the cortex. Simultaneous dendritic and somatic whole-cell voltage recordings combined with Ca2+ fluorescence measurements were made to quantify voltage and Ca2+ signalling in dendritic arbors of bitufted neurons. 8. Action potentials (APs) initiated close to the soma by brief current injection back-propagated into the apical and basal dendritic arbors and evoked a transient increase in volume-averaged dendritic Ca2+ concentration (Delta[Ca(2+)](i)) of about 140 nM peak amplitude per AP. The AP evoked Ca2+ signal decayed with a time constant of about 200 ms. 9. A relatively high endogenous Ca2+ binding ratio of approximately 285 determines the comparatively small rise in [Ca(2+)](i) of bitufted cell dendrites evoked by a back-propagating AP. 10. The [Ca(2+)](i) transient evoked by back-propagating dendritic APs decreased with distance (< or = 50 microm) from the soma in some neurons. At distances greater than 50 microm transients did not show a spatial gradient between the proximal and distal dendritic branches. 11. During trains of APs the mean amplitude of the steady-state increase in dendritic [Ca(2+)](i) encoded the AP frequency linearly up to 40 Hz with a slope of 20 nM Hz(-1). 12. The results suggest that APs initiated in the axon of bitufted neurons back-propagate and also 'copy' the pattern of the axon's electrical activity to the dendritic arbor. The AP pattern is transduced into a transient rise of dendritic [Ca(2+)](i) which, presumably, can regulate the receptive properties of the dendritic arbor for synaptic input.

In this paper, we introduce a time varying smoothing factor for the noise update in the optimal filtering based on QR decomposition (QRD). Conventionally, the noise statistics are updated during noise-only periods and kept fixed during speech present periods in QRD-based multichannel noise reduction [G. Rombouts and M. Moonen, Sept 2003]. Instead of using this conventional scheme that needs an explicit voice activity detector (VAD), we adopt a time varying smoothing factor which is parameterized from the normalized cross correlation (NCC). In a multi-microphone based system, the NCCs between two microphones can be used for finding the direction of signals [M. Omologo and P. Svaizer, 1994]. Provided that we know the direction of the speech signal and the time delays between microphones are compensated, the NCCs can be considered as a measure for the speech presence probability. The NCCs are estimated for a given time interval, and they are averaged over the microphones and smoothed in time. Then the averaged value is mapped to a smoothing factor through a nonlinear function. The simulation results show that the proposed algorithm yields better performance compared to the conventional QRD-based noise reduction.

Sub-pixel image registration on an embedded Nanosatellite Platform

Task automation is essential for efficient and consistent image segmentation in radiation oncology. We report on a deep learning architecture, comprising a U-Net and a variational autoencoder (VAE) for automatic contouring of the prostate gland incorporating interobserver variation for radiotherapy treatment planning. The U-Net/VAE generates an ensemble set of segmentations for each image CT slice. A novel outlier mitigation (OM) technique was implemented to enhance the model segmentation accuracy. The primary source dataset (source_prim) consisted of 19 200 CT slices (from 300 patient planning CT image datasets) with manually contoured prostate glands. A smaller secondary source dataset (source_sec) comprised 640 CT slices (from 10 patient CT datasets), where prostate glands were segmented by 5 independent physicians on each dataset to account for interobserver variability. Data augmentation via random rotation (<5 degrees), cropping, and horizontal flipping was applied to each dataset to increase sample size by a factor of 100. A probabilistic hierarchical U-Net with VAE was implemented and pretrained using the augmented source_prim dataset for 30 epochs. Model parameters of the U-Net/VAE were fine-tuned using the augmented source_sec dataset for 100 epochs. After the first round of training, outlier contours in the training dataset were automatically detected and replaced by the most accurate contours (based on Dice similarity coefficient, DSC) generated by the model. The U-Net/OM-VAE was retrained using the revised training dataset. Metrics for comparison included DSC, Hausdorff distance (HD, mm), normalized cross-correlation (NCC) coefficient, and center-of-mass (COM) distance (mm). Results for U-Net/OM-VAE with outliers replaced in the training dataset versus U-Net/VAE without OM were as follows: DSC=0.82±0.01 versus 0.80±0.02 (p=0.019), HD=9.18±1.22 versus 10.18±1.35mm (p=0.043), NCC=0.59±0.07 versus 0.62±0.06, and COM=3.36±0.81 versus 4.77±0.96mm over the average of 15 contours. For the average of 15 highest accuracy contours, values were as follows: DSC=0.90±0.02 versus 0.85±0.02, HD=5.47±0.02 versus 7.54±1.36mm, and COM=1.03±0.58 versus 1.46±0.68mm (p<0.03 for all metrics). Results for the U-Net/OM-VAE with outliers removed were as follows: DSC=0.78±0.01, HD=10.65±1.95mm, NCC=0.46±0.10, COM=4.17±0.79mm for the average of 15 contours, and DSC=0.88±0.02, HD=7.00±1.17mm, COM=1.58±0.63mm for the average of 15 highest accuracy contours. All metrics for U-Net/VAE trained on the source_prim and source_sec datasets via pretraining, followed by fine-tuning, show statistically significant improvement over that trained on the source_sec dataset only. Finally, all metrics for U-Net/VAE with or without OM showed statistically significant improvement over those for the standard U-Net. A VAE combined with a hierarchical U-Net and an OM strategy (U-Net/OM-VAE) demonstrates promise toward capturing interobserver variability and produces accurate prostate auto-contours for radiotherapy planning. The availability of multiple contours for each CT slice enables clinicians to determine trade-offs in selecting the "best fitting" contour on each CT slice. Mitigation of outlier contours in the training dataset improves prediction accuracy, but one must be wary of reduction in variability in the training dataset.

Pulse wave velocity (PWV) has been shown to be a good predictor of cardiovascular risk. Measuring PWV normally constitutes quantifying the transit time (TT) between proximally and distally measured blood pressure or velocity waveforms. However various factors affect our ability to measure PWV accurately making it a topic of continued attention. Primarily, the selection of the algorithm used to measure TT has been shown to have a remarkable effect upon accuracy. Other factors pertain to the quality and nature of the waveform data. The quality of the data (assuming good sensor function) worsens with increasing signal noise and decreasing sampling frequency, and the nature of the waveform data refers to waveform shape (e.g. pressure vs. velocity) or shape mismatch between the distal and proximal waveforms. Papaioannou et al.’s letter reflects upon an article our group published in the Annals of Biomedical Engineering (2013 Dec; 41(12):2617-29) which assessed current algorithms’ accuracies and variabilities due to waveform signal noise, temporal resolution, shape and shape mismatch. We used waveform data generated by a one-dimensional (1-D) arterial model for which the theoretical TT was known a priori, thus algorithm accuracy could be explicitly measured. Furthermore, the same algorithms were applied to beat-to-beat clinical data to investigate beat-to-beat variability in PWV measurement. Based on this study we proposed a set of recommendations for choosing the most accurate algorithm for a given waveform set. The algorithms tested included two variations of the traditional foot-to-foot method, a least squares fit of the systolic rise, and cross correlation of the entire waveform. The software developed for this study containing all algorithms tested was made available to the public in the interest of continued discussion upon this topic. We agree with the Papainnou et al.’s assertion that pressure and velocity waveforms may need to be addressed differently. Certainly the results we presented in our article (Fig. 4) explicitly show differences between algorithm accuracies when applied to pairs of pressure or velocity waveforms. Furthermore, these differences were outlined as a warning in Point 4 of the algorithm selection recommendations. We found wave shape mismatch between the proximal and distal wave pairs to be a crucial factor in determining which algorithm to use. For example, cross correlation is by definition a comparison of wave shapes weighted by local magnitude. In our article we measured waveshape similarity using a normalised cross-correlation coefficient (CCCoefficient) where a value of 1.0 would indicate identical shapes. Papainnou et al. were interested to know the CCCoefficient for the carotid and femoral arterial waveforms as these are the standard measurements made by clinical devices such as the SphygmoCor system. The CCCoefficient of the carotid-and-femoral-artery pressure waves was 0.78 for the numerical data and 0.84 ± 0.10 for our patient cohort (n = 20). These results indicate substantial wave shape mismatch in clinical assessment. Measuring beat-to-beat variation in carotid femoral PWV in our patient cohort was done retrospectively using 10 s tonometric signals measured sequentially at the carotid, and then the femoral artery. As each signal was measured concurrently with the ECG, individual waveforms could be dissected from the 10 s signal and aligned in time with reference to the R-wave of the ECG. Beat-to-beat variation was therefore assessed as the variation in measured PWV from as many waveAddress correspondence to Nicholas R. Gaddum, King’s College London, British Heart Foundation Centre, St. Thomas’ Hospital, 4th Floor Lambeth Wing, Westminster Bridge Road, London SE1 7EH, UK. Electronic mail: nickgaddum@gmail.com Annals of Biomedical Engineering, Vol. 42, No. 6, June 2014 ( 2014) pp. 1145–1147 DOI: 10.1007/s10439-014-1007-7

A new measure of similarity, suitable for both signal processing and image processing applications, is presented. The measure of similarity ( Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> ) is an F-distributed test statistic that quantifies the degree of alignment, correlation or coincidence between two or more (time-or space-dependent) waveforms. The test statistic may be used to automate detection, classification, localisation, association and registration operations. When used to estimate time-of-arrival differences, which is typically done using cross correlation or beam formation, the technique provides an efficient means of: maintaining a low and constant false-alarm rate, detecting weak signals in noise and reducing angular errors. The method is applied to the problem of acoustic source detection and localisation. Real data are used to compare the method with cross correlation and normalised cross correlation. The new method yields prominent and narrow peaks, at the true source locations, with false peaks due to misalignment, misassociation, and background noise, suppressed. When processing continuous data streams, the test statistic is computed efficiently in the time domain.

An experiment was conducted on a full-scale jet engine to investigate the aerodynamic noise generating regions in the free jet. Cross-correlation measurements were made between the static pressure fluctuations and the farfield radiated sound. These measurements were made for two different static pressure probe positions and a large number of farfield positions (at various angles). In addition, each test geometry was run for four different jet exit velocities. The measured, normalized cross-correlation functions varied between 0.004 and 0.155. A new Q-function, based on the above normalized cross correlation is defined and plotted. This function represents the source strength per unit volume within the jet region. This Q-function shows dependence on the probe position, the angular position of the farfield microphone, and the jet exit Mach number. Third-octave analyses of both the probe signal and the farfield radiated sound were made. The results show that cross-correlation techniques are a valuable tool in the investigation of the aerodynamic noise generating regions of an actual jet engine.

Template matching is used for many applications in image processing. Cross Correlation is the basic statistical approach to image registration. It is used for template matching or pattern recognition. Template can be considered a sub-image from the reference image, and the image can be considered as a sensed image. The objective is to establish the correspondence between the reference image and sensed image. It gives the measure of the degree of similarity between an image and template. This paper describes medical image registration by template matching based on Normalized Cross-Correlation (NCC) using Cauchy-Schwartz inequality. The algorithm for template matching using NCC is implemented in MATLAB. The algorithm does the template matching and uses the Cauchy-Schwartz’s inequality to simplify the procedure. The developed algorithm is robust for similarity measure. An experimental result with medical images registration with noise and without noise is shown in the results section.