Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow.

The pattern of a spatial structure that repeats itself independently of the scale of magnification or resolution is often characterized by a fractal dimension (D). Two-dimensional low-pass filtering, which may serve as a method to assess D, was applied to functional images of pulmonary perfusion measured by positron emission tomography. The corner frequency of a low-pass filter is inversely proportional to the resolution scale. The method was applied to three types of images: random noise images, synthetic fractal images, and positron emission tomographic images of pulmonary perfusion. Images were processed with two-dimensional low-pass filters of decreasing corner frequencies, and a spatial heterogeneity index, the coefficient of variation, was calculated for each low-pass-filtered image. The natural logarithm of the coefficient of variation scaled linearly with the natural logarithm of the resolution scale for the PET images studied (average R(2) = 0.99). D ranged from 1.25 to 1.36 for the residual distribution of pulmonary perfusion after vertical gradients were removed by linear regression. D of the same data without removal of vertical gradients ranged from 1.11 to 1.14, but the fractal plots had systematic deviations from linearity and a lower linear correlation coefficient (R(2) = 0. 96). The method includes all data in the lung field and is insensitive to the effects of misregistration. We conclude that low-pass filtering offers new insights into the interpretation of D of two-dimensional functional images as a measure of the frequency content of spatial heterogeneity.     

空间频率通道中噪声对体视匹配的影响

本工作希望了解噪声在各空间频率通道中对体视的影响.产生从5%至35%每隔5%的七个等级的随机点噪声图象,参照Wilson四通道模型的频率分别用两种不同滤波器对随机点立体图对(RDS)及噪声图象进行滤波,然后在各通道图对中加入不同通道噪声进行匹配观察.得到:1.高频通道的体视抗干扰能力高于低频通道.2.Gabor函数滤波后图对的体视抗干扰能力高于Butterworth滤波器滤波后的,但均低于未滤波的.3.当噪声大于15%时,低频噪声对低频图对及高频噪声对高、低频图对的体视匹配有抑制作用,而低频噪声对高频图对则影响很小.4.未滤波及各通道图对的最大噪声容限均不超过25%.     

Study of parvocellular and magnocellular visual channels in normal subjects and in patients with psychopathology

We measured susceptibility to the Müller-Lyer illusion in schizophrenic patients and normal observers. The images of the Müller-Lyer figure were digitally filtered in a high-frequency and low-frequency band by wavelet filter. Patients with schizophrenia are more susceptible to Müller-Lyer illusion, than mentally healthy examinees. The images of the Müller-Lyer figure with low spatial frequency were perceived in a similar way by the schizophrenic patients on the initial stage of disease and the control subjects. Patients with schizophrenia were more sensitive to the Müller-Lyer illusion when the image contained only high or medium spatial frequency. Schizophrenic patients in advanced stage were more susceptible to the illusion while presented with all types of images of the Müller-Lyer figure than the control group. It is hypothesized that those differences arise from the mismatch work of the magnocellular and parvocellular systems. It is known that images with the high spatial frequencies are most relevant for the parvocellular visual channels. The magnocellular visual channels are most sensitive to the images with the low spatial frequencies. Thus these findings demonstrate a significant impairment in parvocellular pathway function in patients on initial stage of schizophrenia. The patients on advanced stage of schizophrenia demonstrate impairment of both the parvocellular and magnocellular systems.     

基于空间频域滤波高动态光学投影层析的斑马鱼三维成像研究

本文提出了一种基于空间频率滤波的多曝光融合的高动态投影层析三维成像方法,实现了活体斑马鱼（17 mm × 4 mm,最大厚度为2.33 mm,最小厚度为0.29 mm）的三维结构成像. 通过相机采用不同曝光时间记录系列吸收图像,将每张图像取变换到频域去除低频后,将各张滤波后叠加并逆傅里叶变换回空域,对变换后的图像进行归一化处理,最终获得高动态图像. 在每个投影角度获得这种高动态吸收投影图像,进行滤波反投影算法重建,获得高动态的整条斑马鱼三维结构信息. 实验成像结果表明,这种空间频率滤波多曝光融合的高动态光学投影层析三维成像研究,可以获得复杂结构更丰富的空间信息,对斑马鱼等模式生物早期胚胎生长发育进程进行监测和定量评估有一定的应用前景.     

A theory of maximizing sensory information

A theory is developed on the assumption that early sensory processing aims at maximizing the information rate in the channels connecting the sensory system to more central parts of the brain, where it is assumed that these channels are noisy and have a limited dynamic range. Given a stimulus power spectrum, the theory enables the computation of filters accomplishing this maximizing of information. Resulting filters are band-pass or high-pass at high signal-to-noise ratios, and low-pass at low signal-to-noise ratios. In spatial vision this corresponds to lateral inhibition and pooling, respectively. The filters comply with Weber's law over a considerable range of signal-to-noise ratios.     

A computational model of cellular mechanisms of temporal coding in the medial geniculate body (MGB)

Acoustic stimuli are often represented in the early auditory pathway as patterns of neural activity synchronized to time-varying features. This phase-locking predominates until the level of the medial geniculate body (MGB), where previous studies have identified two main, largely segregated response types: Stimulus-synchronized responses faithfully preserve the temporal coding from its afferent inputs, and Non-synchronized responses, which are not phase locked to the inputs, represent changes in temporal modulation by a rate code. The cellular mechanisms underlying this transformation from phase-locked to rate code are not well understood. We use a computational model of a MGB thalamocortical neuron to test the hypothesis that these response classes arise from inferior colliculus (IC) excitatory afferents with divergent properties similar to those observed in brain slice studies. Large-conductance inputs exhibiting synaptic depression preserved input synchrony as short as 12.5 ms interclick intervals, while maintaining low firing rates and low-pass filtering responses. By contrast, small-conductance inputs with Mixed plasticity (depression of AMPA-receptor component and facilitation of NMDA-receptor component) desynchronized afferent inputs, generated a click-rate dependent increase in firing rate, and high-pass filtered the inputs. Synaptic inputs with facilitation often permitted band-pass synchrony along with band-pass rate tuning. These responses could be tuned by changes in membrane potential, strength of the NMDA component, and characteristics of synaptic plasticity. These results demonstrate how the same synchronized input spike trains from the inferior colliculus can be transformed into different representations of temporal modulation by divergent synaptic properties.     

Effects of electrocardiography contamination and comparison of ECG removal methods on upper trapezius electromyography recordings

Electromyography (EMG) recordings from the trapezius are often contaminated by the electrocardiography (ECG) signal, making it difficult to distinguish low-level muscle activity from muscular rest. This study investigates the influence of ECG contamination on EMG amplitude and frequency estimations in the upper trapezius during muscular rest and low-level contractions. A new method of ECG contamination removal, filtered template subtraction (FTS), is described and compared to 30 Hz high-pass filter (HPF) and averaged template subtraction (ATS) methods. FTS creates a unique template of each ECG artifact using a low-pass filtered copy of the contaminated signal, which is subtracted from contaminated periods in the original signal. ECG contamination results in an over-estimation of EMG amplitude during rest in the upper trapezius, with negligible effects on amplitude and frequency estimations during low-intensity isometric contractions. FTS and HPF successfully removed ECG contamination from periods of muscular rest, yet introduced errors during muscle contraction. Conversely, ATS failed to fully remove ECG contamination during muscular rest, yet did not introduce errors during muscle contraction. The relative advantages and disadvantages of different ECG contamination removal methods should be considered in the context of the specific motor tasks that require analysis.     

The filtered Fourier difference spectrum predicts psychophysical letter discrimination in the peripheral retina

We wished to devise a measure of dissimilarity (D) which could predict psychophysical discrimination performance for Snellen letter pairs in peripheral vision. Threshold size for discriminating 33 pairs of Snellen letters was measured at 30 degrees eccentricity in the nasal retina for two subjects. D was computed for each pair by performing an overlap subtraction in the spatial domain, followed by a Fast Fourier Transform on this difference image, and dividing the total power in the resultant 'difference spectrum' by the sum of the powers of the individual letter spectra. A plot of D vs. psychophysical threshold letter size gave a mean correlation of R = -0.81. When D was calculated for letters that were low-pass filtered at different cut-off frequencies, the correlation with psychophysical performance was greatest when cut-off was between 1.25-1.9 cycles/letter (R = -0.85). Conversely, when the difference spectrum was high-pass filtered at different cut-off frequencies, the correlation decreased continuously as the cut-off increased. These results imply that the band of frequencies between zero and 1.25 cycles/letter are most important for letter discrimination in peripheral vision.     

不同空间频率通道的深度知觉及其质地的影响

我们设计了四种不同质地的随机点立体图对(RDS),并按照Wilson的空间频率通道的频带,分别利用Butterworth滤波器及Gabor函数对之进行了数字滤波处理,然后进行各种左右眼配对观察.得结果如下:1、Gabor函数滤波后图对的匹配结果好于Butterworth滤波器滤波后的图对.2、滤波后图对的匹配效果与图象质地有关.3、不同滤波的图对匹配大多也能形成立体感.4、在体视不同通道图对的匹配中,右眼对图象的高频成分更为敏感.     

Spike-frequency adaptation generates intensity invariance in a primary auditory interneuron

Adaptation of the spike-frequency response to constant stimulation, as observed on various timescales in many neurons, reflects high-pass filter properties of a neuron's transfer function. Adaptation in general, however, is not sufficient to make a neuron's response independent of the mean intensity of a sensory stimulus, since low frequency components of the stimulus are still transmitted, although with reduced gain. We here show, based on an analytically tractable model, that the response of a neuron is intensity invariant, if the fully adapted steady-state spike-frequency response to constant stimuli is independent of stimulus intensity. Electrophysiological recordings from the AN1, a primary auditory interneuron of crickets, show that for intensities above 60 dB SPL (sound pressure level) the AN1 adapted with a time-constant of approximately 40 ms to a steady-state firing rate of approximately 100 Hz. Using identical random amplitude-modulation stimuli we verified that the AN1's spike-frequency response is indeed invariant to the stimulus' mean intensity above 60 dB SPL. The transfer function of the AN1 is a band pass, resulting from a high-pass filter (cutoff frequency at 4 Hz) due to adaptation and a low-pass filter (100 Hz) determined by the steady-state spike frequency. Thus, fast spike-frequency adaptation can generate intensity invariance already at the first level of neural processing.     

Somatic evoked high-frequency magnetic oscillations reflect activity of inhibitory interneurons in the human somatosensory cortex

High-frequency potential oscillations in the range of 300–900 Hz have recently been shown to concur with the primary response (N20) of the somatosensory cortex in awake humans. However, the physiological mechanisms of the high-frequency oscillations remained undetermined. We addressed the issue by analyzing magnetic fields during wakefulness and sleep over the left hemisphere to right median nerve stimulation with a wide bandpass (0.1–2000 Hz) recording with subsequent high-pass (> 300 Hz) and low-pass (< 300 Hz) filtering. With wide bandpass recordings, high-frequency magnetic oscillations with the main signal energy at 580–780 Hz were superimposed on the N20m during wakefulness. Isofield mapping at each peak of the high-pass filtered and isolated high-frequency oscillations showed a dipolar pattern and the estimated source for these peaks was the primary somatosensory cortex (area 3b) very close to that for the N20m peak. During sleep, the high-frequency oscillations showed dramatic diminution in amplitude while the N20m amplitude exhibited a moderate increment. This reciprocal relation between the high-frequency oscillations and the N20m during a wake-sleep cycle suggests that they represent different generator substrates. We speculate that the high-frequency oscillations represent a localized activity of the GABAergic inhibitory interneurons of layer 4, which have been shown in animal experiments to respond monosynaptically to thalamo-cortical input with a high-frequency (600–900 Hz) burst of short duration spikes. On the other hand, the underlying N20m represents activity of pyramidal neurons which receive monosynaptic excitatory input from the thalamus as well as a feed-forward inhibition from the interneurons.     

Epoch length to accurately estimate the amplitude of interference EMG is likely the result of unavoidable amplitude cancellation

Researchers and clinicians routinely rely on interference electromyograms (EMGs) to estimate muscle forces and command signals in the neuromuscular system (e.g., amplitude, timing, and frequency content). The amplitude cancellation intrinsic to interference EMG, however, raises important questions about how to optimize these estimates. For example, what should the length of the epoch (time window) be to average an EMG signal to reliably estimate muscle forces and command signals? Shorter epochs are most practical, and significant reductions in epoch have been reported with high-pass filtering and whitening. Given that this processing attenuates power at frequencies of interest (<250 Hz), however, it is unclear how it improves the extraction of physiologically relevant information. We examined the influence of amplitude cancellation and high-pass filtering on the epoch necessary to accurately estimate the “true” average EMG amplitude calculated from a 28 s EMG trace (EMG_ref) during simulated constant isometric conditions. Monte Carlo iterations of a motor-unit model simulating 28 s of surface EMG produced 245 simulations under two conditions: with and without amplitude cancellation. For each simulation, we calculated the epoch necessary to generate average full-wave rectified EMG amplitudes that settled within 5% of EMGref. For the no-cancellation EMG, the necessary epochs were short (e.g., <100 ms). For the more realistic interference EMG (i.e., cancellation condition), epochs shortened dramatically after using high-pass filter cutoffs above 250 Hz, producing epochs short enough to be practical (i.e., <500 ms). We conclude that the need to use long epochs to accurately estimate EMG amplitude is likely the result of unavoidable amplitude cancellation, which helps to clarify why high-pass filtering (>250 Hz) improves EMG estimates.     

Visual mechanisms of recognition of vanishing figures

The acuity test Landolt C's with a complex contour imitating various kinds of high-pass spatial frequency filtering generated as a printed visual acuity charts with a grey background were studied with regard to recognition thresholds. Comparisons were made for recognition thresholds with different complex contours. When the vanishing optotypes are out of focus, their image on the retina fades rapidly into the grey background, rendering them invisible rather than merely blurred as in the standard chart. The data obtained confirm that the recognition distance depends on physical property of complex contour profile and show the importance of the Landolt C spatial frequency spectrum for recognition of different types of the complex contour.     

The accuracy of measuring the kinematics of rising from a chair with accelerometers and gyroscopes

The purpose of this study was to assess the accuracy of measuring angle and angular velocity of the upper body and upper leg during rising from a chair with accelerometers, using low-pass filtering of the accelerometer signal. Also, the improvement in accuracy of the measurement with additional use of high-pass filtered gyroscopes was assessed. Two uni-axial accelerometers and one gyroscope (DynaPort) per segment were used to measure angles and angular velocities of upper body and upper leg. Calculated angles and angular velocities were compared to a high-quality optical motion analysis system (Optotrak), using root mean squared error (RMS) and correlation coefficient (r) as parameters. The results for the sensors showed that two uni-axial accelerometers give a reasonable accurate measurement of the kinematics of rising from a chair (RMS = 2.9, 3.5, and 2.6 degrees for angle and RMS = 9.4, 18.4, and 11.5 degrees /s for angular velocity for thorax, pelvis, and upper leg, respectively). Additional use of gyroscopes improved the accuracy significantly (RMS = 0.8, 1.1, and 1.7 degrees for angle and RMS = 2.6, 4.0 and 4.9 degrees /s for angular velocity for thorax, pelvis and upper leg, respectively). The low-pass Butterworth filter had optimal cut-off frequencies of 1.05, 1.3, and 1.05 for thorax, pelvis, and upper leg, respectively. For the combined signal, the optimal cut-off frequencies were 0.18, 0.2, and 0,38 for thorax, pelvis and upper leg, respectively. The filters showed no subject specificity. This study provides an accurate, inexpensive and simple method to measure the kinematics of movements similar to rising from a chair.     

Latency of evoked potentials in the tasks involving classification of images after wavelet filtration

We studied the characteristics of evoked potentials recorded during the recognition test based on four types of series of images subjected to the wavelet filtration: images of living objects containing either low frequency or high frequency portion of the spatial frequency spectrum, and imaging of non-living objects in the same two spatial frequency bands. Each subject had to classify the image either by its semantic feature (living–non-living), or by its physical feature (low frequency–high frequency). The purpose of this study was to compare the time characteristics of evoked potentials in these two types of tasks, which provides information on the time characteristics of categorization mechanisms of visual images. Analysis of the latent periods and amplitudes of the components of evoked potentials allowed us to detect the occipital areas of the leads where the early components (up to 170 ms) are associated with spatial and frequency characteristics of the image, the frontal and temporal areas where the components of 170–200 ms correspond to the process of categorization, and the later frontal, central, and parietal areas (300–500 ms) correspond to the process of error detection and the organization of motor response.     

The Influence of High-Frequency Envelope Information on Low-Frequency Vowel Identification in Noise

Vowel identification in noise using consonant-vowel-consonant (CVC) logatomes was used to investigate a possible interplay of speech information from different frequency regions. It was hypothesized that the periodicity conveyed by the temporal envelope of a high frequency stimulus can enhance the use of the information carried by auditory channels in the low-frequency region that share the same periodicity. It was further hypothesized that this acts as a strobe-like mechanism and would increase the signal-to-noise ratio for the voiced parts of the CVCs. In a first experiment, different high-frequency cues were provided to test this hypothesis, whereas a second experiment examined more closely the role of amplitude modulations and intact phase information within the high-frequency region (4–8 kHz). CVCs were either natural or vocoded speech (both limited to a low-pass cutoff-frequency of 2.5 kHz) and were presented in stationary 3-kHz low-pass filtered masking noise. The experimental results did not support the hypothesized use of periodicity information for aiding low-frequency perception.     

Estimating Extracellular Spike Waveforms from CA1 Pyramidal Cells with Multichannel Electrodes

Extracellular (EC) recordings of action potentials from the intact brain are embedded in background voltage fluctuations known as the “local field potential” (LFP). In order to use EC spike recordings for studying biophysical properties of neurons, the spike waveforms must be separated from the LFP. Linear low-pass and high-pass filters are usually insufficient to separate spike waveforms from LFP, because they have overlapping frequency bands. Broad-band recordings of LFP and spikes were obtained with a 16-channel laminar electrode array (silicone probe). We developed an algorithm whereby local LFP signals from spike-containing channel were modeled using locally weighted polynomial regression analysis of adjoining channels without spikes. The modeled LFP signal was subtracted from the recording to estimate the embedded spike waveforms. We tested the method both on defined spike waveforms added to LFP recordings, and on in vivo-recorded extracellular spikes from hippocampal CA1 pyramidal cells in anaesthetized mice. We show that the algorithm can correctly extract the spike waveforms embedded in the LFP. In contrast, traditional high-pass filters failed to recover correct spike shapes, albeit produceing smaller standard errors. We found that high-pass RC or 2-pole Butterworth filters with cut-off frequencies below 12.5 Hz, are required to retrieve waveforms comparable to our method. The method was also compared to spike-triggered averages of the broad-band signal, and yielded waveforms with smaller standard errors and less distortion before and after the spike.     

High-pass filtering of input signals by the Ih current in a non-spiking neuron, the retinal rod bipolar cell

Hyperpolarization-activated cyclic nucleotide-sensitive (HCN) channels mediate the I(f) current in heart and I(h) throughout the nervous system. In spiking neurons I(h) participates primarily in different forms of rhythmic activity. Little is known, however, about its role in neurons operating with graded potentials as in the retina, where all four channel isoforms are expressed. Intriguing evidence for an involvement of I(h) in early visual processing are the side effects reported, in dim light or darkness, by cardiac patients treated with HCN inhibitors. Moreover, electroretinographic recordings indicate that these drugs affect temporal processing in the outer retina. Here we analyzed the functional role of HCN channels in rod bipolar cells (RBCs) of the mouse. Perforated-patch recordings in the dark-adapted slice found that RBCs exhibit I(h), and that this is sensitive to the specific blocker ZD7288. RBC input impedance, explored by sinusoidal frequency-modulated current stimuli (0.1-30 Hz), displays band-pass behavior in the range of I(h) activation. Theoretical modeling and pharmacological blockade demonstrate that high-pass filtering of input signals by I(h), in combination with low-pass filtering by passive properties, fully accounts for this frequency-tuning. Correcting for the depolarization introduced by shunting through the pipette-membrane seal, leads to predict that in darkness I(h) is tonically active in RBCs and quickens their responses to dim light stimuli. Immunohistochemistry targeting candidate subunit isoforms HCN1-2, in combination with markers of RBCs (PKC) and rod-RBC synaptic contacts (bassoon, mGluR6, Kv1.3), suggests that RBCs express HCN2 on the tip of their dendrites. The functional properties conferred by I(h) onto RBCs may contribute to shape the retina's light response and explain the visual side effects of HCN inhibitors.     

Eigenschaften diskreter Ortsfilter

Summary Properties of discrete spatial filters are investigated. By introducing rectangular or oblique coordinates it is possible to design filters in a quadratic or hexagonal raster. The design of low-pass, high-pass and band-pass filters is shown. Their properties are evaluated by computing an example; different filters are compared. It is possible to design arbitrary filters; however, there are limitations due to quantization error and approximation of filters by a necessarily finite (and small) number of elements.