{"title": "Noise Characterization, Modeling, and Reduction for In Vivo Neural Recording", "book": "Advances in Neural Information Processing Systems", "page_first": 2160, "page_last": 2168, "abstract": "Studying signal and noise properties of recorded neural data is critical in developing more efficient algorithms to recover the encoded information. Important issues exist in this research including the variant spectrum spans of neural spikes that make it difficult to choose a global optimal bandpass filter. Also, multiple sources produce aggregated noise that deviates from the conventional white Gaussian noise. In this work, the spectrum variability of spikes is addressed, based on which the concept of adaptive bandpass filter that fits the spectrum of individual spikes is proposed. Multiple noise sources have been studied through analytical models as well as empirical measurements. The dominant noise source is identified as neuron noise followed by interface noise of the electrode. This suggests that major efforts to reduce noise from electronics are not well spent. The measured noise from in vivo experiments shows a family of 1/f^{x} (x=1.5\\pm 0.5) spectrum that can be reduced using noise shaping techniques. In summary, the methods of adaptive bandpass filtering and noise shaping together result in several dB signal-to-noise ratio (SNR) enhancement.", "full_text": "Noise Characterization, Modeling, and Reduction for\n\nIn Vivo Neural Recording\n\nZhi Yang1, Qi Zhao2, Edward Keefer3,4, and Wentai Liu1\n\n1 University of California at Santa Cruz, 2 California Institute of Technology\n\n3 UT Southwestern Medical Center, 4 Plexon Inc\n\nyangzhi@soe.ucsc.edu\n\nAbstract\n\nStudying signal and noise properties of recorded neural data is critical in devel-\noping more ef\ufb01cient algorithms to recover the encoded information. Important\nissues exist in this research including the variant spectrum spans of neural spikes\nthat make it dif\ufb01cult to choose a globally optimal bandpass \ufb01lter. Also, multiple\nsources produce aggregated noise that deviates from the conventional white Gaus-\nsian noise. In this work, the spectrum variability of spikes is addressed, based on\nwhich the concept of adaptive bandpass \ufb01lter that \ufb01ts the spectrum of individual\nspikes is proposed. Multiple noise sources have been studied through analytical\nmodels as well as empirical measurements. The dominant noise source is identi-\n\ufb01ed as neuron noise followed by interface noise of the electrode. This suggests\nthat major efforts to reduce noise from electronics are not well spent. The mea-\nsured noise from in vivo experiments shows a family of 1/f x spectrum that can\nbe reduced using noise shaping techniques. In summary, the methods of adaptive\nbandpass \ufb01ltering and noise shaping together result in several dB signal-to-noise\nratio (SNR) enhancement.\n\n1 Introduction\n\nNeurons in the brain communicate through the \ufb01ring of action potentials. This process induces brief\n\u201cvoltage\u201d spikes in the surrounding environment that can be recorded by electrodes. The recorded\nneural signal may come from single, or multiple neurons. While single neurons only require a\ndetection algorithm to identify the \ufb01rings, multiple neurons require the separation of superimposed\nactivities to obtain individual neuron \ufb01rings. This procedure, also known as spike sorting, is more\ncomplex than what is required for single neurons.\nSpike sorting has acquired general attention. Many algorithms have been reported in the litera-\nture [1\u20137], with each claiming an improved performance based on different data. Comparisons\namong different algorithms can be subjective and dif\ufb01cult. For example, benchmarks of in vivo\nrecordings that thoroughly evaluate the performance of algorithms are unavailable. Also, syn-\nthesized sequences with benchmarks obtained through neuron models [8], isolated single neuron\nrecordings [2], or simultaneous intra- and extra- cellular recordings [9] lack the in vivo recording\nenvironment. As a result, synthesized data provide useful but limited feedback on algorithms.\nThis paper discusses a noise study, based on which SNR enhancement techniques are proposed.\nThese techniques are applicable to an unspeci\ufb01ed spike sorting algorithm. Speci\ufb01cally, a proce-\ndure of online estimating both individual spike and noise spectrum is \ufb01rst applied. Based on the\nestimation, a bandpass \ufb01lter that \ufb01ts the spectrum of the underlying spike is selected. This max-\nimally reduces the broad band noise without sacri\ufb01cing the signal integrity. In addition, a com-\nprehensive study of multiple noise sources are performed through lumped circuit model as well\nas measurements. Experiments suggest that the dominant noise is not from recording electronics,\n\n1\n\n\fFigure 1: Block diagram of the proposed noise reduction procedures.\n\nthus de-emphasize the importance of low noise hardware design. More importantly, the measured\nnoise generally shows a family of 1/f x spectrum, which can be reduced by using noise shaping\ntechniques [10, 11]. Figure 1 shows the proposed noise reduction procedures.\nThe rest of this paper is organized as follows. Section 2 focuses on noise sources. Section 3 gives\na Wiener kernel based adaptive bandpass \ufb01lter. Section 4 describes a noise shaping technique that\nuses fractional order differentiation. Section 5 reports experiment results. Section 6 gives concluding\nremarks.\n\n2 Noise Spectrum and Noise Model\n\nRecorded neural spikes are superimposed with noise that exhibit non-Gaussian characteristics and\ncan be approximated as 1/f x noise. The frequency dependency of noise is contributed by multi-\nple sources. Identi\ufb01ed noise sources include 1/f \u03b1\u2212neuron noise [12\u201314] (notations of 1/f x and\n1/f \u03b1 represent frequency dependencies of the total noise and neuron noise respectively), electrode-\nelectrolyte interface noise [15], tissue thermal noise, and electronic noise, which are illustrated in\nFigure 2 using a lumped circuit model. Except electrolyte bulk noise (4kT Rb in Figure 2) that has\na \ufb02attened spectrum, the rest show frequency dependency. Speci\ufb01cally, 1/f \u03b1\u2212neuron noise is in-\nduced from distant neurons [12\u201314]. Numeric simulations based on simpli\ufb01ed neuron models [12]\nsuggest that \u03b1 can vary a wide range depending on the parameters. For the electrode-electrolyte\ninterface noise, non-faradaic type in particular, an effective resistance (Ree) is de\ufb01ned for model-\ning purposes. Ree generates noise that is attenuated quadratically to frequency in high frequency\nregion by the interface capacitance (Cee). Electronic noise consists of two major components: ther-\nmal noise (\u223c kT /gm [16]) and \ufb02icker noise (or 1/f noise [16]). Flicker noise dominates at lower\nfrequency range and is fabrication process dependent. Next, we will address the noise model that\nwill later be used to develop noise removal techniques in Section 3 and Section 4, and veri\ufb01ed by\nexperiment results in section 5.\n2.1 1/f \u03b1\u2212Neuron Noise\n\nBackground spiking activities of the vast distant neurons (e.g. spike, synaptic release [17\u201319])\noverlap the spectrum of the recorded spike signal. They usually have small magnitudes and are\nnoisily aggregated. Analytically, the background activities are described as\n\nVneu =\n\nvi.neu(t \u2212 ti,k),\n\n(1)\n\n(cid:88)\n\n(cid:88)\n\ni\n\nk\n\nwhere Vneu represents the superimposed background activities of distant neurons; i and ti,k repre-\nsent the object identi\ufb01cation and its activation time respectively, and vi.neu is the spiking activity\ntemplate of the ith object. Based on Eq. 1, the power spectrum of Vneu is\n\nP{Vneu} =\n\n|Xi(f)|2fi\n\n2\n\n< e2\u03c0jf (ti,k1+k\u2212ti,k1 ) >,\n\n(2)\n\n(cid:88)\n\n(cid:88)\n\ni\n\nk\n\nwhere < > represents the average over the ensemble and over k1, P{} is the spectrum operation,\nXi(f) is the fourier transform of vi.neu, and fi is the frequency of spiking activity vi.neu (the\nnumber of activations divided by a period of time). The spectrum of a delta function spike pulse\n\n2\n\n\fFigure 2: Noise illustration for extracellular spikes.\n\n(cid:80)\nk < e2\u03c0jf (tk1+k\u2212tk1 ) >), according to [12], features a lower frequency and exhibits a\ntrain (\n1/f \u03b1 frequency dependency. As this term multiplies |Xi(f)|2, the unresolved spiking activities of\ndistant neurons contribute a spectrum of 1/f x within the signal spectrum.\n\n2.2 Electrode Noise\n\nAssume the electrode-electrolyte interface is the non-faradaic type where charges such as electrons\nand ions, can not pass across the interface. In a typical in vivo recording environment that involves\nseveral different ionic particles, e.g. Na+, K+, ..., the current \ufb02ux of any ith charged particle Ji(x)\nat location x assuming spatial concentration ni(x) is described by Nernst equation\n\nJi(x) = \u2212Di\u2207ni(x) + ni(x)\u03c5 \u2212 ziq\nkT\n\n(3)\nwhere Di is the diffusion coef\ufb01cient, \u03a6 electrical potential, zi charge of the particle, q the charge of\none electron, k the Boltzmann constant, T the temperature, and \u03c5 the convection coef\ufb01cient. In a\nsteady state, Ji(x) is zero with the boundary condition of maintaining about 1V voltage drop from\nmetal to electrolyte. In such a case, the electrode interface can be modeled as a lumped resistor Ree\nin parallel with a lumped capacitor Cee. This naturally forms a lowpass \ufb01lter for the interface noise.\nAs a result, the induced noise from Ree at the input of the ampli\ufb01er is\n\nDini\u2207\u03a6(x),\n\n(Ree||j\u03c9Cee||(Rb + j\u03c9Ci))2 =\n\n4kT\nRee\n\n|\n\n1\n\n1/Ree + j\u03c9Cee + 1/(Rb + 1\nj\u03c9Ci\n\n)\n\n|2.\n\n(4)\n\nReferring to the hypothesis that the ampli\ufb01er input capacitance (Ci) is suf\ufb01ciently small, introducing\nnegligible waveform distortion, the integrated noise by electrode interface satis\ufb01es\ntan\u221212\u03c0ReeCeef|f =fc2\n\nNe.edf \u2248\n\n4kT Ree\n\n(5)\n\nf =fc1 <\n\n|1 + 2\u03c0jf ReeCee|2 df =\n\n2kT\n\u03c0Cee\n\nkT\nCee\n\n.\n\nfc1\n\nfc1\n\nEquation 5 suggests reducing electrode interface noise by increasing double layer capacitance (Cee).\nWithout increasing the size of electrodes, carbon-nanotube (CNT) coating [20] can dramatically in-\ncrease electrode surface area, thus, reducing the interface noise. Section 5 will compare conventional\nelectrodes and CNT coated electrodes from a noise point of view.\nIn regions away from the interface boundary, \u2207ni(x) = 0 results in a \ufb02attened noise spectrum. Here\nwe use a lumped bulk resistance Rb in series with the double-layer interface for modeling noise\n\nNe.b = 4kT Rb = 4kT \u03c7\n\n\u03c1tissue\n\n\u03c0rs\n\n,\n\n(6)\n\nwhere Rb is the bulk resistance, \u03c1tissue is the electrolyte resistivity, rs is the radius of the electrode,\nand \u03c7 is a constant that relates to the electrode geometry. As given in [21], \u03c7 \u2248 0.5 for a plate\nelectrode.\n\n2.3 Electronic Noise\n\nNoise generated by electronics can be predicted by circuit design tools and validated through mea-\nsurements. At the frequency of interest, there are two major components: thermal noise of transistors\nand \ufb02icker noise\n\nNe.e =\n\n4kT\nRee\n\n(cid:90) fc2\n\n(cid:90) fc2\n\nNelectronic = Nc.thermal + Nc.f licker = \u03b3\n\n3\n\n4kT\ngm\n\n+ K\n\nCoxW L\n\n1\nf\n\n,\n\n(7)\n\n\fwhere Nc.thermal is the circuit thermal noise, Nc.f licker the \ufb02icker noise, gm the transconductance\nof the ampli\ufb01er (\u2202iout/\u2202vin), \u03b3 a circuit architecture dependent constant on the order of O(1), K\na process-dependent constant on the order of 10\u221225V 2F [16], Cox the transistor gate capacitance\ndensity, and W and L the transistor width and length respectively.\nGiven a design schematic, circuit thermal noise can be reduced by increasing transconductance (gm),\nwhich is to the \ufb01rst order linear to bias current thus power consumption. Flicker noise can be reduced\nusing design techniques such as large size input transistors and chopper modulations [22]. By using\nadvanced semiconductor technologies, also, power and area trade off to noise [16], and elegant de-\nsign techniques like chopper modulation, current feedback [23], the state-of-the-art low noise neural\nampli\ufb01er can provide less than 2\u00b5V total noise [24]. Such design costs can be necessary and useful\nif electronics noise contributes signi\ufb01cantly to the total noise. Otherwise, the over-designed noise\nspeci\ufb01cation may be used to trade off other speci\ufb01cations and potentially result in overall improved\nperformance of the system. Section 5 will present experiments of evaluating noise contribution from\ndifferent sources, which show that electronics are not the dominant noise source in our experiments.\n\n2.4 Total Noise\n\nThe noise sources as shown in Figure 2 include unresolved neuron activities (Nneu), electrode-\nelectrolyte interface noise (Ne.e), thermal noise from the electrolyte bulk (Ne.b) and active circuitry\n(Nc.thermal), and \ufb02icker noise (Nc.f licker). The noise spectrum is empirically \ufb01tted by\n\nN(f) = Nneu + Ne.e + Ne.b + Nc.thermal + Nc.f licker \u2248 N1\n\nf x + N0,\n\n(8)\n\nwhere N1/f x and N0 represent the frequency dependent and \ufb02at terms, respectively. Equation 8\ndescribes a combination of both colored noise (1/f x) and broad band noise, which can be reduced\nby using noise removal techniques. Section 3 presents an adaptive \ufb01ltering scheme used to optimally\nattenuate the broad band noise. Section 4 presents a noise shaping technique used to improve the\ndifferentiation between signals and noise within the passband.\n\n3 Adaptive Bandpass Filtering\n\nSNR is calculated by integrating both signal and noise spectrum. Intuitively, a passband, either too\nnarrow or wide, introduces signal distortion or unwanted noise. Figure 5(b) plots the detected spikes\nfrom one single electrode with different widths and shows the dif\ufb01culty of optimally sizing the\npassband. While a passband that only \ufb01ts one spike template may introduce waveform distortion to\nspikes of other templates, a passband that covers every template will introduce more noise to spikes\nof every template. A possible solution is to adaptively assign a passband to each spike waveform\nsuch that each span will be just wide enough to cover the underlying waveform. This section presents\nthe steps used in order to achieve this solution and includes spike detection, spectrum estimation,\nand \ufb01lter generation.\n\n3.1 Spike Detection\n\nIn this work, spike detection is performed using a nonlinear energy operator (NEO) [25] that captures\ninstantaneous high frequency and high magnitude activities. With a discrete time signal xi, i =\n...1, 2, 3..., NEO outputs\n\n(9)\n\n\u03c8(xi) = x2\n\ni \u2212 xi+1xi\u22121.\n(cid:90)\n\nThe usefulness of NEO for spike detection can be explored by taking the expectation of Eq. 9\n\nP (f, i)(1 \u2212 cos4\u03c0f (cid:52) T )df,\n\n\u03c8(xi) = Rx(0) \u2212 Rx(2 (cid:52) T ) \u2248\n\n(10)\nwhere Rx is the auto correlation function, (cid:52)T is the sampling interval, and P (f, i) is the estimated\npower spectrum density with window centered at sample xi. When the frequency of interest is much\nlower than the sampling frequency, 1 \u2212 cos2\u03c0f \u03c4 is approximately 2\u03c02f 2\u03c4 2. This emphasizes the\nhigh frequency power spectrum. Because spikes are high frequency activities by de\ufb01nition, NEO\noutputs a larger score when spikes are present. An example of NEO based spike detection is shown\nin Figure 4, where NEO improves the separation between spikes and the background activity.\n\n4\n\n\f(a)\n\n(b)\n\nFigure 3: Spike sequence and its corresponding NEO output. (a) Raw sequence of one channel. (b)\nThe corresponding NEO output of the raw sequence in (a).\n\n3.2 Corner Frequency Estimation\n\nSpectrum estimation of individual spikes is performed to select a corresponding bandpass \ufb01lter that\nbalances the spectrum distortion and noise. Knowing its ability to separate bandlimited signals from\nbroad band noise, a Weiner \ufb01lter [26] is used here to size the signal passband. In the frequency\ndomain, denoting PXX and PN N as the signal and noise spectra, Weiner \ufb01lter is\n\nW (f) =\n\nPXX(f)\n\nPXX(f) + PN N (f)\n\n= SN R(f)\n\nSN R(f) + 1 .\n\n(11)\n\nImplementing a precise Weiner \ufb01lter for each detected spike requires considerable computation, as\nwell as a reliable estimation of the signal spectrum. In this work, we are interested in using one of a\nseries of prepared bandpass \ufb01lters Hi (i = 1, 2...n) that better matches the solved \u201coptimal\u201d Weiner\n\ufb01lter\n\n(cid:90)\n\n|Hi(f) \u2212 W (f)|2df,\n\n(12)\n\n(cid:82)\n\narg min\n\n[Hi(f) \u2212 W (f)]df = 0.\n\ni\n\nsubjected to\n\n4 Noise Shaping\n\nThe adaptive scheme presented in Section 3 tacitly assigns a matched frequency mask to individual\nspikes and balances noise and spectrum integrity. The remaining noise exhibits 1/f x frequency\ndependency according to Section 2. In this section, we focus on noise shaping techniques to further\ndistinguish signal from noise.\nThe fundamentals of noise shaping are straightforward. Instead of equally amplifying the spectrum,\na noise shaping \ufb01lter allocates more weight to high SNR regions while reducing weight at low SNR\nregions. This results in an increased ratio of the integrated signal power over the noise power. In\ngeneral, there are a variety of noise shaping \ufb01lters that can improve the integrated SNR [10]. In this\nwork, we use a series of fractional derivative operation for noise shaping\n\nD(h(x)) = dph(x)\ndxp\n\n,\n\n(13)\n\nwhere h(x) is a general function, p is a positive number (can be integer or non-integer) that adjusts\nthe degree of noise shaping; the larger the p, the more emphasis on high frequency spectrum. In Z\ndomain, the realization of fractional derivative operation can be done using binomial series [27]\nH(z) = (1 \u2212 z\u22121)p =\n\n(\u22121)n p(p \u2212 1)...(p \u2212 n + 1)\n\nh(n)z\u2212k = 1 \u2212 pz\u22121 +\n\nz\u2212n,\n\n(14)\n\n\u221e(cid:88)\n\n\u221e(cid:88)\n\nn=0\n\nn=2\n\nwhere h(n) are the fractional derivative \ufb01lter coef\ufb01cients that converge to zero.\nThe SNR gain in applying a fractional derivative \ufb01lter H(f) is\n\nSN Rgain = 10log\n\nIspike(f)|H(f)|2df\nInoise(f)|H(f)|2df\n\n\u2212 10log\n\nIspike(f)df\nInoise(f)df\n\n,\n\n(15)\n\nn!\n\n(cid:82)\n(cid:82)\n\n(cid:82)\n(cid:82)\n\n5\n\n051015x 105\u22121.5\u22121\u22120.500.511.522.5x 104051015x 105\u22122\u2212101234x 107\f(a)\n\n(c)\n\n(b)\n\n(d)\n\nFigure 4: In vivo recording for identifying noise sources. (a) 5-minute recording segment capturing\nthe decay of background activities. (b) Traces of the estimated noise vs. time are plotted. Black (cid:165)\ncurve represents the noise recorded from a custom tungsten electrode; red (cid:78) curve represents the\nnoise recorded from a CNT coated electrodes with the same size. (c), (d) Noise power spectrums es-\ntimated at the 0, 15, 30, 45 minutes after the drug injection. In (c) a conventional tungsten electrode\nis used. In (d), a CNT coated tungsten electrode of equal size is used for comparison.\n\nwhere Ispike(f) and Inoise(f) are power spectrums of spike and noise respectively. Numeric values\nof SNR gain depend on both data and p (the degree of noise shaping).\nIn our experiments, we\nempirically choose p in a range of 0.5 to 2.5, where numerically calculated SNR gains using Eq. 15\nof in vivo recordings are typically more than 3dB, which is consistent with [10].\n\n5 Experiment\n\nTo verify the noise analysis presented in Section 2, an in vivo experiment is performed that uses two\nsharp tungsten electrodes separated by 125 \u00b5m to record the hippocampus neuronal activities of a\nrat. One of the electrodes is coated with carbon-nanotube (CNT), while the other is uncoated. After\nthe electrodes have been placed, a euthanizing drug is injected. After 5 seconds of drug injection,\nthe recording of the two electrodes start and last until to the time of death. The noise analysis\nresults are summarized and presented in Figure 4. In Figure 4(a), a 5-minute segment that captures\nthe decaying of background activities is plotted. In Figure 4(b), the estimated noise from 600Hz to\n6KHz for both recording sites are plotted, where noise dramatically reduces (> 80%) after the drug\ntakes effect. Initially, the CNT electrode records a comparatively larger noise (697\u00b5V 2) compared\nwith the uncoated electrode (610\u00b5V 2). After a few minutes, the background noise recorded by\nthe CNT electrode quickly reduces eventually reaching 37\u00b5V 2 that is about 1/3 of noise recorded\nby its counterpart (112\u00b5V 2), suggesting the noise \ufb02oor of using the uncoated tungsten electrode\n(112\u00b5V 2) is set by the electrode. From these two plots, we can estimate that the neuron noise is\naround 500 \u223c 600\u00b5V 2, electrode interface noise is \u223c 80\u00b5V , while the sum of electronic noise\nand electrolyte bulk noise is less than 37\u00b5V 2 (only \u223c 5% of the total noise). Figure 4(c) displays\nthe 1/f x noise spectrum recorded from the uncoated tungsten electrode (x = 1.8, 1.4, 1.0, 0.9,\nestimated at 0, 15, 30, 45 minutes after drug injection). Figure 4(d) displays 1/f x noise spectrum\nrecorded from the CNT coated electrode (x = 2.1, 1.3, 0.9, 0.8, estimated at 0, 15, 30, 45 minutes\nafter drug injection).\n\n6\n\n012345\u22122.5\u22121.2501.252.5Time, unit minuteRecording, unit mV0102030405060101102103Time, unit minuteNoise power, unit (uV)2 Noise measured using conventinal electrodeNoise measured using CNT coated electrode11.522.533.544.555.56\u221250510152025Frequency (kHz)Power/frequency (dB/Hz) 0 minute15 minute30 minute45 minute11.522.533.544.555.56\u221250510152025Frequency (kHz)Power/frequency (dB/Hz) 0 minute15 minute30 minute45 minute\fTable 1: Statistics of 1/f x noise spectrum from in vivo preparations.\nx \u2265 2\n11\n\nNumber of Recordings\n\n1.5 \u2264 x < 2\n\nx < 1\n\n5\n\n1/f x\n\n1 \u2264 x < 1.5\n\n38\n\n23\n\n(a)\n\n(b)\n\n(c)\n\n(d)\n\nFigure 5: In vivo experiment of evaluating the proposed adaptive bandpass \ufb01lter.\n(a) Detected\nspikes are aligned and superimposed. (b) Example waveforms that have distinguished widths are\nplotted. (c) Feature extraction results using PCA with a global bandpass \ufb01lter (400Hz to 5KHz)\nare displayed. (d) Feature extraction results using PCA with adaptive bandpass \ufb01lters are displayed\nshowing a much improved cluster isolation compared to (c).\n\nIn the second experiment, 77 recordings of in vivo preparations are used to explore the stochas-\ntic distribution of 1/f x noise spectrum. \u201cx\u201d is averaged at 1.5 with a standard deviation of 0.5\n(1/f 1.5\u00b10.5). The results are summarized in Table 1.\nThe third experiment uses an in vivo recording from a behaving cat. This recording is used to\ncompare the feature extraction results produced by a global bandpass \ufb01lter (conventional one) and\nthe proposed adaptive bandpass \ufb01lter, discussed in Section 3. In Figure 5(a), detected spikes are\nsuperimposed, where \u201ca thick waveform bundle\u201d is observed. In Figure 5(b), example waveforms\nin Figure 5(a) that have different widths are shown. Clearly, these waveforms have noticeably dif-\nferent spectrum spans. In Figure 5(c), feature extraction results using PCA (a widely used feature\nextraction algorithm in spike sorting applications) with a global bandpass \ufb01lter are displayed. As\na comparison, feature extraction results using PCA with adaptive bandpass \ufb01lters are displayed in\nFigure 5(d), where multiple clusters are differentiable in the feature space.\nIn the fourth experiment, earth mover\u2019s distance (EMD), as a cross-bin similarity measure that is\nrobust to waveform misalignment [28], is applied to synthesized data for evaluation of the spike\nwaveform separation before and after noise shaping. Assume VA(i), i = 1, 2..., VB(i), i = 1, 2...\nto be the spike waveform bundles from candidate neuron A and B. To estimate the spike variation\nof a candidate neuron, two waveforms are randomly picked from a same waveform bundle, and\nthe distance between them is calculated using EMD. After repeating the procedure many times,\nthe results are plotted as the black (waveforms from VA) and blue (waveforms from VA) traces in\nFigure 6. The x-axis indexes the trial and the y-axis is the EMD score. Black/blue traces describe\nthe intra-cluster waveform variations of the two neurons under testing. To estimate the separation\nbetween candidate neuron A and B, we randomly pick two waveforms, one from VA and the other\nfrom VB, then compute the EMD between them. This procedure is repeated many times and the\nEMD vs.\ntrial index is plotted as the red curve in Figure 6. Four pairs of candidate neurons are\ntested and shown in Figure 6(a)-(d). It can be observed from Figure 6 that the red curves are not well\ndifferentiated from the black/blue ones, which indicate that candidate neurons are not well separated.\nIn Figure 6(e)-(h), we apply a similar procedure on the same four pairs of candidate neurons. The\nonly difference from plots shown in Figure 6(a)-(d) is that the waveforms after noise shaping are\nused rather than their original counterparts. In Figure 6(e)-(h), the red curves separate from the\nblack/blue traces, suggesting that the noise shaping \ufb01lter improves waveform differentiations.\nIn the \ufb01fth experiment, we apply different orders of noise shaping \ufb01lters and the same feature extrac-\ntion algorithm to evaluate the feature extraction results. The noise shaping technique is developed\nas a general tool that can be incorporated into an unspeci\ufb01ed feature extraction algorithm. Here, we\nuse PCA as an example. In Figure 7, 8 \ufb01gures in the same row are results of the same sequence.\nFigures from left to right display the feature extraction results with different orders of noise shaping;\nfrom 0 (no noise shaping) to 3.5, and stepped by 0.5. All the tests are obtained after adaptive band-\n\n7\n\n0510152025303540\u22120.1\u22120.0500.050.10.150.20.250510152025303540\u22120.1\u22120.0500.050.10.150.20.25\u22120.6\u22120.5\u22120.4\u22120.3\u22120.2\u22120.100.10.20.3\u22120.25\u22120.2\u22120.15\u22120.1\u22120.0500.050.10.150.20.25\u22120.5\u22120.4\u22120.3\u22120.2\u22120.100.10.2\u22120.35\u22120.3\u22120.25\u22120.2\u22120.15\u22120.1\u22120.0500.050.10.15\f(a)\n\n(e)\n\n(b)\n\n(f)\n\n(c)\n\n(g)\n\n(d)\n\n(h)\n\nFigure 6: EMD vs. trial index. Black and blue trace: EMDs for intra-cluster waveforms; red trace:\nEMDs for inter-cluster waveforms. (a)-(d) and (e)-(h) are results of 4 different pairs of neurons\nbefore and after noise shaping respectively. Traces in (a)-(d) and (e)-(h) have one-to-one correspon-\ndence. Noise level increases from (a) to (d).\n\n(a)\n\n(b)\n\n(c)\n\n(d)\n\n(e)\n\n(f)\n\n(g)\n\n(h)\n\n(i)\n\n(j)\n\n(k)\n\n(l)\n\n(m)\n\n(n)\n\n(o)\n\n(p)\n\nFigure 7: Feature extraction results using PCA with different orders of noise shaping. Each row\nrepresents a different sequence. Each column represents a different order of noise shaping (p in\ndpf (x)\ndxp ), sweeping from 0 (without noise shaping) to 3.5 , stepped by 0.5. (a)-(h) are results of a\nsynthesized sequence. (i)-(p) are results of an in vivo preparation. Clearly, (f) is better than (a); (m)\nis better than (i).\n\npass \ufb01ltering. The \ufb01rst sequence (a)-(h) is a synthesized one from public data base [2], the second\nsequence is recorded from an in vivo preparation. For both sequences, increased numbers of isolated\nclusters can be obtained by appropriately choosing the order of the noise shaping \ufb01lter.\n\n6 Conclusion\n\nIn this paper, a study of multiple noise sources for in vivo neural recording is carried out. The\ndominant noise source is identi\ufb01ed to be neuron noise followed by interface noise of the electrode.\nOverall, the noise exhibits a family of 1/f x spectrum. The concept of adaptive bandpass \ufb01lter is pro-\nposed to reduce noise because it maintains the signal spectrum integrity while maximally reducing\nthe broad band noise. To reduce the noise within the signal passband and improve waveform sepa-\nration, a series of fractional order differentiator based noise shaping \ufb01lters are proposed. The pro-\nposed noise removal techniques are generally applicable to an unspeci\ufb01ed spike sorting algorithm.\nExperiment results from in vivo preparations, synthesized sequences, and comparative recordings\nusing both conventional and CNT coated electrodes are reported, which verify the noise model and\ndemonstrate the usefulness of the proposed noise removal techniques.\n\n8\n\n050100150200250300051015202530 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance050100150200250300024681012141618 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance0501001502002503000246810121416 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance050100150200250300024681012 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance050100150200250300012345678910 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance050100150200250300012345678910 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance0501001502002503000123456 IntraCluster1 Distance IntraCluster2 DistanceInterClster1to2 Distance0501001502002503000123456 IntraCluster1 DistanceIntraCluster2 DistanceInterCluster1to2 Distance00.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.9100.20.40.60.8100.10.20.30.40.50.60.70.80.91\fReferences\n[1] Lewicki MS. A review of methods for spike sorting: the detection and classi\ufb01cation of neural action\n\npotentials. Network Comput Neural Syst. 1998;9:53\u201378.\n\n[2] Quian Quiroga R, Nadasdy Z, Ben-Shaul Y. Unsupervised spike detection and sorting with wavelets and\n\nsuperparamagnetic clustering. Neural Computation. 2004 Aug;16(8):1661\u20131687.\n\n[3] Bar-Hillel A, Spiro A, Stark E. Spike sorting: Bayesian clustering of non-stationary data. Advances in\n\nNeural Information Processing Systems 17. 2005;p. 105\u2013112.\n\n[4] Zumsteg ZS, Kemere C, O\u2019Driscoll S, Santhanam G, Ahmed RE, Shenoy KV, et al. Power feasibility of\nimplantable digital spike sorting circuits for neural prosthetic systems. IEEE Trans Neural Syst Rehabil\nEng. 2005 Sep;13(3):272\u2013279.\n\n[5] Vargas-Irwin C, Donoghue JP. Automated spike sorting using density grid contour clustering and sub-\n\ntractive waveform decomposition. J Neurosci Methods. 2007;164(1).\n\n[6] Yang Z, Zhao Q, Liu W. Neural signal classi\ufb01cation using a simpli\ufb01ed feature set with nonparametric\n\nclustering. Neurocomputing, doi:101016/jneucom200907013, in press;.\n\n[7] Gasthaus J, Wood F, Dilan G, Teh YW. Dependent dirichlet process spike sorting. Advances in Neural\n\nInformation Processing Systems 21. 2009;p. 497\u2013504.\n\n[8] Smith LS, Mtetwa N. A tool for synthesizing spike trains with realistic interference. J Neurosci Methods.\n\n2007 Jan;159(1):170\u2013180.\n\n[9] Harris KD, Henze DA, Csicsvari J, Hirase H, Buzsaki G. Accuracy of tetrode spike separation as deter-\nmined by simultaneous intracellular and extracellular measurements. J Neurophysiol. 2000;84:401\u2013414.\n[10] Yang Z, Zhao Q, Liu W. Spike feature extraction using informative samples. Advances in Neural Infor-\n\nmation Processing Systems 21. 2009;p. 1865\u20131872.\n\n[11] Yang Z, Zhao Q, Liu W. Improving Spike Separation Using Waveform Derivative. Journal of Neural\n\nEngineering, doi: 101088/1741-2560/6/4/046006. 2009 Aug;6(4).\n\n[12] Davidsen J, Schuster HZ. Simple model for 1/f \u03b1 noise. Phys Rev Lett 65, 026120(1)-026120(4). 2002;.\n[13] Yu Y, Romero R, Lee TS. Preference of sensory neural coding for 1/f signals. Phys Rev Lett 94,\n\n108103(1)-108103(4). 2005;.\n\n[14] Bedard C, Kroger H, Destexhe A. Does the 1/f frequency scaling of brain re\ufb02ect self-organized critical\n\nstates? Phys Rev Lett 97, 118102(1)-118102(4). 2006;.\n\n[15] Hassibi A, Navid R, Dutton RW, Lee TH. Comprehensive study of noise processes in electrode electrolyte\n\ninterfaces. J Appl Phys. 2004 July;96(2):1074\u20131082.\n\n[16] Razavi B. Design of Analog CMOS Integrated Circuits. Boston, MA:McGraw-Hill; 2001.\n[17] Keener J, Sneyd J. Mathematical Physiology. New York: Springer Verlag; 1998.\n[18] Manwani A, N Steinmetz P, Koch C. Channel noise in excitable neural membranes. Advances in Neural\n\nInformation Processing Systems 12. 2000;p. 142\u2013149.\n\n[19] Fall C, Marland E, Wagner J, Tyson J. Computational Cell Biology. New York: Springer Verlag; 2002.\n[20] Keefer EW, Botterman BR, Romero MI, Rossi AF, Gross GW. Carbon nanotube-coated electrodes im-\n\nprove brain readouts. Nat Nanotech. 2008;3:434\u2013439.\n\n[21] Wiley JD, Webster JG. Analysis and control of the current distribution under circular dispersive. IEEE\n\nTrans Biomed Eng. 1982;29:381\u2013385.\n\n\u221a\n\n[22] Denison T, Consoer K, Kelly A, Hachenburg A, Santa W. A 2.2\u00b5W 94nV /\n\nHz, chopper-stabilized\ninstrumentation ampli\ufb01er for EEG detection in chronic implants. IEEE ISSCC Dig Tech Papers. 2007\nFeb;8(6).\n\n[23] Ferrari G, Gozzini F, Sampietro M. A current-sensitive front-end ampli\ufb01er for nano biosensors with a\n\n2MHz BW. IEEE ISSCC Dig Tech Papers. 2007 Feb;8(7).\n\n[24] Harrison RR. The design of integrated circuits to observe brain activity. Proc IEEE. 2008 July;96:1203\u2013\n\n1216.\n\n[25] Kaiser JF. On a simple algorithm to calculate the energy of a signal. In Proc IEEE Int Conf Acoustic\n\nSpeech and Signal Processing. 1990;p. 381\u2013384.\n\n[26] Vaseghi SV. Advanced Digital Signal Processing and Noise Reduction. Wiley-Teubner; 1996.\n[27] Hosking J. Fractional differencing. Biometrika. 1981 Jan;68:165\u2013176.\n[28] Rubner Y. Perceptual metrics for image database navigation. In: Ph.D. dissertation, Stanford University;\n\n1999. .\n\n9\n\n\f", "award": [], "sourceid": 25, "authors": [{"given_name": "Zhi", "family_name": "Yang", "institution": null}, {"given_name": "Qi", "family_name": "Zhao", "institution": null}, {"given_name": "Edward", "family_name": "Keefer", "institution": null}, {"given_name": "Wentai", "family_name": "Liu", "institution": null}]}