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Journal of Neuroscience Methods 196 (2011) 318–326

Contents lists available at ScienceDirect

Journal of Neuroscience Methods

journa l homepage: www.e lsev ier .com/ locate / jneumeth

pike removal through multiscale wavelet and entropy analysis of ocular motoroise: A case study in patients with cerebellar disease

iacomo Veneria,b,c,∗, Pamela Federighia,b, Francesca Rosinib, Antonio Federicob, Alessandra Rufaa,b,∗∗

Eye tracking & Vision Applications Lab - University of Siena, ItalyDepartment of Neurological Neurosurgical and Behavioral Science - University of Siena, ItalyEtruria innovazione Spa, Italy

r t i c l e i n f o

rticle history:eceived 20 September 2010eceived in revised form 2 January 2011ccepted 4 January 2011

a b s t r a c t

Wavelet decomposition of ocular motor signals was investigated with a view to its use for noise analysisand filtering. Ocular motor noise may be physiological, depending on brain activities, or experimen-tal, depending on the eye recording machine, head movements and blinks. Experimental noise, such asspikes, must be removed, preserving noise due to neuro-physiological activities. The proposed method

eywords:ye-trackingpikeavelet

uses wavelet multiscale decomposition to remove spikes and optimizes the procedure by means of thecovariance of the eye signals. To measure the noise on eye motor control, we used the wavelet entropy.The method was tested on patients with cerebellar disorders and healthy subjects. A significant differ-ence in wavelet entropy was observed, indicating this quantity as a valuable measure of physiologicalmotor noise.

ntropy

espikingerebellum

. Introduction

Eye movements are arguably the most frequent of all humanovements and an essential part of human vision (Yarbus, 1967):

hey drive the fovea and consequently the attention towardsegions of interest in space. This enables the visual system to fixatend to process an image or its details with high resolution (Leighnd Zee, 2006): act of fixation. Fixations are samples of pointsround a point, called centroid, with long duration. An averagef three eye fixations per second generally occurs during activeooking (300 ms).

These eye fixations are intercalated by rapid eye jumps, calledaccades, that can be defined as rapid movements with velocities

hat may be higher than 500 deg/s and durations of about 30 ms;ig. 1 illustrates a small portion of gaze during visual explorationn a psychological task, showing five clusters of data points (fix-tions) and three saccades. Eye movements may be recorded by

∗ Corresponding author at: Department of Neurological, Neurosurgical andehavioral Science - University of Siena, Viale Bracci 2, 53100 Siena, Italy.el.: +39 0577 233136; fax: +39 0577 40327.∗∗ Corresponding author at: Department of Neurological, Neurosurgical andehavioral Science - University of Siena, Viale Bracci 2, 53100 Siena, Italy.el.: +39 0577 233136; fax: +39 0577 40327.

E-mail addresses: g.veneri@unisi.it (G. Veneri), federighi@unisi.it (P. Federighi),osini3@student.unisi.it (F. Rosini), federico@unisi.it (A. Federico), rufa@unisi.itA. Rufa).

URL: http://www.evalab.unisi.it (A. Rufa).

165-0270/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2011.01.006

© 2011 Elsevier B.V. All rights reserved.

eye-tracking technologies (see Duchowski, 2002 for a review). Eye-tracking is the process by which eye movements are measuredduring visual exploration of a scene or during the execution of spe-cific tasks. This measurement, can be obtained either by measuringthe position of an eye in the orbit, relative to the head, or the pointof regard, which extracts the coordinates x, y of the eye in space.

Eye gaze analysis and extraction of gaze features is an excitingand challenging field of research for neuro physiologists and neuroscientists, since it offers a good, reproducible method for studyingbasic mechanisms of brain motor control (from motor commandto reached position, see Girard and Berthoz, 2005 for a review) andcognitive behavior. Indeed, the human gaze is direct or indirect evi-dence of human cognition in terms of memory, attention (Corbettaet al., 2002), intention and decision (Shimojo et al., 2003).

Generally speaking, the gaze signal is processed by extractingtwo main classes of features: motor abilities (Table 1 for a shortsummary of the subsystems involved and related features) whichstudies the ocular motor control, and task specific execution, whichprovide insights into ocular motor control, and task specific exe-cution, which provides information about the ability of subjects toperform a command, such as searching for an object, remembering,forming a sequence, making up the mind.

1.1. Eye movements in clinical applications: measuring thephysiological characteristics of motor control noise

The main advances in the study of ocular motor control havebeen obtained by lesion studies in monkeys and recording patients

G. Veneri et al. / Journal of Neuroscienc

Fig. 1. A small portion (1500 ms) of the gaze of a patient with cerebellar disorder ona visual search task: the highlighted fixations are ordered in the time domain, fromfiitt

wwlt2ateipgi(t

mbtdaBKc

TCpca

rst to last. The main clinical features of cerebellar disorders include incoordination,mbalance, and troubles with stabilizing eye movements. In the simplified form ofhe test, subjects are asked to look for a right oriented “E”. The image appeared onhe screen for 20000 ms.

ith selective brain lesions or homogeneous groups of patientsith genetic neuro-degenerative diseases. Recently, however, ocu-

ar motor control has also attracted attention for studying complexasks, such as recognition of facial expression (Xu-Wilson et al.,009) and gaze contingent applications (Veneri et al., 2010a). Someuthors found that humans can adapt ocular motor characteris-ics (velocity, latency) according to the behavior in order to reducenergy consumption or improve efficiency; the hypothesis was ver-fied by van Beers (2008), through resolution of an optimal controlroblem of modulating saccade velocity to minimize variance ofaze during saccades and fixations. The problem can be explainedntuitively as the human ability to reduce energy consumptiongaze variability) in order to improve efficiency (precision on thearget) (van Beers, 2009).

In the clinical context, one of the most interesting analyses ofotor control was applied to patients with disorders of the cere-

ellum, especially patients with spinocerebellar cerebellar ataxiaype 2 (SCA2), a rare disease. SCA2 is one of a group of genetic

isorders characterized by slowly progressive impairment of thebility to control eye movements (slow saccades) (Filla et al., 1996;ürk et al., 1999; Ramat et al., 2007). In this respect, Leigh andennard (2004) proposed using saccades as a research tool in thelinical neuro-sciences and the main sequence (a set of relation-

able 1ommon eye movement features studied: saccade velocity is typically analyzed inatients with cerebellar or brainstem lesions. Saccadic trajectories and microsac-ades are studied in attention and voluntary–involuntary tasks. Fixations and ROIre studied in free visual search tasks.

Subsystem Computation

Gaze shiftSaccades Distance of target from fovea der Stigchel et al., 2006 (deg),

Velocity Leigh and Zee, 2006 (deg/s), Duration (ms),Latency after target appearance Rayner et al., 1983 (ms)

Pursuit Target velocity (deg/s)Vergence Target depth (cm)

Gaze holdingFixations Visual scanning region of interest (ROI), Distance to

nearest ROI (deg), Time spent in ROI (ms), Tremor (deg2),Drifts (deg), Microsaccades Engbert and Kliegl, 2003

Vestibular Rotation, translation of head or body (deg)Optokinetic Speed direction of full-field image motion (deg/s)

e Methods 196 (2011) 318–326 319

ships between saccade amplitude and peak velocity; Bollen et al.,1993) as a valid tool to classify the subject. These results indicatedthe need to investigate a measure of “physiological characteristics ofgaze noise” (PN), such as tremor, square jerks (Leigh and Zee, 2006),nystagmus (Abel et al., 2008) and drift. According to van Beers(2007) PN may be additive with or multiplicative of the eye move-ment, and is lost in recording noise (RN) due to blinks or signal loss;generally speaking, we can measure subject noise = PN + RN = SDN(signal) + ADN + RN where SDN is physiological signal dependentnoise and ADN physiological additive noise.

A natural approach to quantify the degree of order of gaze sig-nals is to consider their spectral features and spectral entropy.Inouye et al. (1993) were the first to apply spectral analysis bya Fourier analysis to the study of brain signals. Recently, someauthors (Quiroga et al., 2001; Kamavuako et al., 2009) proposedthe application of multiresolution wavelet decomposition (Mallat,1989) to overcome the limitations of the Fourier transform andto study the ocular motor abilities in infantile syndromes (Abelet al., 2008). The wavelet method arranges successive wavelettransforms in a hierarchical scheme, enabling the decompositionof the signal. In the present study, we describe a method to esti-mate PN by wavelet entropy and to remove RN by multi-scalewavelet transform (MWT). In particular, we propose a method toremove signal artefacts such as spikes. Spikes are unwanted anduninteresting rapid signal artifacts (Juhola et al., 1987) that maydeceive pattern recognition algorithms and be confused with sac-cades (Fig. 3; see Fischer and Biscaldi, 1993 for the most commonalgorithm of saccades), or induce the fixation search algorithmto over-segmentate (Salvucci and Goldberg, 2000; Veneri et al.,2010b). Techniques based on linear or adaptive filters, or spectrumanalysis may affect the morphological characteristics of gaze noise.It is therefore necessary to use advanced techniques to recognisespikes and to suppress them (despiking), preserving the naturalcharacteristics of ocular noise. We used MWT and covariance todecompose the signal and remove spikes. Implementation of thealgorithm is described in Section 3.2.

After despiking, motor control noise was measured by waveletentropy (WS; Coifman and Wickerhauser, 1992): in the timedomain, entropy is a measure of signal uncertainty and in the spec-tral domain it is a measure of signal complexity. High entropyis associated with signals generated by disordered, random pro-cesses, and low entropy with ordered or partially ordered processes(Zunino et al., 2007). If a process is noisy, its signal wavelet decom-position can be expected to contribute significantly to total waveletenergy in all frequency bands. This makes WS a good candidate offor estimating PN.

We evaluated the method performance in a computer-generated simulation (Section 5.1), and in a small group of SCA2patients and a mixed group of patients with genetically undefinedcerebellar ataxia (NDC) (Section 5.2). The results provided evidencethat the proposed technique can discriminate healthy subjects frompatients.

2. Materials and methods

Eight SCA2 patients, a mixed group of three patients with unde-fined genetic cerebellar ataxia (NDC) and 25 healthy subjects wereenrolled in the study. All were in the age range 25–45 years.Subjects were seated at viewing distance of 78 cm from a 32 in.color monitor (51 cm×31 cm). Eye position was recorded using

an ASL 6000 system, which consists of a remote-mounted cam-era sampling pupil location at 240 Hz. A 9-point calibration and3-point validation procedure was repeated several times to ensureall recordings had a mean spatial error of less than 0.3 deg. Datawas controlled by a Pentium4 dual core 3 GHz computer, which

320 G. Veneri et al. / Journal of Neuroscience Methods 196 (2011) 318–326

Table 2Subjects were seated at viewing distance of 78 cm from a 32 in. color monitor (51 cm×31 cm).

Subjects Type Problem on motor control Taking medicine

GFOD Degenerative cerebellar ataxia Yes and documented YesMS Degenerative cerebellar ataxia Yes and documented YesCN Degenerative cerebellar ataxia Yes and documented YesPP Normal No No

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Then, by correlating the original signal with wavelet functionsat a discrete size and level a, b we obtain details dj of the signalat several scales. This procedure can be organized in a hierarchicalway called multiresolution or multilevel wavelet decomposition

0 0.5 1 1.5−2

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0

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0

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0 1 2 3−2

0

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0.51

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01

bior1.1 reconstruction

GV NormalEU NormalXM NormalSL Normal

cquired signals through a fast UART serial port. Head movementsere restricted using chin rest and bite. The subject was asked

o fixate a central red dot; after 500 ms the dot disappeared andhe subject could explore the scene, which consisted of simplertificial images (Fig. 1). The fixations were identified by the FDTlgorithm developed by Veneri et al. (2010b) and checked manuallynd updated by an expert.

In order to test the despiking algorithm, we selected threeatients and five normal subjects (Table 2).

.1. Computer-generated signal

Computer-generated time series were produced by remov-ng high level frequencies by window-average filter (window = 10amples) from 20 randomly selected signals of healthy sub-ects and adding white noise having a signal-to-noise ratioNR = 20 log 10(Asignal/Anoise)∈ (20 dB, 40 dB); we call this signal. Then, from one to ten spikes were added to the signal � in

andom positions; we call this signal � s. The spikes had a dura-ion of 80 ms (∼=20 samples) and amplitude A+spike ∈ (0, 600 px),−spike ∈ (−600 px,0). Eq. (1) is the formula for spikes:

(t) ={

A+spiketriang(t, t0, t1) ∀t ∈ (t0, t1)

A−spiketriang(t, t1, t2) ∀t ∈ (t1, t2)(1)

here triang is the triangular function. After despiking (� ds) wealculated the ratio of removed spikes to spikes added to the signaly Eq. (2). We evaluated Eq. (2) for all t (˘) and for all t in spikes˘spike).

=

∑t

(� s(t))2 −� (t)

(� ds(t)−� (t))2· 100% (2)

q. (2) is the ratio of “spikes removed” to “spikes added” expresseds a percentage.

.2. Analyzing differences between groups

The ˘ was used to build two small groups of 10×2 computer-enerated time series with SNRg1 = 1.1 · SNRg2. We applied thearametric Holm–Sidak procedure, and we evaluated the F func-ion (variance between items/variance within items) to compareatients and subjects and to evaluate the application of WS.

. Theory

Fourier analysis is a popular technique for processing signalontent. It has the disadvantage of losing time information after

ransforming a signal into the frequency domain. To obviate thisifficulty, the windowed Fourier transform (WFT) can be used: aruncate window, the sine and cosine functions of which fit a win-ow of a given width. However, a unique window is used for allrequencies in the WFT. The resolution of the analysis is the same

No NoNo NoNo NoNo No

over the whole domain and is limited by the size of the window. Inwavelet analysis, the window size can be varied.

3.1. Wavelet

The wavelet transform (WT) is a time–frequency representationof the signal that has two main advantages over conventional meth-ods: it provides an optimal resolution in the time and frequencydomains, and it eliminates the requirement of signal stationarity(Mallat and Hwang, 1992). It is defined as the convolution of thesignal x(t) and the wavelet functions �a,b:∫�

x(t) �a,b(t) dt (3)

where �a,b(t) is the scaled and translated mother wavelet � givenby Eq. (4):

�a,b(t) = 1√a

�(

t − b

a

)a, b∈� (4)

where a and b are the scale and translation parameters, respec-tively. The mother wavelet � is a function of finite energy and zeroenergy (Eq. (5)): see Fig. 2 for a short summary of mother wavelet:∫�

�(t) dt = 0 (5)

Therefore, the WT is usually defined at discrete scales a anddiscrete times b by choosing the set of parameters:

a = 2−j; b = k2−j j, k∈ℵ (6)

0 0.5 1−0.5

0

0 0.5 1−2−1

Fig. 2. Wavelets of five different wavelet families. Other families: Morlet, Mexicanhat and Meyer.

scienc

(stpadtfcr

3

bm(D(t(

d

T

t

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3

E

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E

a

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to the optimum level until the information removed is no longer

G. Veneri et al. / Journal of Neuro

MWT; Mallat, 1989). The multilevel decomposition separates theignal into details at different scales and a coarser representation ofhe signal named “approximation”. The MWT at level l of decom-osition extracts the coefficients {d1, . . ., dl+1}, where dl+1 is thepproximated coefficients and represents overall signal trend, andj is the detailed coefficient and represents the rapid variations inhe signal: d1, . . ., dl are the decompositions at various levels ofrequency, from low to high, respectively. Due to the hierarchicalharacteristic of the MWT, the approximated coefficients can beeconstructed by {dj, . . ., dl, dl+1} coefficients.

.2. Spike removal—despiking

Besides applications in these fields, the wavelet transform haseen applied to recognition of signal discontinuities. One of theost interesting applications involves its ability to recognise spikes

Nenadic and Burdick, 2005). The basic principle proposed byonoho and Johnstone (1994) is based on rejecting or accepting

if we need to identify the spike) only those wavelet coefficientshat exceed a threshold, followed by the inverse wavelet transforminverse hard thresholding).

˘j =

{dj if |dj| ≤ thj

0 otherwise(7)

he threshold is computed by Eq. (8):

hj = �j

√2 loge N (8)

here N is the number of samples and �j is the standard deviation ofoise. The standard deviation �j must be estimated from the coef-cients d1: the basic idea is to consider noise to be Gaussian, whichay not hold in general, and the detailed coefficients of the finest

cale (such as d1) are assumed to be essentially noise coefficientsith standard deviations equal to � (Ehrentreich and Sümmchen,

001; Sharma et al., 2010; Kamavuako et al., 2010). Under thesessumptions it can be shown that the median of its absolute devi-tion �j = median( | d1 |)/0.6745 effectively estimates the standardeviation. It is easy to prove that for a zero mean Gaussian distribu-ion the median should be≈� ·0.6745 (Nenadic and Burdick, 2005,ppendix 1).

Finally, it is important to choose a mother wavelet that is suit-ble for the signal of interest. Quiroga et al. (2004) applied a db1 oroif2 wavelet at four levels. The choice is motivated by the shape ofhe spike which should be approximated by an db1 or coif2 wavelett the high level. In the current context, it is impossible to makeny assumptions.

.3. Wavelet entropy

Given {c1,t, . . ., cl+1,t}= {d1(t), . . ., dl+1(t)} the mean energy is

l,k =

k0+�t∑t=k0

c2l,t

N(9)

here k0 = 1, 1 + �t, 1 + 2�t, . . . and N is the number of waveletoefficients in the time window.

k =∑

l

El,k (10)

nd the probability distribution for each level can be defined as

l,k =El,k

Ek(11)

e Methods 196 (2011) 318–326 321

from the definition of entropy given by Shannon (1948), the time-varying wavelet entropy (Blanco et al., 1998)

WSk = −∑

l

pl,k · log2 pl,k (12)

and the WS is the mean of Eq. (12).

4. Calculations

As shown in Ehrentreich and Sümmchen (2001) and Quirogaet al. (2004), we applied the method of Eq. (7) to gaze signals ofpatients. When we needed to eliminate spikes with high precisionto reconstruct the signal, the despiking worked well, but not aswell as we wanted; in particular, the application of Eq. (7) withMWT at a low level of decomposition affected saccades, and at ahigh level of decomposition the spikes were “spread” over moredetailed coefficients dj.

The key idea was to set the level of decomposition of MWT tothe maximum level lmax

1 admissible by the algorithm and to applyEq. (7) for j = 1, . . ., loptim and for �j = median( | dj |)/0.6745, whereloptim < lmax must be estimated.

4.1. Choosing the correct optimum level

To find the optimum level, we decomposed the signal at themaximum level in order to separate saccades and spikes as muchas possible and to find the loptim that maximized the ratio of “spikesremoved” to “signal preserved”.

An interesting characteristic of WT is the ability to maintain therelationship between signals: if a relation exists between x and y,the WT(x) has the same relation with WT(y). In eye tracking, werecorded the position of an eye along x and y. van Beers (2007)found an interesting correlation between x and y during saccades,and we confirmed this result: the local covariance between x andy was high during spike and saccade (see Fig. 3). Thanks to thephysiological characteristics of ocular motor signals, we used thevariance and specifically the covariance between x and y to defineloptim. We choose:

loptim =∀j∈ (1,lmax)

argmin(j − 1) :∥∥covw(x, y)∥∥− ∥∥covw(

�dxj,

�dyj)

∥∥ ≤ 0

∨∥∥covw(�dxj,

�dyj)

∥∥− ∥∥covw(�dxj−1,

�dyj−1)

∥∥ ≤ 0

(13)

where ||◦ | | is the median and

covw(x, y) = |diag1,2 (cov (x(t0, t1), y(t0, t1))) |

t0 = t − w

2, t1 = t + w

2(14)

and w is larger than spike or saccade duration. Since the meansaccade duration is ≈ 30 ms, w = 40 ms should be a good value.

In other words, despiking by Eq. (7) was stopped when themedian of covariance of detailed coefficients d̆x, d̆y was more thanthe median covariance of the signal or less than the covarianceof d̆x, d̆y at j−1. Algorithm A.1 describes the implemented pro-cedure. Intuitively, the algorithm proceeds to despike from level 1

significant (condition 1) or there is no meaningful information tobe removed (condition 2).

1 See function wmaxlev of Mathworks (2007).

322 G. Veneri et al. / Journal of Neuroscienc

Fig. 3. (a) Signal of patient CN (samples 1500–3000). A spike is a rapid change onthe signal that can be confused with a saccade, which represents eye movements.(b) Covariance x, y of signal of patient CN. (c) Spikes s1 and s2 on the signal are easyto identify by WT: reconstructing the signal by detail coefficient d1, spikes weremore evident than saccades and hard thresholding was applied; unfortunately, toremove spikes as much as possible and to preserve saccades, extension to the otherddi

4

rafns(ow

TP

j s with j > 1 was necessary. (d) Evaluating the ratio between the covariance onetailed coefficients and the covariance of the signal (graph (b)), the procedures

dentified the level j where to apply hard thresholding.

.2. Using wavelet entropy for noise analysis

A ten order MWT was used to separate the signal by scale, and weemoved the main component of spikes from detailed coefficientsccording to the method of Eq. (7). Then we applied the entropyormula to the detailed coefficients to estimate the motor control

oise: WS was applied to each component x and y of the recordedignal using bi-orthogonal splines and a time window �t = 400 msat least 100 points; Eq. (12)), but we only evaluated the meanf WSk for linf ≤ lmax + 1 scales, where l = lmax = 10 was the level athich the signal was decomposed:

able 3erformance of the algorithm with different mother wavelets. The best performance was

Mother wavelet ˘spike ˘ Reg

db1 0.835 0.881 p >db2 0.799 0.801 p >coif2 0.901 0.954 p >sym2 0.795 0.911 p >

e Methods 196 (2011) 318–326

WS =

linf∑k=1

WSk

linf(15)

linf was chosen according to

linf =∀j∈ (1,lmax)argmax(j) :

cov(� dxj,�dyj)

cov(x, y)≤ 0.05 (16)

where cov(x, y) = |diag1,2(cov(x, y))|. From an intuitive point ofview, we calculated WS only on coefficients from level 1 to levellinf, where linf was the maximum level at which x and y covariancewas less than 5% of complete signal covariance.

5. Results and discussion

5.1. Experiment 1: computer-generated case

We tested the algorithm on a computer-generated time seriesbuilt as described in Section 2.1. We used the mother waveletshown in Fig. 2. Results did not report any correlation betweenperformance (Eq. (2)) and the level of noise or amplitude of spikes(Table 3). This means that the algorithm is sufficiently robust tonoise and spike amplitude. Performance varied from 88% (db1) to92% (coif2). The algorithm preserved the signal and only removed3–1% of the original signal � .

Wevelt entropy, WS, defined in Eq. (15), was tested in a small20×2 sample of two groups of computer-generated time series� made by adding white noise to filtered signals with differentSNR derived from subjects (�SNR = 10% · SNRg2). The implementedprocedure proved to estimate 94.8% of the white noise entropy forSNR = 20 dB and 91.01% for SNR = 40 dB. The maximum performance(≈111% of the mean) of Eq. (15) was obtained for linf ∈ (2, 5) andlmax = 10. It provided evidence that WS may be a good candidate forestimating motor control noise.

Fig. 4 shows the trend of p-values and F over x and y varying SNRand the level of approximated coefficients: we found a significantdifference (p < 0.05) between groups when WS was estimated fordetailed coefficients from level 5 to 2 (linf≈5).

We obtained a highly significant difference (p < 0.001) for highSNR, which can be explained as the native property of WS to mea-sure the microscopic disorder within the system.

5.2. Experiment 2: patients analysis

We applied the despiking algorithm, implemented by “db1”ten levels, to the subjects of Table 2. Fig. 5 shows the differencesbetween signal covariance and detailed coefficients of level 1, 2, 3and Table 4 reports loptim calculated by Eq. (16).

The signals of subjects EU and PP did not report any spikes, andthe algorithm only applied the hard thresholding to PP, but without

any consequence. In the case of EU, the procedure skipped the hardthresholding. The procedure also worked well on normal subjectsSL, GV and XM (Fig. 6).

In the case of patients GFOD (Fig. 7), MS and CN (Fig. 8),the procedure removed spikes, but on grouped spikes, such as

obtained through coif2 and db1.

ression over noise amplitude Regression over spike amplitude

0.05 p > 0.050.05 p > 0.050.05 p > 0.050.05 p > 0.05

G. Veneri et al. / Journal of Neuroscience Methods 196 (2011) 318–326 323

10−6

10−4

10−2

100

← SNR = 20dB

p−va

lue

x (l

og s

cale

)← SNR = 40dB

10−6

10−4

10−2

100

← SNR = 20dB

p−va

lue

y (l

og s

cale

)

← SNR = 40dB

12345678910l+1

0

10

20

30

Fx(1

,38)

level12345678910l+1

0

10

20

30

Fy(1

,38)

level

5%

p−mean

p−max/min

Fig. 4. Ability of wavelet entropy to discriminate two groups of 10×2 computer-generated time series having different signal to white noise ratio (�SNR = 10% · SNRg2). Wevaried signal to noise ratio and the level of detailed coefficients where WS was calculated. The maximum partition was found for linf ∈ (2, 5).

−10

0

10

30

Δco

v

patient MSpatient CNpatient GFODnormal PPnormal GVnormal EUnormal XM

F

ts

s8

nfnw

pt

TO

4 4.1 4.2 4.3 4.4 4.5 4.6

x 104

200

400

600

800

normal XMx

(px)

time (ms)

4 4.1 4.2 4.3 4.4 4.5 4.6

x 104

200

400

600

y (p

x)

time (ms)

originaldespiked

s1

s2

s4

s5

l1

s3

Fig. 6. Healthy subject XM. Group of spikes s1, s2, s3, a large spikes s4 and s5 arehighlighted in the figure; small signal 11 was loss of pupil. There were no spikes onx and the signal remained unchanged.

600

800

1000patient GFOD

px)

originaldespiked

s1s4

s3

1 2 3level

normal SL

ig. 5. Differences of covariance of patients and healthy subjects defined by Eq. (13).

he last part of GFOD’s signal, it was unable to reconstruct theignal.

When a harder despiking is required, it is possible to apply aimple median filter on spikes identified by the procedure (see Fig.).

Statistical analysis of patients and subjects (Fig. 9) reported sig-ificant differences on the x and y axes for WS applied to coefficients

rom 8 to 1 (Fx = 5.29, Fy = 10.07, px = 0.0003, py = 0.02765) and sig-ificant differences in coefficients linf to 1 as expected, where linf = 5

as chosen according to Eq. (16).

The best performance was obtained for linf = 4 or linf = 3 (px < 0.01,y < 0.01): Fig. 10c shows the scatter diagram and probability dis-ribution for linf = 4 and is a further evidence that the procedure

able 4ptimum level of subjects according to Eq. (16).

Subjects loptim Spikes

MS 2 Small sparseCN 2 Small sparse spikesGFOD 2 Small sparse and grouped spikesPP 1 NoneGV 1 Sparse spikesEU 0 NoneXM 2 Small sparse spikes only on YSL 2 Small sparse and grouped spikes

4 4.2 4.4 4.6 4.8 5

x 104

200

400x (

time (ms)

4 4.2 4.4 4.6 4.8 5

x 104

200

400

600

y (p

x)

time (ms)

s1

s3

s2

s4

s2

Fig. 7. Patient GFOD. The implemented technique removed sparse spikes s1, s2 ands3 well, but was unable to reconstruct the signal on grouped spikes s4.

324 G. Veneri et al. / Journal of Neuroscience Methods 196 (2011) 318–326

1000 2000 3000 4000 5000 6000 7000 80000

500

1000

time (ms)

posi

tion

(px)

1000 2000 3000 4000 5000 6000 7000 80000

500

1000despiking by median filtering after the recognition of spikes

time (ms)

posi

tion

(px)

originaldespiking by median filtering

Fig. 8. (Top) x data of patient CN after application of the method; the magnifiedboxes show two spikes not completely removed by the procedure. (Bottom) x dataof patient CN after application of the median filter to spikes identified by hard thresh-olding; the same two spikes were completely removed but the filter caused artefactson saccades.

145l+1

100

p−va

lue

(log

sca

le)

145l+1

0

10

20

30

F(1,

34)

valu

e

12345678910l+1−1

0

1

2

cov 1,

2

level

xy

xy5%1%

linf

Fig. 9. Results of statistical analysis of patients and healthy subjects applying WSat various levels of wavelet coefficients. The best separation was found from coef-ficient 4: the approximated coefficient (l + 1) indicated the contribution of visualsearch exploration and the highly detailed coefficients were influenced by machinerecording or saccades.

1.2

1.2

y en

trop

y of

{d 1,…

,dl+

1}

x entropy of {d1,…,d

l+1}

EU

GV

PP

SL

XM CNMSGFOD

CTRLSCA2NDC

σ

2σ

σ

(a)

0.8

0.8

y en

trop

y of

d1

x entropy of d1

EU

GV

PPSL

CN

MS

GFOD

σ

σ

2σ

(b)

pdf x

pdfy

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

y en

trop

y of

{d 1,…

,d4}

x entropy of {d1,…,d

4}

EUGV

PP

SL

XM

CNMS

GFOD

CTRLSCA2NDC

(c)

Fig. 10. Scatter diagram of WS. In order to estimate motor control noise, we applied wavelet entropy (WS). (a and b) t-Test of WS applied to entire signal (using all coefficients)and d1 coefficients did not find any significant difference between patients and healthy subjects (p > 0.05). (c) t-Test analysis and post hoc Holm–Sidak procedure on WSapplied to coefficients d1, . . ., d4 showed a significant difference on x (px < 0.01) and y (py < 0.01) between patients and healthy subjects. Probability distributions over x (pdfx)and y (pdfy) were calculated by kernel density (Bowman and Azzalini, 1997). Similar results were found for WS applied to coefficients d1, . . . , dlinf

with linf = 5 (px < 0.05,py < 0.01).

G. Veneri et al. / Journal of Neuroscienc

150 200 250 300 350120

140

160

180

200

220

240

260

280

300σ

y

σx

0 0.2 0.4 0.6−0.2

0

0.2

0.4

0.6

0.8

1

σy o

n fi

xatio

ns

σx on fixations

FNc

ssp

cWfsrfit

arfcnatpo

6

vJpimgrctvo1

icge

tmu

ig. 11. Standard deviation evaluated on the entire signal or only on the fixation.o significant difference (p > 0.05) was found between groups. Standard deviationannot be used to evaluate motor control noise on visual search.

uccessfully separated normal subjects and patients, and especiallyubjects and SCA2. The correlation between entropy over x and yrovided further evidence of the method’s efficacy.

No significant difference was found using the approximatedoefficients of d1, . . ., dl+1 (Fig. 10a) and only at level 1 (Fig. 10b).

e argue that motor control noise had no contributions at highrequencies or was difficult to estimate, confirming the hypothe-is that the coefficients d1, . . ., d2 were influenced by the machineecording or the saccades; on the contrary, the approximated coef-cients d11 = dl+1 and less detailed coefficients d9, d10 only indicatedhe variability of visual search exploration.

The group NDC did not have a uniform distribution and post hocnalysis did not find any significant difference: we found similaresults in a pro-saccade test not yet published. No differences wereound in the variance, particularly within fixations variance, whichould be a good candidate for estimating additive motor controloise (Fig. 11).We could not make any assumptions about the role ofdditive noise and signal-dependent noise. Indeed, SCA2 is knowno affect movement, due to the role of the cerebellum, but not therocess of fixation. We obtained results similar to those of the testf simulated cases (Fig. 4).

. Conclusions

We used the multiscale wavelet transform to remove spikes,erifying that our algorithm, based on the work of Donoho andohnstone (1994), can be applied to eye-tracking and signals ofatients. We implemented an easy procedure for “fine despik-

ng” and preserving signal characteristics as well as physiologicalotor control noise. When the procedure was tested on computer-

enerated signals and those of healthy subjects, despiking proved toemove the 90% of spikes. It allowed us to investigate the role of theerebellum in motor control, avoiding artefacts due to spikes. Wehen estimated the motor control noise by wavelet entropy duringisual search: the procedure differentiated patients from controlsn y and x, y when applied to coefficients from 8 to 1 and from 4 to, respectively.

The ability to measure motor control noise made it possible tonvestigate the role of the cerebellum in free visual search in oururrent research. Our preliminary results, not yet published, sug-est that humans adapt exploration in order to reduce “saccade

nergy”. The present method will be used to verify this hypothesis.

Future research will be addressed to mother wavelet construc-ion to discover characteristic signals, such as square jerks and

icrosaccades: correntropy applied to wavelet transform may beseful to identify important waveforms in fixations. Correntropy

e Methods 196 (2011) 318–326 325

is defined as a generalization of correlation of random processes,avoiding any assumption of Gaussian distribution (Liu et al., 2007).It can be used to identify the correlation between x and y duringfixation and therefore “small synchronization” of motor control,providing a quantitative measure of physiological noise.

Acknowledgments

The authors would like to thank the editor and reviewers forimprovements and suggestions, and Helen Ampt for the formalimprovements.

Appendix A. Algorithm

Algorithm A.1. This algorithm describes the implemented pro-cedure. WTDECOMPOSITION and WTRECONSTRUCTION are thewavelet decomposition and reconstruction. HARDTHRESHOLDINGare the function that implements Eq. (7). COVw is the covariance oftwo signals on window w.

covxy ←median(COVw(x, y))cAx, dx ←WTDECOMPOSITION(x, lmax)cAy, dy ←WTDECOMPOSITION(y, lmax)for j = 1 to lmaxdo

covdxdy ←median(COVw(dxdy))pcovxy ← covdxdy

if covxy − covdx (j)dy(j) < 0 or covdx (j)dy(j)−p covxy < 0thenbreak

end ifdx(j)← HARDTHRESHOLDING(dx(j))dy(j)← HARDTHRESHOLDING(dy(j))p covxy ← covdx (j)dy(j)

end forx←WTRECONSTRUCTION(cAx, dx, lmax)y←WTRECONSTRUCTION(cAy, dy, lmax)

Appendix B. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jneumeth.2011.01.006.

References

Abel LA, Wang ZI, Dell’Osso LF. Wavelet analysis in infantile nystagmus syndrome:limitations and abilities. Invest Ophthalmol Vis Sci 2008;49(8):3413–23.

van Beers RJ. The sources of variability in saccadic eye movements. J Neurosci2007;27(33):8757–70.

van Beers RJ. Saccadic eye movements minimize the consequences of motor noise.PLoS One 2008;3(4):1–8.

van Beers RJ. Motor learning is optimally tuned to the properties of motor noise.Neuron 2009;63(3):406–17.

Blanco S, Figliola A, Quiroga RQ, Rosso OA, Serrano E. Time–frequency analysis ofelectroencephalogram series. iii. Wavelet packets and information cost function.Phys Rev E 1998;57(1):932–40.

Bollen E, Bax J, van Dijk JG, Koning M, Bos JE, Kramer CG, et al. Variability of the mainsequence. Invest Ophthalmol Vis Sci 1993;34(13):3700–4.

Bowman AW, Azzalini A. Applied smoothing techniques for data analysis. OxfordUniversity Press; 1997.

Bürk K, Fetter M, Abele M, Laccone F, Brice A, Dichgans J, et al. Autosomal dominantcerebellar ataxia type i: oculomotor abnormalities in families with sca1, sca2,and sca3. J Neurol 1999;246(9):789–97.

Coifman RR, Wickerhauser MV. Entropy based algorithms for best basis selection.IEEE Trans Inform Theory 1992;32:712–8.

Corbetta M, Kincade JM, Shulman GL. Neural systems for visual orienting and theirrelationships to spatial working memory. J Cogn Neurosci 2002;14(3):508–23.

Donoho DL, Johnstone JM. Ideal spatial adaptation by wavelet shrinkage. Biometrika1994;81(3):425–55.

Duchowski AT. A breadth-first survey of eye-tracking applications. Behav Res Meth-ods Instrum Comput 2002;34(4):455–70.

Ehrentreich F, Sümmchen L. Spike removal and denoising of aman spectra by wavelettransform methods. Anal Chem 2001;73(17):4364–73.

Engbert R, Kliegl R. Microsaccades uncover the orientation of covert attention. VisionRes 2003;43(9):1035–45.

Filla A, Michele GD, Campanella G, Perretti A, Santoro L, Serlenga L, et al. Autosomaldominant cerebellar ataxia type i. Clinical and molecular study in 36 Italian

3 scienc

F

G

I

J

K

K

L

L

L

M

M

oN

26 G. Veneri et al. / Journal of Neuro

families including a comparison between sca1 and sca2 phenotypes. J NeurolSci 1996;142(1–2):140–7.

ischer BM, Biscaldi PO. Saccadic eye movements of dyslexic adults. Neuropsycholo-gia 1993;31:887–906.

irard B, Berthoz A. From brainstem to cortex: computational models of saccadegeneration circuitry. Prog Neurobiol 2005;77(4):215–51.

nouye T, Shinosaki K, Iyama A, Matsumoto Y. Localization of activated areas anddirectional EEG patterns during mental arithmetic. Electroencephalogr ClinNeurophysiol 1993;86(4):224–30.

uhola M, Jäntti V, Pyykkä I, Schalén L, Akesson M, Magnusson M. An identifica-tion technique for the spike artefact of saccadic eye movements. Biol Cybern1987;57(6):415–20.

amavuako EN, Jensen W, Yoshida K, Kurstjens M, Farina D. A criterion for signal-based selection of wavelets for denoising intrafascicular nerve recordings. JNeurosci Methods 2010;186(2):274–80.

amavuako EN, Yoshida K, Jensen W. Variance-based signal conditioning tech-nique: comparison to a wavelet-based technique to improve spike detectionin multiunit intrafascicular recordings. Biomed Signal Process Contr 2009;4(2):118–26.

eigh RJ, Kennard C. Using saccades as a research tool in the clinical neurosciences.Brain 2004;127(Pt 3):460–77.

eigh RJ, Zee D. The neurology of eye movements (Book/DVD). 4th ed. New York:Oxford University Press; 2006.

iu W, Pokharel PP, Principe JC. Correntropy: properties and applications innon-Gaussian signal processing. IEEE Trans Signal Process 2007;55(11):5286–98.

allat S, Hwang WL. Singularity detection and processing with wavelets. IEEE Trans

Inform Theory 1992;38(2):617–43.

allat SG. A theory for multiresolution signal decomposition: the wavelet repre-sentation. IEEE Trans Pattern Anal Mach Intell 1989;11(7):674–93.

f Mathworks M. Matlab 7.5 for windows, wavelet toolbox; 2007.enadic Z, Burdick JW. Spike detection using the continuous wavelet transform.

IEEE Trans Biomed Eng 2005;52(1):74–87.

e Methods 196 (2011) 318–326

Quiroga RQ, Nadasdy Z, Ben-Shaul Y. Unsupervised spike detection and sortingwith wavelets and superparamagnetic clustering. Neural Comput 2004;16(8):1661–87.

Quiroga RQ, Rosso OA, Bahar E, Schürmann M. Wavelet entropy in event-relatedpotentials: a new method shows ordering of EEG oscillations. Biol Cybern2001;84(4):291–9.

Ramat S, Leigh RJ, Zee DS, Optican LM. What clinical disorders tell us about the neuralcontrol of saccadic eye movements. Brain 2007;130(Pt 1):10–35.

Rayner K, Slowiaczek M, Clifton C, Bertera J. Latency of sequential eye movements:implications for reading. J Exp Psychol Hum Percept Perform 1983;9(6):912–22.

Salvucci DD, Goldberg JH. Identifying fixations and saccades in eye-tracking proto-cols. In: ETRA ‘00: Proceedings of the 2000 symposium on eye tracking research& applications; 2000. p. 71–8.

Shannon CE. A mathematical theory of communication. Bell Syst Tech J1948;27:379–423.

Sharma L, Dandapat S, Mahanta A. ECG signal denoising using higher order statisticsin wavelet subbands. Biomed Signal Process Contr 2010;5(3):214–22.

Shimojo S, Simion C, Shimojo E, Scheier C. Gaze bias both reflects and influencespreference. Nat Neurosci 2003;6(12):1317–22.

der Stigchel SV, Meeter M, Theeuwes J. Eye movement trajectories and what theytell us. Neurosci Biobehav Rev 2006;30(5):666–79.

Veneri G, Federighi P, Rosini F, Federico A, Rufa A. Influences of data filteringon human–computer interaction by gaze-contingent display and eye-trackingapplications. Comput Hum Behav 2010a;26(6):1555–63.

Veneri G, Piu P, Federighi P, Rosini F, Federico A, Rufa A. Eye fixations identifica-tion based on statistical analysis—case study. In: 2nd international workshopon cognitive information processing (CIP); 2010b. p. 446–51.

Xu-Wilson M, Zee DS, Shadmehr R. The intrinsic value of visual information affectssaccade velocities. Exp Brain Res 2009;196(4):475–81.

Yarbus AL. Eye movements and vision. volume chapter VII. New York: Plenum Press;1967.

Zunino L, Pérez D, Garavaglia M, Rosso O. Wavelet entropy of stochastic processes.Phys A: Stat Mech Appl 2007;379(2):503–12.