atomic decomposition

8/11/2019 Atomic Decomposition

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2 EURASIP Journal on Advances in Signal Processing

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related to the phenomena typically observed at power sys-tems. That is, the components employed are coherent to

power system phenomena. The signal components, each oneassociated to a different phenomenon, are identified throughan atomic decomposition algorithm. The algorithm em-ployed is based on the matching pursuit (MP) [2428]. Thisstrategy identifies the different natural phenomena repre-sented in the signal that originated during the disturbance.

Paper organization

The damped sinusoids signal model is discussed inSection 2.Atomic decompositions are discussed inSection 3. The de-composition algorithm is described inSection 4along withsome examples and a brief discussion of the improvements

implemented with respect to the work in [22]. InSection 5,we discuss some applications of the atomic decompositionsobtained using this algorithm. These applications include co-herent signal modeling, signal denoising, nonlinear filteringof the so-called DC component, and a compression schemefor disturbance signals.Section 6closes the paper.

2. DAMPED SINUSOIDAL MODELING OFDISTURBANCE SIGNALS

Regardless of the quantities measured, the aim of power sys-tem monitoring is to study the evolution in time of dis-turbance phenomena. These phenomena are represented, in

general, as sinusoidal oscillations of increasing or decreasingamplitudes, and are highly influenced by circuit switching,

as well as by nonlinear equipments. In order to analyze andcompress signals from power systems, it is important to usea model that is capable of precisely representing the com-ponents that may compose those signals. Xu [29] discussescommon phenomena in power systems.

(i) Harmonics are low-frequency phenomena rangingfrom the system fundamental frequency (50/60 Hz) to3000 Hz. Their main sources are semiconductor appa-ratuses (power electronic devices), arc furnaces, trans-formers (due to their nonlinear flux-current charac-teristics), rotational machines, and aggregate loads (agroup of loads treated as a single component).

(ii) Transients are observed as impulses or high-frequency

oscillations superimposed to the voltages or currentsof fundamental frequency (50/60 Hz) and also expo-nential DC and modulated components. The morecommon sources of transients are lightnings, trans-mission line, and equipment faults, as well as switch-ing operations, although transients are not restrictedto these sources. Their frequency range may span up tohundreds of thousands of Hz, although the measure-ment system (and the power line) usually filters com-ponents above few thousands of Hz.

(iii) Swells and Sags are increments or decrements, respec-tively, in the RMS voltage of duration from half cycleto 1 minute (approximately).


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Lisandro Lovisolo et al. 3

D D

Signal Atom indices ReconstructedsignalAnalysis Synthesis

Coefficients

Figure 2: Signal analysis and synthesis based on atomic signal decompositions using a dictionaryD.

When analyzing disturbance signals, it is interesting to becapable of detecting, modeling, and identifying those phe-nomena. Some techniques commonly employed for model-ing and analyzing power disturbance signals are Fourier fil-tering [9,10]; Prony analysis [11,12]; autoregressive mov-ing average models [7]; state-space tracking methods [7];wavelets [11,1319]. In some cases, these methods are usedalong with artificial intelligence strategies [8,12,30,31].

Roughly, one can consider that electric power systems are

basically formed by sources, loads, and transmission lines,that is, RLC circuits, whose transient behaviors are modeledby damped sinusoids. In addition, discontinuities may ap-pear in these signals due to circuit switching. Following thesepremises, a disturbance signalx(t) can be approximated by[22,32,33]

x(t) =M

m=1me

m(ttsm) cos

2kmFt+ m

ut tsm ut tem,(1)

whereMis the number of expansion elements,Fis the fun-damental frequency (50/60 Hz),u(

) corresponds to the unit

step function, and each element is represented by a 6-tuple(m, km,m, m, tsm, t

em). In this 6-tuple, m is the amplitude,

km is an integer multiple of the fundamental frequency, mis the decaying factor, m is the phase, and tsm and t

em are,

respectively, the starting and ending times of themth signalcomponent.

The well-known Prony method [7, 11, 12] largely em-ployed for analyzing power system signals obtains a similarmodel. However, the Prony method does not consider thatdistinct damped sinusoids can start at different time instantsneither that they can have different time supports. Therefore,the proposed model adds a time localization feature to Pronyanalysis.

In the signal processing community, damped sinusoidsare present in several applications. For example, in [3436] such components were used for transient detection andanalysis. The large amount of potential applications of suchcomponents is motivated by the fact that damped sinusoidsare solutions for ordinary differential equations that oftenappear in physical system models [27, 28, 37, 38]. For along time, researchers have been designing systems and algo-rithms to estimate the parameters of damped sinusoids em-bedded in several signals[3946].

In [21,47], disturbance signals are modeled using a fun-damental, a set of harmonics, and after subtracting thesecomponents from the signal, the resulting signal is decom-

posed using a wavelet transform. The signal model in (1)differs from those in [21,47], since it does not restrict thefundamental and the harmonics to have constant amplitudesneither full nor the same time support.

How can one represent a given signal in accordance to thesignal model in (1)? For that purpose, we employ an adap-tive atomic decomposition algorithm. Before discussing thealgorithm, we address some important concepts of atomicdecompositions.

3. ATOMIC DECOMPOSITIONS

Define a dictionaryDas the set of all possible structures, pre-defined waveforms, that can be used to represent signals. Theaim of atomic signal decomposition algorithms is to select asubset ofMelementsg(m)from the dictionary that approx-imatesxusing the linear combination given by the M-termapproximation or representation (or simply,M-term)

x

x=

Mm=1

mg(m), g(m) D. (2)

The atoms g(m) in the M-term are indexed by the map-ping(m) that is defined as : Z+ {1, . . . , #D}; #D is thedictionary cardinalitythe number of elements in D , thus(m) {1, . . . , #D}. The parameterm denotes the coeffi-cient, that is, the weight ofg(m), and M is the number ofatoms used to approximatex. TheM-term representation ofa signal is the result of an analysis-synthesis procedure whichis illustrated in Figure 2. The analysis of the signal obtains thecoefficients and atom indices while the synthesis of the signalis accomplished using(2).

Atomic representations differ from classical transform-based signal representations, because the atoms used in the

M-term may be linearly dependent. In addition, since, in

general, D has more elements than necessary to span thesignal space, the selection of the atoms may be signal-dependent, leading to an adaptive signal decomposition(analysis-synthesis).

Atomic representations have been employedfor signal fil-tering and denoising [25,48], analysis of the physical phe-nomena behind the observed signal together with patternrecognition and signal modeling [25,27,28,4952], time-frequency analysis [24,25], and harmonic analysis [52,53].Atomic representations can also provide good signal com-pression tools [5357]. Recently, atomic representations wereused to discriminate outcomes from different Gaussian pro-cesses [58].


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The distortion of theM-term approximation of a signalxis

d(x,M, D) = x x = xM

m=1mg(m)

. (3)This distortion depends on (i) the number of elementsMused to representx; (ii) the atoms g(m) used to express thesignal; (iii) and the weightsmof the atoms. SinceD definesthe atoms that can be used in the M-term, the distortion de-pends onD. ForM-terms that use atoms from a dictionaryD being capable of representing any signal x X with anarbitrarily distortiond(x,M, D), D must be complete in X[25,5961]. That is, there will be at least one linear combi-nation of elements fromD that givesx= x, for allx X,that is,Dmust span X. When Dhas more elements than nec-essary to span the signal space, it is said to be overcompleteor redundant [25,54,59,61].

Ideally, the atoms used in the M-term expansion should

depend on the signal, and in this case the decompositionis said to be adaptive [24, 25, 27, 51, 59, 60, 62]. Since anovercomplete dictionary allows expressing the same signalusing differentM-terms (the representation is not unique),an overcomplete or redundant dictionary is a requirementif adaptive signal decompositions are desired. Ideally, adap-tive approximations should discriminate the relevant infor-mation represented in the signal ignoring noise, being therelevant information defined by the dictionary atoms.

Most signal processing applications deal with outcomesfrom physical processes. In these cases, the observed signalxis a mixture of components pm, representing physical phe-nomena, given by

x= m

mpm+ n, (4)

wheren is the noise, inherent to the measurement process.From the perspective of signal modeling, it is interesting forthe atomsg(m) used to approximate the signal to be similarto the phenomena pm that are represented inx. The closerthe selected dictionary elementsg(m) and weightsm are tothe physical phenomenapmand weightsm, the better is thesignal expansion for modeling and pattern recognition pur-poses. We say that the representation is coherent to the signalwhen it is a meaningful signal model.

The most compact or sparse representation ofx is the

one using the smallest number of atoms [25,61] with nulldistortion. However, in practice, a small number of termsMproviding an acceptable distortion may suffice for represent-ing the signal in a sparse manner.

In essence, atomic decompositions may provide an accu-rate, sparse, and coherent signal model with low distortion.A very popular algorithm to obtain atomic decompositionsis the matching pursuit (MP) [24,25].

3.1. Matching pursuit

The MP[24,25] approximates signals iteratively finding thebest possible approximation at each iteration. The MP has

emerged more or less at the same time in several scientificfields, for example, in signal processing in [63], in statisticsin [64,65], and in control applications [66].

LetD= {g} and {1, . . . , #D} such that g = 1 forallk , and let #D be dictionary cardinality, that is, the num-ber of elements in D . In each decomposition step or itera-

tion m 1, the MP searches for the atom g(m) D, thatis,(m) {1, . . . , #D}, with largest inner product with theresidual signalrm1x [24,25]. The initial residue is set to ber0x= x. The selected atomg(m) is then subtracted from theresidue to obtain a new residue

rmx= rm1x mg(m), m=

rm1x , g(m)

. (5)

The MP obtains the M-term signal representation/approx-imation of (2) with distortionrMx= x x(theMth residue).In practice, the decomposition step (the calculation ofm,(m), and the residue rmx) is iterated until a prescribed distor-tion (rmx ), a maximum number of stepsM, or a minimumfor an approximation metric are reached [22,24,25,60].

Localfitting

Due to its greediness [67, 68], the MP algorithm confuses sig-nal components[69]. This happens because the MP searchesfor the atom that best matches the overall signal, which mayproduce a bad local fitting. For example, to solve this draw-back, the high-resolution pursuits (HRP) [51, 70] use B-spline windows to locally fit the atom found by the MP to theresidue. The algorithm inSection 4uses a local fitting strat-egy for eliminating pre-echo and post-echo artifacts that of-ten appear in MP-like algorithms, which is accomplished bywindowing the atoms with a rectangular window. In addi-tion, this algorithm includes a set of heuristics inside the MPloop to instruct the MP for correct atom selection.

The MP is capable of obtaining compact and efficient sig-nal representations. However, an important aspect for that isthe dictionary, since the elements in it should be coherent tothe components represented in the signal.

3.2. Parameterized dictionaries

If the class of components that may be represented in thesignal is previously known, then it would be wise to use adictionary containing atoms that resemble these components[25, 59, 71]. A common strategy is to define the dictionary el-

ements from a set of prototype functions/signals. In such dic-tionaries, the actual waveforms of the dictionary atoms de-pend on a set of parameters modifying the prototype signal.These dictionaries are said to be parameterized since eachdictionary elementg is defined by a given value of the pa-rameter set, that is,

= 0, 1, . . . , #D1, (6)where #Dis the number of possible distinct parameter set val-ues defining different atomsgand is the set of all possibleparameters. For example, the popular Gabor dictionary [2427,51,60,7274] is composed by Gaussian shaped atoms in


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Pure sinusoididentification

Figure3: Block diagram of the atomic decomposition algorithm. In the first iteration, the switch is in position 1 and in the remainingiterations, it stays in position 0.

different scales, with varying centers in time and, multipliedby different complex sinusoids, the so-called time-frequencyatoms [24,25,75].

The use of a parameterized dictionary allows for esti-mating the signal and obtaining coherent decompositions.For example, parameterized dictionaries were employed forpattern recognition [51] and signal modeling [49, 76] us-ing atomic decompositions. The decomposition algorithm inSection 4employs a parameterized dictionary of damped si-nusoids in order to obtain an atomic signal model accordingto (1).

Continuous parameters

In some cases, one may have to adapt or fit the structuresused in the signal representation to the actual signal being de-composed. For that purpose, the parameter set valuedefin-ing an atom could be any point inside a region of the param-eter space instead of one chosen from a set of #D values. Inthis case, it is said that the parameters of the atoms are con-tinuous. In general, to obtain continuous parameter atoms,one uses optimization algorithms to find the values of the pa-rameter set defining each atom in theM-term. One starts theoptimization using a guess for the atom parameters, which is

obtained from a finite cardinality dictionary. The decompo-sition algorithm inSection 4employs this approach.

4. DECOMPOSITION ALGORITHM

This section presents an atomic decomposition algorithmthat obtains the signal representations in accordance with thesignal model in (1). The algorithm is based on the MP anduses a parameterized dictionary of damped sinusoids withcontinuous parameters. The simple use of the MP with a pa-rameterized dictionary of damped sinusoids does not grantobtaining a good signal model. To improve the signal mod-eling, a set of heuristics is introduced in the decomposition

loop in order to guide the atom selection. The procedure de-scribed here derives from the one in [22].

The elements of the parameterized damped sinusoidalatomgare given by

g(n) = Kg(n)cos(n + )

u

n ns un ne,n = {0, . . . , N 1},

g(n) =

1 if = 0 pure sinusoid ( /= 0),DC or unit impulse (= 0),

e(nns) if >0 decreasing exponential,

e(ne

n)

if


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Figure 4: Result of the optimization of the atoms parameters.

The discrete parameters found for the atomdare then opti-mized to find the from a set of continuous parameters max-imizing the match between the atom and the current residueusing a Newton-like optimization method [22].Figure 4il-lustrates the result of this optimization.

The simple use of the MP with a damped sinusoid dic-tionary does not guarantee the generation of a coherent de-composition (a physically interpretable representation with

respect to the phenomena in disturbance signals).Figure 5shows an example of what occurs when a fault signal is de-composed by the MP using a damped sinusoid dictionary.The fault occurs after the 200th sample of the signal. How-ever, the atom found does not represent the fault.

Aiming at a coherent decomposition, after selecting adamped sinusoid to approximate the atom, the algorithmperforms inherent phenomena recognition by reducing thetime support of the atom (determined byns andne). The re-gion of support of the atom is reduced sample by sample bybox-windowing the atom in order to verify whether a newtime support produces better fit between the atom and thecurrent residue.

The next step of the decomposition algorithm is to quan-tize the atom frequency to a multiple of the fundamental andrepeat the time support search for the new quantized fre-quency. After that, the algorithm decides if it is worth to usea pure sinusoid instead of a damped one. This decision re-lies on a heuristic that is based on a similarity metric. Theheuristic (decision criterion) is basically a tradeoffbetweenthe error per sample of the resulting residue in the region ofsupport of the atom and the inner product of the atom withthe current residue [22].

Figure 6shows how the whole decomposition algorithmbehaves in the first four decomposition steps for a naturaldisturbance signal from [77]. The first residue is the signal

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Figure5: Failure of the MP in finding coherent structures.

itself. Note that the components found in each iteration ofthe algorithm closely match the correspondent residues.

The decomposition algorithm stops when the approxi-mation achieved is good enough. Otherwise, it scales andsubtracts the atom from the current residue and producesa new residue to be approximated in the following iteration.To decide if the decomposition should or should not con-tinue, we employ the following criterion: is there any dictio-nary atom sufficiently coherent to the remaining residue? Ifthe answer is yes, the decomposition continues; otherwise itstops. To answer this question, we measure if the dictionary


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Figure6: Finding of the coherent structures for a natural distur-bance signal available in [77].

atoms are capable of providing a good signal approximation.For that, we employ the approximation ratio [24,60]

(m) =rm1x , g(m)rm1x . (9)

It measures how much of the residue rm1x is approximated atthe stepm. Note that the residue norm rm1x is a measureof the approximation error, but it does not measure if theresidue is still highly correlated to any atom in the dictionar y.The coefficient magnitude|rm1x , g(m)| depends on theresidue energy since the atoms have unit norm. Therefore,if one employs |rm1x , g(m)| as halting criterion, the haltingwould also be influenced by the residue norm. The use of theapproximation ratio eliminates such influence [22].

At the end of the decomposition algorithm, we obtainthe signal approximation in (1) represented by the sequenceof pairs (m, (m)), m = 0, . . . ,M 1, where (m) =(m, m, m, nsm, n

em) (see (1) and (7)). Note that the algorithm

delivers discrete values for the atom parametersnsm,nem, and

m, while the remaining parameters of the atomm andmand the atom amplitudemare continuous.

5. APPLICATIONS OF THE SIGNAL MODEL ANDTHE DECOMPOSITION ALGORITHM

5.1. Coherent signal modeling

What happens if the signal to be decomposed is acquired in asevere noise environment? Ideally, one wants the signal com-ponents to be identified in spite of the noise that may beadded to the signal. However, if the noise has an energy thatis comparable to the energy of a given component, then itwould be difficult to distinguish between them. We addressnow how the decomposition algorithm presented performs

in detecting the signal components when the signal is cor-rupted by noise.

Define the noisy signal

xnoise= x+ n, (10)

where n is any noise signal. From this definition, we can com-pute

SNRC= 10log10

x2n2

= 10log10

x2x xnoise2

(dB)

(11)

to measure how much xis corrupted by noise.Figure 7 showsthe components identified in a given signal corrupted bynoise signals with different levels of SNRCby the decompo-sition algorithm of the previous section. The original syn-thetic signal (uncorrupted by noise) is shown at the top of

Figure 7(a)and the components used in its generation areat the bottom ofFigure 7(a).Figure 7(b)shows the signal inFigure 7(a)corrupted with noise such that SNRC = 30dBand the structures found by the decomposition algorithm.Note that they are very similar to the ones used to generatethe signal. Figures7(c)and 7(d)show the same signal cor-rupted by noise such that SNRC= 20 dB and SNRC= 10 dB,respectively. One notes that in these cases, the three struc-tures of larger energy are identified, but the fourth is not.The energy of the fourth structure is indeed smaller than theone of the noise in these cases. When the noise added to thesignal is such that SNRC=5 dB, seeFigure 7(e),just the twostructures with larger energy are identified (although not aswell as in the previous cases). Note that in this case, the noisehas an energy that is larger than the ones of the third andfourth structures.

5.2. Denoising by synthesis

As we have seen, our decomposition algorithm can reason-ably identify/obtain the signal components even subject tohigh-level noise. Therefore, we can use the decompositionalgorithm to remove the noise that may be present in thesignal. To access the capability of this analysis-synthesis de-noising strategy, we first generate a set of corrupted signalversions with different values of SNRC, see (11). Then, wedecompose each corrupted signal version and compute thereconstruction signal-to-noise ratio

SNRR= 10log10

x2x x2

(dB), (12)

wherexis the synthesized signal (see (2)) for the differentcorrupted versions ofx.

Figure 8shows SNRRin function of SNRCfor the signalin the first row ofFigure 6taken from [77]. One can notethat SNRRis always larger than SNRC, specially at low SNRC,showing that the analysis-synthesis denoising approach is ef-fective for signal denoising.


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5.3. Fundamental extraction and transient separation

Several works have proposed analysis methods that start byextracting the signals fundamental and then use the remain-

ing signal (the transient, error or innovation signal) for an-alyzing the disturbance and classifying it [20,23,78]. Sinceour decomposition method automatically extracts the signalfundamental when it has a strong presence in the signal, wecan subtract the fundamental from the signal in order to ob-tain the transient signal.

Figures9(a)and9(b)show examples of the above tran-sient separation. For example, inFigure 9(b), one can ob-serve that our method detects the presence of a DC com-ponent with a transient (power event) occurring at 0.015 sec-ond.

5.4. Filtering the DC component

We now study the capability of the MP for filtering the DCcomponent that sometimes appears in current quantities af-ter the disturbance occurs [9]. A signal corrupted by a DCcomponent (exponential decay) can be modeled as

Aet

u

t ts ut te+ B sin 2F t+ , (13)where ts and te are the start and end times of the DC compo-nent phenomenon (for simplicity, the start and end times ofthe sinusoidal component are not presented) andexpressesthe exponential decay constant. Since(13) is a particular caseof (1), the decomposition algorithm presented is capable ofextracting/identifying the DC component. Once the signal

is decomposed, the DC component can be filtered out atthe signal synthesis. This filtering is achieved by ignoring inthe signal synthesis all the low-pass structures (the ones withzero frequency) and that are not of impulsive nature (timesupport not smaller than 10% of the fundamental frequencyperiod) obtained by in the signal analysis.

Several analyses of disturbance signals are based on com-parisons of the values of current and voltage quantities, oftenin phasor form. For that, the signal is filtered to obtain justthe fundamental frequency contribution using, for example,Fourier filters [9,10]. Therefore, this measurement was usedto evaluate the ability of our method to filter the DC com-ponent. An example of the DC component filtering on a

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Figure9: Fundamental extraction and transient separation for dis-turbance signals.

synthetic signal that was generated using the model equation(1) can be seen inFigure 10.The components of the origi-

nal signal are two sinusoids of 60 Hz with amplitudes 1 and2 and phases 0 and 90 that go from samples 0 to 50, and50 to 100, respectively. To the signal formed by the sum ofthese components, a DC component is added starting atsample 50 and ending at sample 100. Its decay is 0.05 and itsamplitude is 3. InFigure 10,one can see that in the filteredsignal the, DC component is almost totally eliminated. Inaddition, the voltage and current phasors in the filtered sig-nal are very close to the ones of the nondisturbed signal. Thisfiltering has shown to be effective when applied to syntheticand natural signals as well as signals obtained through ATP-EMTP [79]. Another example of this filtering process can beseen in [22].


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of the filtered signal

Figure10: Fourier filter applied after DC component filtering of a synthetic signal.

5.5. Compression of disturbance signals

For compression, the coefficients and atom parameters needto be quantized after the decomposition process. The quan-

tizations of the parameters and of the coeffi

cients give rise tothe reconstructed signal

x= M1m=0

Q

m

gQi{(m)}, (14)

where Q{} is the quantizer of the coefficients and Qi{} de-notes the quantizer of the parameters. Each different quanti-zation rule Qi{} corresponds to a distinct dictionaryDi D(Dis the original continuous parameter dictionary). That is,the dictionaryDiis defined by the mappingQi{} andxcor-responds to a weighted sum of its elements. The weights ofthe atoms in

xdepend on the quantizer of the coefficients

Q{}. Figure 11 illustrates this compression framework. Theoptimum rate distortion solution for this compressionscheme is provided by finding the quantizers Q{} andQi{} that lead to the minimum distortion for a given rate.

Signal compression based on the MP usually retains a cer-tain number of termsMand quantizes just the coefficients[71]. The compression framework we employ substantiallydiffers from these. Since we use a dictionary of some contin-uous parameters, for compression it is necessary to quantizethe parameters of atoms. This is equivalent to using multipledictionaries in the decomposition process and selecting oneof them for coding a given signal.

Rate distortion optimization is employed in compres-sion systems to achieve the best signal reproduction for a de-sired compression target [80]. In the framework at hand, onehas to find a compromise between the number of atoms inthe signal representation, the quantization of the coefficients,


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1

0.5

0

0.5

1

Amplitude

0 0.02 0.04 0.06 0.08 0.1

Samples

OriginalReconstructed

(a)

1.5

1

0.5

0

0.5

1

1.5

Amplitude

0 0.02 0.04 0.06 0.08 0.1

Samples

OriginalReconstructed

(b)

Figure12: Examples of the compression performance for two signals from [ 77].

104

103

102

101

Distortion(MSE)-logscale

0 0.5 1 1.5 2 2.5 3

Rate (bits/sample)

(a)

105

104

103

102

101

100

D

istortion(MSE)-logscale

0 0.5 1 1.5 2 2.5 3

Rate (bits/sample)

(b)

Figure13: Rate distortion performance of the compression system presented for two signals from [77].

faults and disturbances. In addition, we are developing amethodology to evaluate compression systems for distur-bance signals using the techniques normally employed foranalyzing these signals.

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Symposium on Circuits and Systems (ISCAS 05), vol. 6, pp.54175420, Kobe, Japan, May 2005.

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for: image and video compression, IEEE Signal ProcessingMagazine, vol. 15, no. 6, pp. 2350, 1998.[81] M. P. Tcheou, L. Lovisolo, E. A. B. da Silva, M. A. M. Ro-

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Lisandro Lovisolo was born in Neuquen,Argentina. He received the Engineering de-gree in electronics in 1999 and the M.S.and D.S. degrees in electrical engineeringin 2001 and 2006, respectively, all from theFederal University of Rio de Janeiro. Since

2003, he has been with the Department ofElectronics and Telecommunications Engi-neering at University of the State of Rio deJaneiro (UERJ). His research interests arein signal processing, especially adaptive and overcomplete sig-nal/image decompositions for analysis and coding purposes.

Michel P. Tcheou was born in Rio deJaneiro, Brazil. He received the Engineeringdegree in electronics, in 2003, and the M.S.degree in electrical engineering, in 2005,from Federal University of Rio de Janeiro(UFRJ), Rio de Janeiro, Brazil. He is cur-rently pursuing the D.S. degree at the Sig-nal Processing Laboratory (LPS), UFRJ. In2006, he joined the Electric Power ResearchCenter (CEPEL). His research interests arein signal processing, especially atomic decompositions with appli-cations to multimedia and power systems.

Eduardo A. B. da Silvawas born in Rio deJaneiro, Brazil, in 1963. He received the En-gineering degree in electronics from Insti-tuto Militar de Engenharia (IME), Brazil,in 1984, the M.S. degree in electrical engi-neering from Universidade Federal do Riode Janeiro (COPPE/UFRJ) in 1990, and thePh.D. degree in electronics from the Uni-versity of Essex, England, in 1995. In 1987

and 1988, he was with the Department ofElectrical Engineering at Institute Militar de Engenharia, Rio deJaneiro, Brazil. Since 1989, he has been with the Department ofElectronics Engineering, UFRJ. He has also been with the Depart-ment of Electrical Engineering, COPPE/UFRJ, since 1996. He iscoauthor of the book Digital Signal Processing-System Analysis andDesign, published by Cambridge University Press in 2002. He hasserved as Associate Editor of the IEEE Transactions on Circuits andSystems Part I and Part II. He has been a Distinguished Lecturerof the IEEE Circuits and Systems Society in 2003 and 2004. His re-search interests lie in the fields of digital signal and image process-ing, especially signal compression, digital television, wavelet trans-forms, mathematical morphology, and applications to telecommu-nications. He is a Senior Member of the IEEE.

Marco A. M. Rodrigues was born in Riode Janeiro, Brazil, in 1964. He received theEngineering degree in electronics, the M.S.and the D.S. degrees in electrical engineer-ing from the University of Rio de Janeiroin 1986, 1991, and 1999, respectively. Hehas worked at the Electric Power Research

Center (CEPEL) in Rio de Janeiro, Brazil,since 1987, in data acquisition systems de-sign, software design, algorithms for dataanalysis, and control and signal processing applications related topower systems. He is also an Invited Professor in a postgraduatecourse in protection for power systems, held at the University ofRio de Janeiro. His current research interests are signal process-ing, power system measurements, oscillographic analysis automa-tion, and power system protection systems. Dr. Rodrigues is SeniorMember of IEEE and Member of Cigre (Conseil International desGrands ReseauxElectriques) and of SBrT (the Brazilian Telecom-munications Society). He participated in the steering committee ofthe Brazilian Protection and Control Technical Seminary (STPC)in 2003 and 2005.

Paulo S. R. Diniz was born in Niteroi,Brazil. He received the Electronics Eng. de-gree (cum laude) from the Federal Univer-sity of Rio de Janeiro (UFRJ) in 1978, theM.S. degree from COPPE/UFRJ in 1981,and the Ph.D. degree from Concordia Uni-versity, Montreal, PQ, Canada, in 1984, allin electrical engineering. Since 1979, he hasbeen with the Department of ElectronicEngineering (the Undergraduate Depart-ment), UFRJ. He has also been with the Program of Electrical En-gineering (the Graduate Studies Department), COPPE/UFRJ, since1984, where he is presently a Professor. He wrote the books Adap-tive Filtering: Algorithms and Practical Implementation, Springer,

Third Edition 2007, and Digital Signal Processing: System Analy-sis and Design, Cambridge University Press, Cambridge, UK, 2002(with E. A. B. da Silva and S. L. Netto). He is also a Fellow of IEEEandhas served as an Associate Editor for several Journals. He servedas Distinguished Lecturer of the IEEE Signal Processing Society andreceived the 2004 Education Award of the IEEE Circuits and Sys-tems Society.


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EURASIP JOURNAL ONADVANCES IN SIGNAL PROCESSING

Special Issue on

Wireless Cooperative Networks

Call for PapersMotivations

Cooperative networks are gaining increasing interest fromICT society due to the capability of improving the perfor-mance of communication systems as well as providing a fer-tile environment for the development of context-aware ser-vices.

Cooperative communications and networking is a newcommunication paradigm involving both transmission anddistributed processing promising significant increase of ca-pacity and diversity gain in wireless networks, by counteract-ing faded channels withcooperative diversity.

On one hand, the integration of long-range and short-range wireless communication networks (e.g., infrastruc-tured networks such as 3G, wireless ad hoc networks, andwireless sensor networks) improves the performance interms of both area coverage and quality of service (indeedrepresenting a form of diversity reflected in a greater capacityand number of potential users). On the other hand, the coop-eration among heterogeneous nodes, as in the case of wire-

less sensor networks, allows a distributed space-time signalprocessing supporting, with a reduced complexity or energyconsumption per node, environmental monitoring, localiza-tion techniques, distributed measurements, and so forth.

The relevance of this topic is also reflected by numeroussessions in current international conferences on the field aswell as by the increasing number of national and interna-tional projects worldwide financed on these aspects.

List of topics

This issue tries to collect cutting-edge research achievementsin this area. We solicit papers that present original and un-

published work on topics including, but not limited to, thefollowing:

Physical layer models, for example, channel models(statistics, fading, MIMO, feedback)

Device constraints (power, energy, multiple access,synchronization) and resource management

Distributed processing and resource managementfor cooperative networks, for example, distributed

compression in wireless sensor networks, channel andnetwork codes design

Performance metrics, for example, capacity, cost, out-age, delay, energy, scaling laws

Cross-layer issues, for example, PHY/MAC/NET in-teractions, joint source-channel coding, separation

theorems Multiterminal information theory

Multihop communications

Integration of wireless heterogeneous (long- andshort-range) systems

Authors should follow the EURASIP JASP manuscriptformat described athttp://www.hindawi.com/journals/asp/.Prospective authors should submit an electronic copy of theircomplete manuscript through the EURASIP JASP Manu-script Tracking System at http://mts.hindawi.com/, accord-ing to the following timetable:

Manuscript Due November 1, 2007First Round of Reviews February 1, 2008

Publication Date May 1, 2008

GUEST EDITORS:

Andrea Conti, Engineering Department in Ferrara(ENDIF), University of Ferrara, 44100 Ferrara, Italy;[email protected]

Jiangzhou Wang, Department of Electronics, University ofKent, Canterbury, Kent CT2 7NT, UK;[email protected]

Hyundong Shin, Department of Radio CommunicationEngineering, School of Electronics and Information, KyungHee University, Gueonggi-Do 449-701, South Korea, Korea;[email protected]

Ramesh Annavajjala, ArrayComm Inc., San Jose,CA 95131-1014, USA;[email protected]

Moe Win, Department of Aeronautics and Astronautics,Massachusetts Institute of Technology, Cambridge, MA02139, USA; [email protected]

Hindawi Publishing Corporation

http://www.hindawi.com
http://www.hindawi.com/journals/asp/http://www.hindawi.com/journals/asp/http://mts.hindawi.com/mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://mts.hindawi.com/http://www.hindawi.com/journals/asp/


17/17

Call for Papers

This first workshop on Cognitive Information Systems(CIS) aims at bringing together researchersfrom the machine learning, pattern recognition, signal processing, and communications communitiesin an effort to promote and encourage cross-fertilization of ideas and tools. The focus of the first CISworkshop will be on Cognitive Radios.

The first workshop will take place in one of the worlds most beautiful and impressive places, theGreek island of Santorini.

The workshop is sponsored by the International Association for Pattern Recognition (IAPR) and inparticular the Signal Analysis and Machine Intelligence Technical Committee. The workshop willfeature keynote addresses and technical presentations all of which will be included in theregistration. Papers are solicited for, but not limited to, the following areas:

Learning theory and modell ing

Bayesian learning and models

Graphical and kernel methods

Adaptive learning algorithms

Ensembles: committees, mixtures, boosting, etc.

Data representation and analysis: PCA, ICA, CCA, etc.

Other related topics

Cognitive radios

Cognitive component analysis -- Blind source separation, ICA, etc.

Cognitive dynamic systems

Distributed, cooperative, and adaptive processing Other related topics

Plenary Speakers:

Prof. Simon Haykin (MacMaster Univ., Canada)

Prof. Jose Principe (Univ. of Florida, USA)

Prof. Ali Sayed (Univ. Of California, USA)

Prof. Bernhard Scholkopf (Max Plank Inst., Germany)

CIS2008 webpage: http://cis2008.di.uoa.gr./

Paper Submission Procedure

Prospective authors are invited to submit a double column paper of up to six pages using theelectronic submission procedure described at the workshop homepage. Accepted papers will bepublished in a bound volume by the IEEE after the workshop and a CDROM volume will bedistributed at the workshop.

Co-Chairmen:

Simon Haykin (Canada)Sergios Theodoridis (Greece)

Program Co-Chairs

Tlay Adali (USA)Eleftherios Kofidis (Greece)

Programme Committee Members

Fernando Perez Cruz (U.S.A)

Merouane Debbah (France)Konstantinos Diamantaras (Greece)Deniz Erdogmus (USA)Jeronimo Arenas Garcia (Spain)

Georgios Giannakis (USA)Konstantine Halatsis (Greece)

Anil Jain (USA)Michael Jordan (USA)

Jan Larsen (Denmark)Danilo Mandic (UK)

David Miller (USA)Sanjit Mitra (USA)

Anant Sahai (USA)Mihaela van der Schaar (USA)Johan Seulkens (Belgium)Konstantinos Slavakis (Greece)

Joos Vandewalle (Belgium)

Schedule

Submission of full paper:January 5, 2007

Notification of acceptance:March 5, 2007

Camera-ready paperand author registration:March 15, 2007

2008 IAPR Workshop onCognitive Information Systems

June 9-10, 2008, Santorini, GreeceSponsored by the Intl. Association for Pattern Recognition

in Cooperation with EURASIP and IEEE

atomic decomposition

Documents