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One simple improvement of the thermal impedance will be tobond
these devices pside down. Thus a flipchip bondingscheme is required
to allow separate current injection into th egain and grating
sections. Another option is a long gratingsection where the
increased volume of the p n junction sup-presses heating
effects.The published results for buried heterostructure DBR
lasersreport CW tuning ranges of up to lOnm indicating thatthermal
problems do not dominate. Thus it remains to be Seenwhether the
thermal impedance in ridge waveguide DBRlasers can be reduced in a
modified structure and henceachieve the wide tuning ranges reported
for buried hetero-structure DBR lasers.A ck no w l ed g ment s :
The authors are grateful to S. Judge, T.Spooner, B. Quartermain, D.
Ranasinghe, M. Harlow, I. Reidand W. Duncan for the fabrication of
these lasers.n. SUNDARESANI. D. HENNlNG 24th July 1991British
Telecom Research Laboratories,Martlesham Heath, Ipswich, IP S 7R
EUnited KingdomReferences1 KOCH, T. L., KOREN, U,, NALL, R. P.,
BURRUS, c. A.,and MILLER, B. I.:Continuously tunable 1 . 5 ~
ultiple-quantum-well GaInAs/GaInAsP distributed-Bragg-reflector
lasers, Electron. Lett., 1988,24, pp. 1431-14332 h ~ u n ~ T *
,.,WTO, I., and KOBAYASHI,.: Tuning ranges for 1 . 5 ~wavelength
tunable DBR lasers, Electron. Lett., 1988, 24, pp.
511-5193 SUNDAIWAN, H.,and FLETCHW, N.c.: Direct observation of
shotnoise in linewidth broadeningofDBR lasers,Electron. Lett.,
1990,26, pp. 2004-2005
VECTOR MED IA N D EB LU R R IN G F ILTERFOR COLOUR I M A G E R E
S T OR A T IO NIndexing terms: Filters, Signal processing, Image
processingA new technique is described which couples median
filteringand image deblurring techniques to filter noisy
imageswithout introducing defocusing side effects. To deal
withcolour images a vector median filtering procedure is pro-posed.
Using this procedure a better edge preserving filter isobtained
which does not introduce new colours. The deblur-ring operation is
performed componentwise by fitting anARMA model to the image. The
AR part of the model esti-mates the image and the MA part estimates
and blurringfunction. Finally the MA part is inverted and applied
toremove the blur introduced by the median filter.
Introduct ion: Colour image data bases are becoming moreand m
ore important in many different application fields suchas in
artwork acquisition and documentation, museum man-agement, textile
product da ta bases, high quality printing etc.A fundamental topic
when dealing with colour image archivesis fidelity to the original
objects and scenes. An importantpoint to this end is the
development of suitable tools capableof filtering the images
without blurring them and withoutchanging their original chromatic
contents. Classical noisereduction techniques are problematic in
both these aspectsbecause they smooth the original image and change
its col ourspan. Even by using edge preserving filters, such as
medianfilters, the final result is a badly smoothed image where
finespatial and chromatic details, which can be very useful
inscientific analysis, are lost. For these reasons, in this letter
atwo step processing chain is presented which employs a vecto-rial
extension of an edge preserving filter followed by adeblurring
algorithm that compensates for the bl ur generatedduring the
initial filtering step.Vector median f i l tering: A
straightforward generalisation ofmedian filters to the colour image
case is the componentwise
application of the filter itself to each colour band.
Neverthe-less such a technique adds new colours to the original
imageand this effect, in general, cannot be tolerated (for
examplewhen dealing with artwork pictures). This is why a
gener-alisat ion of the usual scalar median lilter is proposed
whichworks directly on colour vectors and gives better results
interms of spike noise suppression capabilities.++2Fig. 1 Signal
beforefiltering
Given N vectors (say x1 .. xN). inside a rectangularwindow, the
output of the vector median filter is defined bythe following
equations:(1)M,{x, x2 ... XN } = x Y M
withXYM E(X1, x2 ,. XN}N N
i = 1 i = I1 IxYM- xillL 5 1 Ixj- illL i = 1, 2 .. .N (2)where V
M , denotes the vector filtering operator. I n practice, ifa
suitable L metric is stated, the output of the filter is thepoint
in the window which minimises the sum of the L dis-tances from the
other N-1 points. If there are many pointsthat satisfy eqn. 2 the
output is determined according to theirposition in the window; a
common solution is to favourchoice of the central points. It is
important t o note that eqn. 2depends on the metric used to
calculate the distance betweentwo points.The use of different
metrics has two important effects: first achange in computational
speed, and secondly a different finalfiltering quality. From the
first point of view the squaredEuclidean norm (L:) s the best one
because a fast algorithmexists for its calculation. The L, norm is
relatively fast becauseit uses only algebraic sums and absolute
values. Finally theL,norm, which involves square root operations,
is the slowestone.As regards the filter effectiveness, the previous
ranking scaleis reverted to, the L , norm being the best one and
the L$ heworst. This is because the L$ orm is the closest to a
simpleaverage operation applied to the points in the window.
4I.c2Fig. 2 Filtered signal
Two major features of vector median filtering, as opposedto
componentwise scalar filtering, must be emphasised: first
itproduces colour closed operations (i.e. no new colour
isgenerated), and secondly it allows a better spike noise
filtering.Colour closed operations are a direct consequence of
thevector median filter definition, and its good filtering
propertiescan be better understood considering the following
example,that, for the sake of simplicity, refers to a 1-D signal in
2-Dspace. The signal consists of a step function with a noise
spikein the first component of the vector. If the signal is
filteredcomponentwise by means of a 5 x 5 pixel window, only
thespike is shifted leading to an overlap between the originalsteps
(Fig. 2). It is easy to see that this is not the case with anL,
vector filter that completely eliminates the spike (Fig. 3).
&47128613)
Fig. 3 &filtered signalELECTRO NICS LETTERS l o th October
1991 Vol. 27 No . 21 1899
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Deblurring algori thm: It is very difficult to extend
deblurringprocedures directly to a vector space; this is why a
com-ponentwise ARMA deblurring method has been adopted tocompensate
for the smoothing.The aim of the deblurring step is to estimate the
pointspread function ( PSF) of the unknown degrading system.
Theimage is described through a nonsymmetric half plane(NSHP)
models(m, n) = 1 dk,M m - , n - 0 + w(m, n ) ( 3 )
where 0I < M ) u - M 5 IO,1 5 l I ) } and w(m, n ) is a zero
mean white Gaussian noisewith variance U The observed image is a
distorted version ofHm, n) . If we model the distortion as an FIR
noncausalsystem, the resulting image will be
(k. ) E C
C = {( lI I ,
r ( m, n ) = 1 (i, ) s ( m - , n - ) + v(m, n ) (4)11, j ) C
where C= { - H 5 i 5 H , - H I j I H} and v(m, n) is addi-tive
noise. If we assume that the additive noise is negligible,
bysubstituting eqn. 3 into eqn. 4 we obtainr(m, n)= 1 (k , 0r(m- ,
n - )
(k, ) E C+ h(i, ) w ( m- , n - ) ( 5)(i . ) E CThe observed
image may then be modelled by an ARMAmodel, where the AR part is
based on the image modelparameters and the MA part is based on the
blur parameters.The parameters and the order of the ARMA model must
bedetermined. A least squares estimate of the parameters isachieved
by searching the minimum of the quantity Zw(m, n ).When the
function H(o,,2 ) s decomposed into a four quad-rant
fact~risation~~he previous minimum can be achievedby means of a
recursive procedure. This is possible if H(o,,w 2 )2 0 (e.g. a
Gaussian blurring function). Once the param-eters of the MA part
have been determined, the deblurringstep is completed by using such
parameters in inverse filteringthe observed image.E x p er i ment a
l resu l t s : To evaluate the algorithm previouslydescribed (a
vector median filter followed by an ARMAdeblurring technique), some
experiments have been performedby using art images. When dealing
with artwork images it ismandatory to filter the acquisition noise
without blurring theimage themselves and without generating new
colours; hencethe proposed processing chain is particularly
suitable.
Fig. 4 Original imageFig. 4 shows the original image before
noise filtering. Byapplying a 3 x 3 vector median filter the result
shown in theupper left part of fig. 5 is obtained. Evidently some
noise isremoved and some blur is generated. By
componentwiseapplying the ARMA deblurring algorithm outlined
previously,the result shown in the upper right part of fig. 5 is
obtained,where the blur effect is almost completely eliminated.
Similarresults have been obtained by using a 5 x 5 vector
medianfilter (lower part of Fig. 5).
Conclusions: A technique which allows the filtering of noise
incolour images with a significant reduction of the image blur
has been described. Such a result has been achieved by chain-ing
a vector median filter and an ARMA deblurring tech-nique. Vector
median filters allow good results in terms ofspike noise
suppression and ensure colour closed operations.
,Fig. 5 Vec tor median filtered images before (left) and after
(rig ht)deblurringThe deblurring part of the algorithm can be
applied to theluminance component of the image if colour closed
operationsare required. In this Letter the blurring function has
beenassumed to be positive and symmetric to achieve four quad-rant
factorisation. When this hypothesis does not hold, onlyan
approximation to the correct PSF can be obtained and thisreduces
the final quality of the deblurred image.F. ARGENT1M. BARN1V.
CAPPELLINIA. MECOCCIUniuersita di Firenze, Dipartimento di
Ingegneria Elettronica, Via S.Marta, 3-50139 Firenze,
ItalyReferences
15th July 1991
ASTOLA, I., HAAVISTO,., and WO , Y. : Vector median
filters,Proc. IEEE, 78, (4), April 1990TEKALP, A. M., KAUFMAN, H.,
and WOODS,. w.:Identification ofimage and blur parameters for the
restoration of noncausal blurs,IEEE Trans., 1986,A S P - 3 4 , (4),
pp. 963972EKSTROM, M. P., and WOODS,. P.: Two-dimensional pectral
factor-ization with applications in recursive digital filtering,
IEEETrans.,April 1976,A S P - 2 4 , pp. 115-128ROGERS, D. F.:
Procedural elements for computer graphics(McGraw Hill 1985).
PH O TO VO LTA IC G A TE B IA S IN G ED G EEFFEC T IN G aA s
MESFETsIndexing terms: Gallium arsenide, Field-effect
transistors,Semiconductor devices and materialsA new effect in
planar GaAs MESFETs, whereby a sharpincrease in optical gain at the
transistor edges occurs, isreported for the first time. This gain
effect only appears whena large resistor is inserted in series with
the gate, to producethe conditions for photovoltaic gate biasing.
The mechanismfor increased gain at the edges is suggested to be due
tocarrier photogeneration in the substrate that is
subsequentlycollected by the gate. Application in the area of X-Y
ddress-able transistor array imagers is proposed.
The photoresponse of the GaAs MESFET has received muchattent ion
due to the potential application of the GaAsMESFET in high speed
optoelectronic communications,OEICs and optical tuning of microwave
devices. Variousoptical gain mechanisms have been reported,
including photo-voltaic gate biasing. This effect occurs when the
gate photo-current flows through an external series gate resistor
R,, thusincreasing the gate voltage and hence drain current.
Toproduce a significant increase in drain current, a large R ,1900
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