Journa2 of Harbin Institute of Technolo (New Series),Vo!.15,No.1,2008
Speed-up for N-FINDR algorithm
WANG Li guo ,ZHANG Ye
王 立 国 . 张 晔
(1.Dept.of Information Engineering,Harbin Institute of Technology,Harbin 150001,China;
2.College of Information and Conmunications Engineering,Harbin Engineering University,Hanbin 150001,China)
Abstract:N—FINDR is a very popular algorithm of endmember(EM)extraction for its automated property and
high出 ciency. Unfortunately,innumerable volume calculation,initial random selection of EMs and blind
searching f0r EMs lead to low speed of the algorithm and limit the applications of the algorithm.So in this paper
two measures are proposed to speed up the algorithm.One of the measures is substituting distance calculation
for volume calculation.Thus the avoidance of volume calculation greatly decreases the computational cost.The
other measure is resorting dataset in terms of pixel purity likelihood based on pixel purity index(PPI)concept.
Then.initial EMs can be selected wel1.founded and a fast searching for EMs is achieved.Numerical experi—
ments show that the two measures speed up the original algorithm hundreds of times as the number of EMs is
more than ten.
Key words:endmember extraction;N—FINDR
CLC number:TP75 Docum ent code:
algorithm;PPI algorithm ;spectral unmixing
A Article ID:1005-9113(2008)01-0141-04
In resent years hyperspeetral remote sensing has been
applied in many fields and the corresponding processing
techniques of hyperspectral images(HSI)have been de-
veloped greatly. In HSI,mixed pixels are a mi xture of
more than one distinct substance.an d thev exist for one of
two reasons.First,some different ma terials may occupy a
single pixel for the low spatial resolution of HSI;Second,
distinct materials are combined into a homogeneous mi x-
ture.In these cases,the resulting spectrum wi11 be some
composite of individual spe ctra.One of the most important
HSI processing techniques is spectral unmixing which
aims at analyzing of mi xed pixels. Spectral unmi xing is
the decomposition of a mixed pixel into a collection of dis-
tinct endmembers (EMs) th a set of fractional abun-
dances which indicate the proportion of each EM¨j. As
the basic step of spectral unmi xing,EM extraction is aim-
cial for computing fractional abundances accurately. In
this case.a number of EM extraction techniqu es -43 have
been propo sed over the past decade.
Pixel purity index (PPI)technique ,based on
the geometry of convex sets,is one of the most Success-
ful EM extraction algorithms.The algorithm projects
every data to a large number of random N—dimensional
vectors(called“skewers”)。along which positions are
pointed out. The points that correspond to extrema in
the direction of a skewer are tallied and the pixels with
the highest tallies are considered the purest ones.A re-
duction of dimensionality is first applied to the original
dataset by using the minimum noise fraction (MNF)
transformation.The shortcoming of PPI algorithm is that
it does not identify a final list of EMs. Th e selected
pure pixels should be compared with library spectra.
Another famous EM extraction technique is N.FIN.
DR algorithm L which is a fully automated identifica.
tion of EMs from multidimensional data space,and re.
duction of dimensionality is also necessary . Th e algo.
rithm is described in the next section. In this algo.
rithm ,the most time consuming part is a trial volume
calculation. Random selection of initial EM s is vulnera.
ble of local optimization,and blind searching for final
EMs leads to a very low speed of the algorithm .
In order to get an automated and efficient EMs ex.
traction algorithm ,two important measures are proposed
to speed up N-FINDR algorithm :substituting distance
calculation for volume calculation:resorting dataset in
terms of pixel purity likelihood based on PPI concept.
1 Original N—FINDR Algorithm
After MNF transformation of original data set,the
spectra of pixels in transform ed space are denoted as s£
(t=1,2,…,M).LetNbe the number of dimensional-
ity of these spectra,then they may be modeled in term s
of a linear combination of(N +1)EM vectors e (i=
1,2,… ,Ⅳ +1),i.e.
=
∑ t
= l
N+1
s.t.∑ t =1,0≤ t ≤1,t=1,2,…,M,(1)
Received 2oo5—09 —15.
Sponsored by the National Natural Science Foundation of China(Grant No.60402025 and 60302019)
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