afastandefficientclutter rejection algorithm for sar imageryash/murthy_aero.pdf · speckle noise...

A Fast and Efficient Clutter

Rejection Algorithm for SAR

Imagery

K. RAMACHANDRA MURTHY

SAMBHUNATH BISWAS

ASHISH GHOSH, Member, IEEE

Indian Statistical Institute

A clutter rejection scheme is proposed for synthetic aperture

radar (SAR) imagery based on two-stage two-dimensional

principal component analysis (two-stage 2DPCA) followed by

a bipolar eigenspace separation transformation (BEST) and a

multilayer perceptron (MLP). For this, we have examined and

analyzed four different algorithms. They are based on principal

component analysis (PCA) both in one dimension (conventional

PCA) and in two dimension with three different forms (2DPCA,

alternative 2DPCA and two-stage 2DPCA), followed by BEST

and MLP in each case. Feature extraction in different cases is

carried out using respective PCA scheme. Each algorithm uses

the BEST to further reduce dimensionality and enhance the

generalization capability of the classifier. Classification between

target chips and clutter chips is finally made through an MLP

classifier. Experimental results on MSTAR public release database

of SAR imagery are presented. Comparison of all the 2DPCA

algorithms with an existing technique shows improvement both

in performance and time. Moreover, all the 2DPCA algorithms

compute eigenvectors and eigenvalues of image covariance

matrix accurately and very efficiently with respect to time, and

further reduces the effect of noise better than that in the case of

PCA. Comparison reveals the fact that two-stage 2DPCA-based

algorithm is the best (both in performance and time) between all

algorithms.

Manuscript received December 6, 2010; revised November 15,

2011, August 9, 2012, and January 2, 2013; released for publication

January 30, 2013.

IEEE Log No. T-AES/49/4/944709.

Refereeing of this contribution was handled by P. Lombardo.

This work was funded by the U.S. Army through the project

“Processing and Analysis of Aircraft Images with Machine

Learning Techniques for Locating Objects of Interest,” Contract

FA5209-08-P-0241.

Authors’ address: Machine Intelligence Unit, Indian Statistical

Institute, 203 B. T. Road, Kolkata, West Bengal 700108, India,

E-mail: ([email protected]).

0018-9251/13/$26.00 c° 2013 IEEE

I. INTRODUCTION

Military surveillance systems rely on a varied

number of sensor information to locate, identify, and

track oppositional forces. This task becomes more

difficult for a large number of potential targets when

they are found over large land areas. An automatic

target recognition (ATR) [4] system appears as one

of the solutions [5—8] for this problem. A typical

ATR system is as shown in Fig. 1. One of the main

sensors used in ATR systems is the synthetic aperture

radar (SAR) [9, 10]. The SAR is an airborne or

orbital active sensor, most of which operates in

the microwave frequency range. This characteristic

plays a significant role in providing substantial

advantages in SAR, carried all day and in all weather.

However, SAR images suffer from reflections from

the background and other objects. Echoes from the

surface exhibit a noise-like behavior that might hinder

target detection and/or introduce false alarms. These

clutter returns can be moduled as the superposition

of a slowly varying, spatially correlated component

(texture) and multiplicative noise (speckle), as

illustrated in [10].

Fig. 1. Block diagram of three-stage SAR ATR system. Input

consists of SAR imagery representing many square kilometres of

terrain and potentially containing several targets of interest; output

consists of locations and classification labels for these targets.

This article proposes improved version of clutter rejection stage.

The target detection module is certainly one of

the most important components in a SAR-based

ATR system, as the whole system may not function

properly without an excellent detector [11, 12]. A

common problem of the target detection algorithm is

false alarms (clutter), which become more prominent

when high accuracy in target detection is sought,

causing computational burden and degradation in

performance of SAR ATR [13—15]. Potential targets

identified in the detection stage are passed to a clutter

rejection stage, which is intended to reject further

false alarms based on some simple properties of

the potential target, including both geometrical and

electromagnetic effects [10]. Most false alarms are

derived from man-made objects, though some may

arise from natural clutter [10]. This necessitates the

use of an effective clutter rejection scheme. Unless

the excessive false alarms are reduced substantially,

the subsequent classifier (target recognizer) in the

SAR-based ATR system may not perform well.

The existing automatic clutter rejection technique

in [16] used a bipolar eigenspace separation

transformation (BEST) for feature extraction and a

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 49, NO. 4 OCTOBER 2013 2431

multilayer perceptron (MLP) for clutter rejection in

forward looking infrared (FLIR) images. Eigenvectors

are computed from the normalized, clipped, and

scaled training data for a subspace projection using

the BEST method. The resulting projected values

are then fed to an MLP for training to perform a

two-class classification. Thus, in their experiment

[16] computation needed to carry out the BEST is

more than that required for the subsequent MLP-based

classifier. Different eigenspace transforms are also

used in the field of clutter rejection and target

detection [17—20].

As clutters have similar signature and

characteristics to those of targets, the decision

boundary between these two classes will be highly

nonlinear and hence it will be much more difficult to

approximate the boundary. To simplify the decision

boundary and the further reduction of dimensionality,

one therefore needs a subspace projection on the

input data. Preprocessing of the input data with

eigenspace separation transform (EST) [2] allows

reduction of the size of a neural network while its

generalization accuracy is enhanced as a binary

classifier [2]. In the case of image data, EST may

not drastically decrease the size of the concerned

neural classifier and hence, the time complexity

may not also be considerably reduced. To get rid of

these difficulties, we have used BEST having equal

number of dominant eigenvectors corresponding

to both positive and negative eigenvalues [16].

But for SAR images, due to strong correlation and

multiplicative speckle noise, behavior of BEST is

unpredictable, i.e., it might generalize or degrade the

performance of a subsequent classifier. Moreover,

correlation difference matrix and its eigenvectors in

BEST may not be evaluated accurately because of

huge dimensional input space. In our experiments

BEST alone fails in generalizing the capability of

the classifier; whereas, by reducing the effect of

speckle noise and decorrelating the feature space,

generalization improves a lot. Therefore, one can

use a feature extraction technique like principal

components analysis (PCA) to reduce the effect of

speckle noise.

PCA appears to have one fundamental use in SAR image

series i.e., speckle noise reduction. From this perspective some

significant advantages accrue: (i) identification of dominant

spatio-temporal modes of backscattering within the scene; (ii)

partitioning of the variance into a set of discrete images that

can be submitted to segmentation and classification algorithms;

and (iii) production of a high spatial resolution, low spatial

noisy image that can serve as a template for georeferencing and

multi-sensor fusion [21].

We have used two-dimensional PCA (2DPCA)

[1] for this purpose because the classical 1D-PCA

always transforms a 2D image matrix into a 1D image

vector. This usually leads to a high-dimensional vector

space, and hence it becomes difficult to evaluate

the covariance matrix accurately. In such cases the

eigenvectors can be calculated efficiently using

the singular value decomposition (SVD) [22, 23]

technique, where the process of generating the

covariance matrix is actually avoided. However, this

does not imply that the eigenvectors can be evaluated

accurately in this way, since the eigenvectors are

determined by solving a huge set of linear equations

with a huge number of unknowns [24]. Also for a

high-dimensional matrix, SVD may be very expensive.

This problem has been reflected in our experimental

results also. 2DPCA avoids this problem and extracts

features from the image matrix directly. Furthermore,

it has been reported in [1] that 2DPCA constructs the

covariance matrix directly from 2D image matrices

rather than 1D vectors, and evaluates the covariance

matrix more accurately. Even more, in this case the

size of the covariance matrix is much smaller. But one

of the drawbacks of 2DPCA is that it only eliminates

the correlations between rows, necessitating more

features, leading to large storage requirements and

more cost (in time) for classification. One can easily

note the equivalence of 2DPCA to line-based PCA

as proved in [25]. Alternative 2DPCA (A2DPCA)

has been proposed in [26], which is also poor in

reducing dimensionality, because it works in the

column direction only. However, two-stage 2DPCA

eliminates correlation between rows as well as

columns achieving more reduction in dimensionality

and has been used for efficient face recognition

and representation [26]. Since a SAR image has

texture correlation in both directions (row and column

wise), one can think about the novel use of two-stage

2DPCA in the area of target/clutter recognition.

Feature extraction as well as recognition based

on subspace projection, might also be an option,

such as Fisher’s linear discriminant analysis (LDA)

technique [27].

In this article we propose three cascaded subspace

projection schemes, i.e., 2DPCA, A2DPCA, and

two-stage 2DPCA along with BEST. Finally, based

on experimental results, we have concluded that the

cascading of two-stage 2DPCA along with BEST

is superior to the other two cascades as well as the

method in [16]. The projected data in the subspace

are used to classify actual targets from clutters

through the well-known MLP classifier [3, 28]. To

compare with [16], we have implemented PCA,

2DPCA, A2DPCA, and two-stage 2DPCA along with

BEST and MLP in each case. The method based on

two-stage 2DPCA is seen to be the best with respect

to classification accuracy and time.

The rest of the paper is organized as follows.

Section II describes the three algorithms that we have

analyzed to select the proposed method. Section III

presents the experimental results, comparisons, and

discussions. Finally conclusion is made in Section IV.

2432 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 49, NO. 4 OCTOBER 2013

Fig. 2. Block diagram of proposed algorithms.

II. DESCRIPTION OF THE PROPOSED ALGORITHMS

In this section we describe the proposed technique.

Initially, we have examined and analyzed four

different new algorithms and depending on their

performance and merits, we have chosen the best one.

These algorithms are based on 2DPCA, A2DPCA, and

two-stage 2DPCA. BEST and MLP have been used in

conjunction with each algorithm. The 2DPCA, in fact,

uses 2D matrices against the standard PCA, based

on 1D vectors, to ensure requirement of less time

for computation and better features for classification

[1]. As BEST compresses data that can be suitably

used to improve the performance of a binary classifier,

we have incorporated this in our algorithm. In one

of the cases we have implemented a 1D PCA-based

algorithm for comparison purpose. We briefly describe

all 2DPCA-based algorithms in the following sections.

The block diagram of the proposed algorithms can be

found in Fig. 2.

A. Algorithm 1

Let us first briefly describe Algorithm 1 based

on 2DPCA. Let A be an m£ n random image matrix

and X 2 Rn£d a matrix with orthonormal columns,n¸ d. Projecting A onto X, we can write the projectedmatrix Y = AX, Y 2 Rm£d. The total scatter J(X) isthe trace of the covariance matrix of the projected

samples, i.e.,

J(X) = trfE[(Y¡E[Y])(Y¡E[Y])T]g= trfE[(AX ¡E[AX])(AX ¡E[AX])T]g= trfXTE[(A¡E[A])T(A¡E[A])]Xg: (1)

Here E[:] denotes the expected value and T denotesthe transpose. The image covariance matrix G =E[(A¡E[A])T(A¡E[A])] is an n£ n nonnegativedefinite matrix. For M training chip images (potential

target chips, i.e., true target and clutter chips), Ak(k = 1,2, : : : ,M), each of size m£ n, the averageimage is

A=1

M

Xk

Ak:

Hence, G can be evaluated as

G =1

M

MXk=1

(Ak ¡ A)T(Ak ¡ A): (2)

Therefore,

J(X) = tr(XTGX): (3)

Maximization of J(X) is equivalent to minimization ofcorrelation between the features; and the maximum

value of J(X) can be obtained from Xopt, whichconsists of the orthonormal eigenvectors X1, : : : ,Xdof G corresponding to the d largest eigenvalues, i.e.,Xopt = [X1, : : : ,Xd]. As the size of G is only n£n,computation of its eigenvectors is very easy. Also, like

in PCA the value of d can be controlled by setting athreshold μ, according to (4)Pd

i=1¸iPni=1¸i

¸ μ: (4)

Note that ¸1,¸2, : : : ,¸n are the n dominant eigenvaluesof G. Algorithm 1 is the cascading of 2DPCA along

with BEST followed by an MLP. Schematically,

Algorithm 1 is described in Fig. 2 and its time

complexity is O(nm2 +M2dm), where O(nm2) isthe time complexity of 2DPCA and M2dm is thetime complexity of BEST, which is a biquadratic

time complexity. It is straightforward to observe that

m and n are fixed and M2À nm2, therefore nm2 isnegligible. PCA- and BEST-based algorithms are also

biquadratic time algorithms with time complexity

of O(M2nm)). One main advantage of Algorithm 1

is that it is efficient for both noise reduction and

simplification of decision boundary. These two criteria

are responsible to fasten the convergence of MLP. On

the other hand, as PCA does not preserve the class

discrimination information and the BEST (existing)

based algorithm does not reduce speckle noise, both

will require more time to approximate the decision

boundary. As a result, Algorithm 1 is faster than PCA-

and BEST-based algorithms.

B. Algorithm 2

Algorithm 2 uses A2DPCA and examines its

merits over Algorithm 1. A2DPCA is merely an

alternative definition of 2DPCA because 2DPCA

works in the row direction of images, whereas

A2DPCA works in the column direction of images.

One can also construct the covariance matrix Gconsidering the outer product between column vectors

of images. This only needs a straightforward and

minor modification of (1). For this we consider Ak =

[(A(1)k )(A(2)k ) : : :(A

(m)k )] and A= [(A(1))(A(2)) : : : (A(m))],

where A(j)k and A(j) denote the jth column vector of Akand A, respectively. An alternative definition for imagecovariance matrix G therefore becomes

G =1

M

MXk=1

nXj=1

(A(j)k ¡ A(j))(A(j)k ¡ A(j))T: (5)

Let Z 2 Rm£q be a matrix with orthonormalcolumns. The orthonormal columns are eigenvectors

of the matrix G. Projection of the random matrix Aonto Z yields a matrix B = ZTA of size q by n.

MURTHY, ET AL.: A FAST AND EFFICIENT CLUTTER REJECTION ALGORITHM FOR SAR IMAGERY 2433

The optimal projection matrix Zopt can be obtainedby computing the eigenvectors Z1, : : : ,Zq of G, derivedfrom (5), corresponding to the q largest eigenvaluesof G, i.e., Zopt = [Z1, : : :Zq]. The value of q can bedetermined by setting a threshold μ in (4). Because theeigenvectors of the matrix G reflect the informationbetween columns of images, the A2DPCA is found

to work in the column direction of images. Thus,

Algorithm 2 differs from Algorithm 1 mainly in the

construction of covariance matrix G. Fortunately,this change in construction of the covariance matrix

leads to a significant positive gain in time, on our

data particularly. This is clearly demonstrated in our

experimental results. Schematically Algorithm 2 is

similar to Algorithm 1 (Fig. 2). Similarly, Algorithm 2

also has biquadratic time complexity of (O(M2nq+n2m)) and is faster than PCA and BEST (existing)based algorithms.

C. Algorithm 3

Algorithm 3 is based on two-stage 2DPCA.

2DPCA and A2DPCA work in the row and column

direction of images, respectively. Let us assume that

the two projection matrices X and Z are obtainedfrom Algorithm 1 and Algorithm 2, respectively. By

projecting an arbitrary input image A onto X and Z,we get an output C as shown in (6):

C = ZTAX: (6)

Algorithm 3 is similar to the above algorithms, except

2DPCA/A2DPCA is replaced by Two-Stage 2DPCA

(Fig. 2). The time complexity of Algorithm 3 is

O(M2dq+ n2m+ nm2), which is also biquadratic.Even though two-stage 2DPCA has to compute two

projection matrices X and Z, better dimensionalityreduction will be achieved. So the subsequent BEST

and MLP are faster than that of Algorithms 1 and 2.

Therefore, Algorithm 3 is expected to be faster than

Algorithms 1 and 2.

These projected features undergo the BEST

for adequate separation between two classes in the

subspace, e.g., the target and clutter. Finally, an MLP

classifies the targets. Algorithm 3 is also described

schematically in Fig. 2.

Note that both 2DPCA [1] and BEST [16] are

feature extraction methods, but they are used with

different objectives in our case. In the case of the

2DPCA family, the objective is to minimize the

energy loss to reduce noise, while the objective

of BEST is to further reduce dimension and

preserve adequate separation between classes in the

projected subspace. This adequacy in separation is

achieved through the consideration of both positive

and negative eigenvalues in BEST, contrary to

either positive or negative eigenvalues as done in

EST [2].

Fig. 3. A few samples of target and clutter chips. (a) Targets.

(b) Clutters.

III. EXPERIMENTAL RESULTS AND DISCUSSION

In order to examine the performance of the

proposed algorithm, and the existing (BEST-based)

algorithm mentioned in [16], we have used standard

SAR image data collected by DARPA and Wright

Laboratory as a part of the Moving and Stationary

Target Acquisition and Recognition (MSTAR)

program [29]. The targets in the MSTAR database

contain three T72 main battle tanks (MBT), three

BMP2 armored personnel carriers (APC), a BTR70

and a SLICY canonical target. The database also

contains clutter scenes at the Redstone Arsenal,

Huntsville. The data consists of X-band SAR images

with 1 ft by 1 ft resolution measured in the spotlight

mode. The targets have been measured over the full

360± azimuth angles with an increment from 1±—5±

considering depression angles of 15±, 17±, 30±, and45±. The target data in the database is presented assubimage chips centered about the target and each of

these chips has a size of 128£ 128 pixels.From the MSTAR database we extracted clutter

chips of our interest and targets manually. Figures 3(a)

and (b) show a sample of clutter and target chips,

respectively. The potential target images, obtained

from the target detection stage, generally consist of

either a part of shadow, or a part of target and shadow,

or only a part of target, or background objects etc.

Previous research shows that this type of potential


target image, obtained from the detection stage, is the

main cause of a substantially large number of false

alarms. This ultimately results in a poor performance

of an ATR system on real-life data. In our analysis

we have used different types of clutters, namely

the SLICY canonical target, shadows (due to their

different rotations), shadows and a part of target,

only a part of target (MBT, APC, and BTR70), and

background objects (houses, buildings etc.) from

clutter scenes at the Redstone Arsenal, Huntsville,

from the MSTAR database. Thus, our analysis

includes a wide variety of clutter samples. The size of

these image chips is fixed at 51£ 41 pixels. The sizeof the target as well as the clutter chips are also the

same. We have considered 4000 target chips and 5945

clutter chips. The choice of the size of target/clutter

chips at 51£ 41 pixels has been made because themaximum size of the target present in the extracted

images is 51£41 pixels.To perform the experiment we have randomly

chosen 5% to 15% samples from each class and

extracted features through different techniques, already

mentioned in our algorithms, to train the standard

MLP, and we have computed the success rate.

Training has been carried out 50 times for a particular

sample size, while testing has been made with the rest

of the samples, and in each case the success rate has

been computed. All the three proposed algorithms are

compared with the existing (BEST-based) algorithm.

Note that we have also included 1D PCA in order to

check its performance against those of 2DPCA. Thus,

the entire PCA family members (1D as well as 2D)

are taken into consideration.

To extract the features efficiently, we have

preserved 95% energy information within the data of

all PCA family members. Dimensionality reduction,

on an average, was seen to be 963, 51£ 35, 41£ 30,and 30£ 35 features with PCA, 2DPCA, A2DPCA,and two-stage 2DPCA, respectively, from 51£41 features. Note that there is more reduction of

dimensionality in the case of A2DPCA compared

with 2DPCA because of different resolution in

row and column directions. To carry out the BEST

on extracted features, one can consider the most

dominant positive as well as the negative eigenvalues

with the corresponding eigenvectors for the projection

matrix. Figure 4(a) shows the plot of eigenvalues

of the correlation difference matrix in increasing

order for the existing (BEST-based) method, whereas

Fig. 4(b) shows the same for Algorithm 3. We have

considered the eigenvalues which are greater than

0.01 and less than ¡0:01, because the huge numberof eigenvalues in the interval (¡0:01,0:01) (Fig. 4)increases the network size and may subsequently

degrade the performance [16] and does not contribute

anything in enhancing the generalization capability of

a binary classifier. An MLP was selected with eight

hidden layers with ten nodes in each of them. The

Fig. 4. Eigenvalue numbers versus eigenvalues for existing

(BEST-based) and proposed algorithms. (a) Existing (BEST-based)

method. (b) Algorithm 3.

number of hidden layers and nodes in each layer was

decided through experimental observations for the best

results. The number of input nodes depends on the

number of features, i.e., the number of eigenvalues

considered through BEST.

Figure 5 shows the average success rate on

training data with varied sample size. It is observed

that in all the algorithms success rate (learning) does

not improve with increase in training size. For the

existing (BEST-based) algorithm, training performance

is good, but the test performance is found to be very

poor (Fig. 6). This is because the computation of a

huge correlation difference matrix and its eigenvectors

may involve loss of information, and the BEST

feature space is affected by speckle noise and so is

the subsequent classification. Clearly in the existing

(BEST-based) algorithm there is a downward trend

on increasing training data size and the same is also

reflected on test data. In the case of PCA, training


Fig. 5. Average success rate for different training sample sizes.

is found to be oscillatory in nature, but for other

cases it is not prominent. The performance on the

test data, in the case of PCA, shows only marginal

oscillation (almost unnoticeable). The reason for

this is the inaccuracy in computation of eigenvectors

for a huge covariance matrix and noise in the data.

Since the eigenvectors of a huge covariance matrix

are not computed correctly, it introduces some error.

The classifier, therefore, learns the decision boundary

under noisy environment and as a result, the decision

boundary can be assumed to be oscillatory. Because

of these reasons the performance of PCA on the test

data is poor and the small oscillation in the test phase

is due to the huge number of test data points. Note

that the existing algorithm (BEST-based) has better

performance compared with that of the PCA-based

algorithm for consideration of the bipolar nature of

eigenvalues.

Figure 6 shows the average success rate on test

data with varied sample size. The performance is

more or less the same for Algorithm 1, Algorithm 2,

and Algorithm 3, but always superior to that of the

PCA-based algorithm and the existing (BEST-based)

algorithm. Performances of Algorithm 1, Algorithm 2,

and Algorithm 3 are better because for each of them

computation of eigenvectors is efficient for smaller

size of the covariance matrix, that ultimately helps

to reduce speckle noise effectively. The performance

of the existing (BEST-based) algorithm is only

comparable to that of the PCA-based algorithm. The

performance of the PCA-based algorithm is poorer

than any other algorithm because of poor learning

(Fig. 5) and evaluation of eigenvectors of the huge

covariance matrix.

Clearly, there is a downward trend on test

data (Fig. 6) for all the algorithms because of

fixed network size and huge training leading to

overlearning. A simple linear regression model has

been used to assess the downward tendency in the

performance of various algorithms with training

Fig. 6. Average success rate for different training sample sizes.

sample size. It has been found that with the increase

in training sample size the performance of all

algorithms is decreasing significantly. However, the

rate of decrement in the performance is relatively

small in the case of the proposed algorithms compared

with the existing (BEST-based) and PCA-based

algorithms. The rate of decrease in the performance

of Algorithms 1, 2, and 3 is ¡0:242, ¡0:228,and ¡0:223, respectively, and for the existing(BEST-based) and PCA-based algorithms is ¡0:357and ¡0:276, respectively. Note that there is nosignificant difference in the slopes of average success

rate curve for Algorithms 1, 2, and 3. It is understood

that performance may increase with the network

size but unfortunately this will also increase the

computational time. Therefore, to maintain a trade off

between the performance and time complexity, the

number of eigenvalues (for BEST) and the network

size should remain fixed.

From the time complexity point of view, one can

easily observe that Algorithm 3 is the best. Time

required for training and testing with various training

sample sizes is shown in Fig. 7. From Fig. 7 it is clear

that the existing (BEST-based) method is superior

only initially to the PCA-based algorithm and as

the training size increases, it becomes poorer and

poorer, and finally takes almost the same time as that

of the PCA-based algorithm. It is also seen that the

2DPCA-based algorithm (Algorithm 1) is inferior to

the A2DPCA-based algorithm (Algorithm 2) for all

training sample sizes. Algorithm 3, i.e., the two-stage

2DPCA-based algorithm, on the other hand, is found

to take the least amount of time for all training sample

sizes, and hence is the most superior among all the

algorithms.

IV. CONCLUSION

To find a good clutter rejection scheme for SAR

images, we have examined algorithms from PCA


Fig. 7. CPU time in seconds for different training sample sizes.

family members. All the 2DPCA-based algorithms

are found to be superior, both with respect to time

and recognition rate as well as with respect to the

existing (BEST-based) method and the PCA-based

method. Clearly, preprocessing based on the 2DPCA

family reduces the effect of noise in SAR images

and hence produces good results. Again, of all the

methods discussed and analyzed, Algorithm 3 (i.e.,

two-stage 2DPCA-based algorithm) has been found to

be the fastest with its performance comparable to that

of other 2DPCA-based algorithms, and is by far the

best relative to the existing (BEST-based) algorithm.

The success rate as well as speed in Algorithm 3 is

mainly due to a significantly reduced number of noisy

features by the properties of two-stage 2DPCA and

the subspace separation capability of the BEST on

less noisy data obtained through two-stage 2DPCA.

Algorithm 3 is found to be the most suitable one for

clutter rejection in SAR imagery.

In a future work, based on our algorithmic

concept, the 2DPCA family will be replaced by a

supervised dimensionality reduction technique for

real-time clutter rejection in FLIR imagery and target

recognition.

ACKNOWLEDGMENT

Ramachandra Murthy is grateful to the Council

of Scientific & Industrial Research (CSIR), India

for providing him a Senior Research Fellowship

[9/93(0138)/2011-EMR-I].

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K. Ramachandra Murthy received his B.S. in computer science from the

S. V. University, India, in 2002, M.S. in mathematics from the University of

Hyderabad, India, in 2005, and M.Tech. in computer science from the Indian

Statistical Institute in 2008.

He worked as a senior research fellow in the U.S. Army project at Machine

Intelligence Unit, Indian Statistical Institute during 2009—2011. He is now a

CSIR-SRF at Machine Intelligence Unit, Indian Statistical Institute from 2011

to the present. His area of research includes manifold learning, distance metric

learning, pattern recognition, artificial neural networks, fuzzy theory, image

processing, and optimization techniques.

Sambhunath Biswas obtained his M.Sc. degree in physics, and Ph.D. in radio

physics and electronics, from the University of Calcutta, India, in 1973 and 2001,

respectively. In 1983—1985 he completed courses of M.Tech. (computer science)

from Indian Statistical Institute, Calcutta.

He was a UNDP Fellow at MIT, USA, to study machine vision in 1988—1989

and was exposed to research in the Artificial Intelligence Laboratory. He visited

the Australian National University at Canberra in 1995 and joined the school

on wavelets theory and its applications. In 2001 he became a representative of

the Government of India to visit China for holding talks about collaborative

research projects in different Chinese universities. He visited Italy and France in

June, 2010. He, at present, is a system analyst, GR-I (in the rank of professor)

at the Machine Intelligence Unit of the Indian Statistical Institute, Calcutta,

where is engaged in research and teaching. He is also an external examiner

of the Department of Computer Science at Jadavpur University in Calcutta.

He has published several research articles in international journals of repute

and is a member of IUPRAI (Indian Unit of Pattern Recognition and Artificial

Intelligence). He is the principal author of Bezier and Splines in Image Processing

and Machine Vision (Springer, London).

Ashish Ghosh is a professor with the Machine Intelligence Unit, IndianStatistical Institute. He has already published more than 150 research papers in

internationally reputed journals and refereed conferences, and has edited eight

books. His current research interests include pattern recognition and machine

learning, data mining, image analysis, remotely sensed image analysis, video

image analysis, soft computing, fuzzy sets and uncertainty analysis, neural

networks, evolutionary computation, and bioinformatics. Dr. Ghosh received the

prestigious Young Scientists Award in Engineering Sciences from the Indian

National Science Academy in 1995, and in computer science from the Indian

Science Congress Association in 1992. He was selected as an Associate of

the Indian Academy of Sciences, Bangalore, India, in 1997. He is a member

of the founding team that established the National Center for Soft Computing

Research at the Indian Statistical Institute, Kolkata, in 2004, with funding from

the Department of Science and Technology, Government of India, and is currently

in charge of the Center. He is acting as a member of the editorial boards of

various international journals.


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