Efficacy of Filtering Techniques in Improving Lands at SLC – off Thermal Infra-Red Data Journal: Journal of Selected Topics in Applied Earth Observa… [601866]

For Review Only

Efficacy of Filtering Techniques in Improving Lands at SLC –
off Thermal Infra-Red Data

Journal: Journal of Selected Topics in Applied Earth Observa tions and Remote
Sensing
Manuscript ID JSTARS-2016-00261
Manuscript type: Regular
Date Submitted by the Author: 09-Mar-2016
Complete List of Authors: Jain, Madhavi; Jawaharlal Nehru University, School of Environmental
Sciences
Dimri, A. P.; Jawaharlal Nehru University, School o f Environmental Science
Keywords: Image analysis, Temperature measurement, Filtering

For Review Only
Abstract—In 2003, Landsat-7 Enhanced Thematic Mapper
Plus (ETM+) encountered a defect in its Scan Line C orrector
(SLC) mechanism resulting in the loss of about 22% pixels in
each image. Thermal Infra-Red (TIR) band is used in
applications such as temperature estimation and req uire a
single source image for estimation of dead pixels. The present
analysis tests the efficacy of various Radar, Morph ological and
Convolution filters in reconstruction of dead pixel s and
improving the quality of Landsat SLC-off image. Eff icacy has
been based on visual, histogram and image quality m etrics viz.
Root Mean Square Error (RMSE), Peak Signal to Noise Ratio
(PSNR), and Structural SIMilarity (SSIM).
Of all the experimented filters, non-linear filters e.g.
Median and Morphological perform better. However,
Morphological filter is able to eliminate dead pixe ls using 7*7
kernel window size while Median filter is able to d o so with
29*29 window. All four functions viz. Open, Close, Erode, and
Dilate of Morphological filter are able to suppress noise (fill
dead pixel gaps) while preserving edges and details resulting
in sharp output images. On the basis of image quali ty metrics,
use of Open Morphological filter is suggested.

Index Terms — Histogram, Image quality, Landsat SLC-
off, Morphological filter, Thermal Infra-Red.

I. INTRODUCTION

Since the past four decades with the launch of Land sat-1
in July 1972, the Landsat Data Continuity Mission ( LDCM)
has provided with an uninterrupted supply of Earth-
observation data [1]-[3]; its applicability ranging in the
fields of cartography, agriculture, geography, geol ogy,
geophysics, land use planning, oceanography and
environmental monitoring [4]. On 31 May 2003, Lands at-7
Enhanced Thematic Mapper Plus ( ETM+) encountered a
hardware defect due to the permanent failure of its Scan
Line Corrector (SLC) mechanism resulting in the los s of
about 22% pixels in each image [5]. SLC keeps the E TM+
sensor’s whiskbroom module in position with the cro ss-
track motion of satellite’s path producing a rectil inear scan
pattern [6]. With its malfunction, the captured SLC -off
images contain stripe artifacts at regular interval s that are
devoid of data. Processing these images to fill the dead
pixels/ gaps becomes necessary for extracting usefu l
information out of the scene.
Landsat-7 ETM+ comprises of eight bands (including
panchromatic) that operate in the electromagnetic s pectrum
range 0.45 µm to 12.5 µm. Of its various uses, band 6
(Thermal Infra-Red; TIR) is used for thermal applic ations.
Though a number of methodologies have been develope d to correct for the stripe artifacts in SLC-off images, their
practicality remains limited in correcting TIR data .
Previous approaches include local linear histogram-
matching method using one or more SLC-off or SLC-on
images [7], semi-physical fusion method with MODIS data
[8], morphology-stitching method [6] and others, wh ich
also incorporate the use of auxiliary images to obt ain data
for gaps. Chen et al. [9] showed Neighborhood Similar
Pixel Interpolator (NSPI) technique can restore val ue of gap
pixels with high accuracy but its use is limited in thermal
applications. Discrepancies especially in TIR band are
observed when using single source based ordinary kr iging
interpolation method; which overestimates the pixel values
in the lower quantiles and underestimates in the hi gher [10].
Thermal applications like Land Surface Temperature (LST)
estimation requires same time instant data and cann ot be
integrated with images having minimum date separati on or
those having anniversary dates. Therefore, multi-so urce
image correction methodologies have no useful
applicability in this dimension and simple yet effe ctive
methodologies operating on a single image are requi red.
In theory, any standard test image is taken and is
corrupted with noise (generally gaussian or salt an d
pepper). Various filtering techniques are performed on this
noisy (corrupted) image and are compared with the o riginal
uncorrupted image to assess a filter’s ability to r estore the
image. A filter is a matrix of numbers defined usin g
arithmetic functions which when applied to any imag e has
the capability to either enhance or suppress partic ular
frequencies in that image [11]. However, the Landsa t SLC-
off data has peculiar horizontal wedge shaped artif acts
covering the entire image except for its central po rtion;
exact replication (for integration of this error in to the
standard image) of which is not easy. The current p aper
aims to analyze the efficacy of various filters in resolving
the stripe artifact problem associated with Landsat SLC-off
TIR data.
Mean, Median, Lee-Sigma, Local Region, Lee, Frost a nd
Gamma-MAP filters available in the Radar Interprete r
module of ERDAS Imagine ver. 9.3 and all functions of
Morphological filter- Open, Close, Erode and Dilate present
in the Image Interpreter module were applied to the
corrupted images. In addition, Low and High pass fi lters
were also tested. In each filtering technique, a k* k kernel
window is passed over the test image and the new va lue of
the central pixel (pixel of interest) of the window is
determined. New value of the pixel of interest vari es with
the kernel window size. For a smaller window only
adjacent pixels to the central pixel are considered while for
a larger window, pixels much far away from the cent ral
pixel are also considered. Since it is difficult to set an
optimum size of the window, various windows have to be
applied and the best is selected on the basis of re sulting Efficacy of Filtering Techniques in Improving
Landsat SLC-off Thermal Infra-Red Data
Madhavi Jain and A. P. Dimri

The work of M. Jain was supported by Junior Researc h Fellowship
granted by the Council of Scientific and Industrial Research (CSIR), India.
M. Jain and A. P. Dimri are with t he School of Environmental Sciences,
Jawaharlal Nehru University, New Delhi, India (e -mail: Page 1 of 13
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For Review Onlyfiltered images [12]. A brief discussion on these f ilters is
provided in the next section.
II. FILTER DESCRIPTION
A. Mean Filter
Mean filter takes the arithmetic average (mean) of all the
pixel values in the considered k*k kernel window an d
replaces the central pixel of the moving window wit h this
new value. This filter however is incapable of elim inating
the noise in the data and simply averages it into t he data
[13]. Landsat SLC-off images contain 22% data as ze ro
pixel values which get incorporated into the mean a nd is
not an effective method theoretically.
B. Median filter
The Median filter is a nonlinear processing techniq ue
useful for noise reduction while preserving edges i n any
image [14]. Median filter sequentially orders all p ixel
values in the defined k*k kernel window and replace s the
central pixel of the moving window with the median value
of the pixels. Operation of this type of filter is useful for
eliminating pulse or spike noise while not affectin g step
functions [13].
C. Lee-Sigma filter
Lee-Sigma filter is local smoothing statistical fil ter that is
based on probability of Gaussian distribution. The
algorithm replaces the central pixel Digital Number (DN)
value by the average of only those pixels in the mo ving
window that fall within a fixed standard deviation
(generally 2) range [15]. The coefficient of variat ion, a
scene-derived parameter is used as an input. Overal l, it has
the capability to preserve edges and retain subtle details
within the image.
D. Local Region filter
It is also known as Nagao-Matsuyama filter and is
designed to adapt to linear features in the image. This filter
works by dividing the moving window into eight regi ons
(North, South, East, West, North East, North West, South
East and South West) at different orientations. The
algorithm calculates the mean and variance of the p ixels in
each region surrounding the central pixel. The filt er takes
the most homogenous (least variance) local region i n the
window and replaces the central pixel DN with this region’s
mean [16]. It has the capability to suppress noise in a flat
region without destroying boundary details or blurr ing
edges [17].
E. Lee filter
The Lee filter is a minimum mean-square error algor ithm
which works on the basic assumption that the sample mean
and variance of the central pixel is equal to the l ocal mean
and variance of the pixels in k*k kernel window [18 ].
DN Igv9v5Igv93lIgv93̅ =Ig467̅Mean Ig467l+ KIg467̅DN Igv9l9Igv9v4 −MeanIg467l (1)
where,
Mean = average of pixels in a moving window
K = Var(x) Mean Igv87̅σIgv87̅+Var(x) ⁄
Var (x)
= Ig4678Ig467̅Variance within window+Ig467̅Mean within windowIg467lIgv87̅
Ig467̅SigmaIg467lIgv87̅+1Ig4679
−Ig467̅Mean within windowIg467lIgv87̅
Lee filter is not effective for either too small or too large
window sizes where minute image details are during processing.
F. Frost filter
The Frost filter is also a minimum mean square erro r
algorithm which was developed to correct multiplica tive
noise in an image. This edge preserving filter is a daptive in
nature as it applies local statistics inside homoge nous areas
of the image [19].
DN = ∑KαeIgv879Igv96l|Igv93̅|
Igv9vl Igv934 Igv9vl (2)
where,
K= Normalization constant
I̅= local mean
σ = local variance
Igv̅v6 Ig3364 = Igl86lIgl865Igl853Igl859Igl857 Igl855Igl867Igl857Igl858Igl858Igl86lIgl855Igl86lIgl857Igl866Igl87v Igl867Igl858 Igl874Igl853Igl87̅Igl86lIgl853Igl87vIgl86lIgl867Igl866 Igl874Igl853Igl864Igl873Igl857
|t|=|X−XIgv868|+|Y−YIgv868|
k = moving window size
α = (4/nσ Ig3365Igv87̅)(σIgv87̅/I̅Igv87̅)
G. Gamma-MAP filter
Many filters (e.g., Lee, Lee-Sigma, Frost) assume a
Gaussian distribution for the speckle noise which i s not the
case with all types of noise. Lopes et. al [20] rep laced the
Gaussian distribution with Beta and Gamma distribut ion.
The Maximum A Posteriori (MAP) filter attempts to
estimate the original pixel DN, which is assumed to lie
between the local average and the degraded (actual) pixel
DN using the equation,
IIg463vIgv87l−I̅IIg463vIgv87̅+σ(IIg463v−DN) (3)
where,
IIg463v= sought value
I̅= local mean
DN = input value
σ = original image variance
Gamma-MAP filter has the capability of smoothing no ise
while not blurring subtle details.
H. Morphological filter
Morphology deals with structure and form of objects .
Mathematical morphology utilizes the concepts of se t
theory to analyze and remove noise in images. A
‘structuring element’ which is a small template of
coordinate points, is moved all across the image an d is
compared with corresponding neighborhood pixels. Fo ur
non-linear functions- Erode, Dilate, Open and Close exist.
Erosion and dilation translate the structuring elem ent to
various points in the input image, and examine the
intersection between the translated kernel coordina tes and
the input image coordinates. Erode operator strips away
layer of pixels from the boundaries of foreground p ixels,
while dilation adds pixels to those boundaries. Ope n
operator is erosion followed by dilation whereas cl ose
operator is a dilation followed by erosion [21]. Th is filter
can be used to target specific pixels in the image. Erroneous
values (zero in the case of Landsat SLC-off) can be ignored
in the filter algorithm and the constructed kernel can be
applied at only these erroneous values. This way th e DN of
non-erroneous pixels are not altered and dead pixel s are
reconstructed, providing a very sharp resultant fil tered
image.
I. Low pass filter
Low pass filter is based on the convolution theorem ,
according to which a convolution operation in the s patial
domain is equivalent to multiplication operation in the Page 2 of 13
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For Review Onlyfrequency domain. In a low pass filter, frequencies lower
than the threshold frequency are allowed to pass wh ile the
filter blocks higher frequencies. Noise is reduced in the
output images but often get blurred.
J. High pass filter
High pass filter sharpens the input image by attenu ating
frequency signals lower than the cut-off frequency and
letting the higher frequency signals pass through. This filter
also works on the convolution theorem.
III. DATA AND RESULTS
A. Lena Test Image
Standard test image of Lena (Fig. 1(a)) has been ta ken
and induced with wedge shaped artifacts resembling that of
Landsat SLC-off. Landsat SLC-off artifacts are 14 p ixels
wide at the edges and gradually decrease in width o n
moving towards the center with the central band com pletely
devoid of dead pixels. The error repeats itself in the y-axis
after every 34 pixels. A typical Landsat scene has nearly
8000*8000 pixels while Lena comprises of 256*256 pi xels.
Due to its repeating nature in the y-axis, the cons tructed
error for introduction in Lena image was scaled onl y in the
x-axis. This noise was added to the uncorrupted Len a image
using the ‘either-if’ conditional model (Fig. 2) re presented
the following equation
g( x,y ) = EITHER η(x,y ) IF η(x,y ) = 0 OR f( x,y ) (4)
where,
g( x,y ) = corrupted image
η(x,y ) = noise term
f( x,y ) = uncorrupted image
All filters described in the previous section have been
applied to the resultant corrupted image (Fig. 1(b) ) using
varying k*k kernel window sizes to test their effic acy. The
filtered/restored images with the use of only 3*3 w indow
size are presented (Fig. 1(c)-(o)). From visual per spective it
is noted that Median, Local Region, and all functions of
Morphological filter perform well and considerably
improve image quality by suppressing noise. Mean, L ee-
Sigma, Lee Frost, Gamma-MAP and Low Pass filter do not
show any considerable noise suppression while High Pass
filter further degrades the image quality. However, with the
use of 3*3 window, noise is cleared mostly from the central
portion of the image where dead pixels are less and not
entirely from the edges. This necessitates that larger
window sizes be applied till a noise suppressed ima ge is
obtained. It should be noted that there is always a trade-off
between noise suppression and image smoothening/qua lity
and window sizes should be selected with caution.
Histograms depicting variation of number of pixels with
pixel gray level intensity are plotted for varying k*k
window sizes for all filters in Fig. 3(a)-(c). The uncorrupted
(original) Lena image is shown as shaded region in the
graphs and the corrupted (noise induced) Lena image as a
solid black line. A shift in the pattern of pixel d istribution
can be noted as the number of dead pixels have incr eased.
On application of filters, the histogram distributi on changes
in accordance to the transformation operators/ func tions
defined for each window size. The performance of an y
filter is determined by how closely its histogram m atches
with the uncorrupted Lena histogram. This histogram
matching method in explicit terms can establish whi ch
filters have the best capability to restore corrupt ed images. In Fig. 3(a), noise has been filtered with 3*3 Rada r
filters, 3*3 Morphological filters and 3*3 Convolut ion
filters. All four functions of Morphological filter s, Median
filter as well as Local Region filter show consider able
improvement from the corrupted pixel distribution. Mean,
Low Pass, Lee Sigma and Lee filters overestimates t he
number of pixels in 0-40 range. Gamma-MAP filter sl ightly
improves the image quality but a left shift is obse rved as
compared to original Lena pixel distribution. High Pass
filter produces a unimodal distribution and is unab le to
capture the multiple peaks in the original Lena his togram.
Frost filter does not perform well. Fig. 3(b) show filtering
capability 15*15 Radar filters and 5*5 Morphologica l and
Convolution filters, while Fig. 3(c) represents 29* 29 Radar
filters and 7*7 Morphological and Convolution filte rs.
When larger window sizes of the same filters are ap plied on
the corrupted Lena image striking differences in th e
histogram pattern are observed. In Fig. 3(b), histo grams of
Median filter and all Morphological filters show
improvement as compared to corrupted Lena image. Le e
Sigma and Local Region filter histograms match well with
original Lena image except in the initial 0-40 end of the
pixel intensity spectrum. Rest of the filters are u nable to
perform well. Similar is the case in Fig. 3(c). He re, except
for the Morphological filters, histograms of no oth er filter is
able to match closely with the original Lena image.
As a quantitative measure of image improvement, Roo t
Mean Square Error (RMSE), Peak Signal to Noise Rati o
(PSNR) and Structural SIMilarity (SSIM) metrics hav e
been employed (TABLE I(A)-(C), TABLE II(A)-(C) and
TABLE III).
RMSE is a measure of difference between the filtere d
images and the uncorrupted image. Aggregate of resi dual
differences of each predicted pixels and observed p ixels is
used to calculate RMSE using the formula
RMSE = Ig3495Igv869
Igv9v3Igv9v4 ∑ ∑ Ig3435xIgv9l9Igv9v̅ −xIgv9l9Igv9v̅ Ig4593Ig3439Igv87̅Igv9v4Igv879Igv869
Igv9v̅Igv88̅Igv868Igv9v3Igv879Igv869
Igv9l9Igv88̅Igv868 (5)
where,
xij = uncorrupted pixel
x′ij = filtered pixel
m = number of pixels in each row
n = number of pixels in each column
PSNR (decibel units) is a measure of image quality based
on pixel differences between filtered and uncorrupt ed
images and is defined as
PSNR = 10log Igv869Igv868 (IIgv9v3Igv9llIgv934 Igv87̅MSE ⁄ ) (6)
where,
I = maximum power of the pixel
MSE = Mean Square Error
Lastly, SSIM a quality assessment tool based on
degradation of structural information [22] has been
considered to compare local patterns of pixel inten sities
between filtered and uncorrupted image. It is expre ssed as
SSIM =
(2μIgv934μIgv934Ig4594+CIgv869)(2σ Igv934Igv934 Ig4594+CIgv87̅)Ig3435μIgv934Igv87̅+μIgv934Ig4594Igv87̅+CIgv869Ig3439Ig3435σIgv934Igv87̅+σIgv934Ig4594Igv87̅+CIgv87̅Ig3439 ⁄
(7)
where,
µ and σ are local mean and local standard deviation
respectively and C 1 and C 2 are constants.
RMSE has been calculated between uncorrupted Lena
image and the output images after applying various filters
(TABLE I(A), TABLE II(A) and TABLE III). Error
tending to zero indicates that the filtered pixels do not have Page 3 of 13
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For Review Onlymuch different DN than that of uncorrupted Lena i.e . the
filter performs well. In general, RMSE is found to be
decreasing with increasing window size. As many adj acent
rows of pixels (14 near the edges) are dead it is e asy for the
Radar filters to interpolate values if a kernel gre ater than k
= 15 is used. Higher kernel size is able to predict values at
edges of the image but also causes loss of informat ion in
the center due to increase in number of approximati ons.
Thus there is a trade-off between noise suppression and
quality preservation. Out of all the filters, Media n, Local
Region and all functions Morphological filters tend to have
lower RMSE. On the contrary, High Pass filter shows
increasing error and performs the worst.
High PSNR is associated with how close the noisy im age
has been reconstructed to the match the original re sulting in
higher image quality. For Lena image analysis, PSNR is
found to be high for Mean, Median, Local Region and all
Morphological filters (TABLE I(B), TABLE II(B) and
TABLE III). Higher value of PSNR indicates that hig her
power of signals are present as compared to power o f noise
term. In the present case, it is highest for Open a nd Close
Morphological filter and least for High Pass filter .
For Radar filters, it is noted that SSIM is highest for 3*3
kernel window, it decreases till it reaches a windo w size of
around 17*17 and then again increases as window siz e
reaches 29*29 (TABLE I(C)). SSIM index given in TAB LE
II(C) suggests that edge and feature preservation i s done
best in Morphological filters (SSIM > 0.70). Struct ural
similarity of filtered image as compared to origina l image
increases with increasing window size. A 7*7 Open
Morphological filter has SSIM of 0.88. Convolution filters
perform poorly in terms of SSIM (TABLE III).
It is interesting to note that for Morphological fi lter a 3*3
window kernel applied sequentially thrice, 5*5 wind ow
kernel applied sequentially twice and a single appl ication of
7*7 window kernel produces almost the same results in all
the considered image quality metrics viz. RMSE, PSN R
and SSIM. In essence, the best filter is the one wh ich
suppresses highest amount of noise with the least w indow
size, while preserving edge and other local feature s. On the
basis of the above parameters- visual analysis, his togram
matching, and image quality metrics, Median, Local
Region, and all four functions of Morphological are
considered for further analysis in improving a simu lated
Landsat SLC-off image.
B. Simulated Landsat SLC-off Image
A February 3, 2003 Landsat-7 ETM+ SLC-on image
(TIR band), covering Los Angeles (USA) and nearby a reas
(Path/Row 041/036) was acquired from USGS (Fig. 4(a ))
and was used to simulate a Landsat SLC-off image. F or this
purpose, the gap mask file (containing information about
dead pixels) provided in the November 18, 2003 Land sat-7
ETM+ SLC-off image over the same region was used. T he
corrupted image was constructed using the ‘either-i f’
conditional model (4) and has been restored by filt ers
selected based on Lena image analysis. Fig. 4(b) pr esents
the corrupted test image while Fig. 4(c) shows a zo omed in
portion of it where the dead pixel (noise) pattern can be
seen. Each uncorrupted pixel in this image contains a
radiance value from which LST can be estimated. App lied
filter should be capable eliminating dead pixels an d
reassigning the closest to correct DN value to them . As the
image is quite large and many adjacent rows of pixe ls are dead, window size bigger than 3*3 is required. Medi an and
Local region filters have been tested for (2n+1)*(2 n+1)
window size where n = 1 to 14, while Morphological filters
have been tested for 3*3, 5*5, and 7*7 window sizes . The
reason for this range difference is that the Radar filters
showed increasing dead pixel suppression in the inp ut
image as the window size increased; 29*29 window cl eared
the input image of all dead pixels. In the case of
Morphological filters, the same could be achieved w ith a
single application of 7*7 window or by sequential
application of 3*3 or 5*5 window filters.
The results of only the filters with best noise sup pression
capability, as deduced from Lena image analysis, ar e shown
in the paper. Fig. 5(c)-(d) shows restoration of si mulated
Landsat SLC-off image with 3*3 window Radar filters and
Fig. 5(e)-(h) with 3*3 window Morphological filters .
Similarly, effect of 15*15 window Radar filters (Fi g. 6(c)-
(d)), 5*5 window Morphological filters (Fig. 6(e)-( h)),
29*29 window Radar filters (Fig. 7(c)-(d)), and 7*7
window Morphological filters (Fig. 7(e)-(h)) have b een
shown. In Fig. 5(c)-(h) – Fig. 7(c)-(h), it can be seen that
greater expanse of the central portion of the image is
cleared of dead pixels if larger window size of the same
filter is used. A 29*29 Median, 7*7 Open Morphologi cal
and 7*7 Close Morphological filter perform well fro m a
visual perspective.
Histogram analysis for the above mentioned Radar an d
Morphological filters of the image has been carried out
(Fig. 8(a)-(c)). Large number (>10 6) of pixels have a zero
intensity value. Of these pixels, a portion is the background
zero pixels while the rest are noisy dead pixels. T he
histogram of filtered images matches well with the original
Landsat image in all three considered cases of vary ing
window sizes. In Fig. 8(a), the order of filter per formance is
noted as Local Region < Median < Erode = Dilate < C lose
= Open. In Fig 8(b), 5*5 Morphological filters tend to
perform better. The order of filter performance cha nges to
Local Region < Median = Erode = Dilate < Close = Op en.
As window size is increased in Fig. 8 (c), histogra m of
Open and Close Morphological filtered images matche s
very well with the original Landsat image. Local Re gion
filter overestimates the pixels in the 110-130 rang e while
Median filter overestimates the pixels in the regio n of the
two peaks in the distribution. On the basis of visual and
histogram analysis, Open and Close functions of
morphological filters should be considered for rest oring
dead pixels in the image.
Similar analysis of image quality metrics- RMSE, PS NR,
and SSIM for the selected filters of varying window sizes
has been performed. Results for Radar filters are p resented
in TABLE IV and for Morphological filters in TABLE
V(A) – (C). RMSE drops to 0.03 for Median and 0.04
Local Region filter at 29*29 window application. In case of
Morphological filters, RMSE is least for Open and C lose
functions (= 0.03 for 7*7 window) than Erode and Di late
functions. PSNR values greater than 30 are obtained for
29*29 Median filter, 3*3 Open and Close Morphologic al
filter applied sequentially thrice and for 7*7 Open
Morphological filter; highest being for Open Morpho logical
filter. Structural similarity metric SSIM, suggests 98%
similarity between filtered and uncorrupted image w hen
restored with three times sequential application of either
Open or Close Morphological filter. This level of s imilarity
in image features is remarkable. Good performance o f other Page 4 of 13
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For Review Onlywindow sizes of these two filters is evident from T ABLE
V(C).
Based on the above results Open Morphological filte r is
found to be the best reconstructive algorithm. Brig htness
temperature (T B), a pre-requisite to LST estimation is
calculated for images reconstructed using Open
Morphological filter and compared with those calcul ated
from original Landsat image.
TB can be derived from satellite measured top of the
atmosphere (TOA) radiances by using the Planck’s
equation [23]. Atmospheric, angular, and emissivity effects
have to be compensated for extraction of LST from T B [23].
At-satellite radiances have been computed using the
formula,
LIgv97l=((LMAX Igv97l−LMIN Igv97l) (QCALMAX−QCALMIN ) ⁄ ) ∗
(QCAL−QCALMIN )+LMIN Igv97l) (8)
where,
Lλ is the spectral radiance at the sensor’s aperture,
QCAL is quantized calibrated pixel value in DN,
LMIN λ and LMAX λ are spectral radiances scaled in
QCALMIN and QCALMAX respectively and,
QCALMIN and QCALMAX are minimum and maximum
quantized calibrated pixel values respectively.
The radiances are then converted to at-satellite br ightness
temperatures by
TIgv886= KIgv87̅lnIg467vIgv895Ig3ll7
Igv896Ig3vl9+1Ig4673Ig34l5 (9)
where,
TB is the brightness temperature measured in Kelvin,
K1 and K 2 are calibration constants of Landsat-7 ETM+
satellite and,
Lλ is the spectral radiance calculated through (8).
Fig. 9 (a)-(d) shows T B estimated from original image
and from the image corrected using 3*3 (applied thr ice),
5*5 (applied twice) and 7*7 (applied once) Open
Morphological filter. It can be seen that T B calculated from
Open Morphological filter restored image (Fig. 9 (b )-(c)) is
similar to that calculated from the original image. Spatial
variations in T B due to the diverse topographical and land
use patterns present in the region as seen in the o riginal
image are captured well in the filtered images. T B for 20
random points ‘A-T’ spread across the image as show n in
Fig. 9 (a) are tabulated for all the four cases (TA BLE VI).
The temperature values derived from filtered images match
well with those from original image thereby demonst rating
the filter’s efficacy.
IV. CONCLUSION
In order to test the efficacy in improving image qu ality,
various filters viz. Radar, Morphological and Convo lution
were applied on simulated (corrupted) Lena and Land sat
images. Apart from visual inspection and histogram
analysis, image quality indices of RMSE, PSNR and S SIM
were employed. Selection of k*k kernel window size is
dependent on the type of filter and its ability to suppress
noise. A 7*7 Morphological filter is able to clear away dead
pixels in simulated Landsat SLC-off image; 29*29 Me dian
filter gives the same result. A trade-off between n oise
suppression and image quality is present, and for s imilar
resulting images from different k*k kernels, the on e with
smaller window size should be preferred.
In Lena image, non-linear filters viz. Median, Loca l
Region, and all four functions of Morphological fil ter show
better noise suppression capability. When tested on simulated Landsat SLC-off image, Morphological filt ers
provide the best results. From the four different f unctions of
this filter, results of histogram analysis along RM SE and
SSIM suggest the use of Open and Close Morphologica l
filters. Based on PSNR calculations, more signals a re
preserved on the application of Open Morphological filter
(for all window sizes). Due to its highest image qu ality
improvement capability, the use of Open Morphologic al
filter in reconstructing dead pixels of Landsat SLC -off TIR
data is suggested.
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“A model for radar images and its application to ad aptive
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For Review OnlyMach. Intell ., vol. 2, pp. 157-166, 1982.
[20] A. Lopes, E. Nezry, R. Touzi and H. Laur, “Maximum a
posteriori speckle filtering and first order textur e models in
SAR images,” in Geoscience and Remote Sensing Symposium ,
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[21] M. Roushdy, “Comparative study of edge detection al gorithms
applying on the grayscale noisy image using morphol ogical
filter,” GVIP journal , vol. 6, no. 4, pp. 17-23, 2006.
[22] Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simonc elli,
“Image quality assessment: from error visibility to structural
similarity,” IEEE Trans. Image Process. , vol. 13, no. 4, pp.
600-612, 2004.
[23] P. Dash, F. M. Göttsche, F. S. Olesen and H. Fische r, “Land
surface temperature and emissivity estimation from passive
sensor data: theory and practice-current trends,” Int. J. Remote
Sens. , vol. 23, no. 13, pp. 2563-2594, 2002.Page 6 of 13
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For Review OnlyTABLE I(A)
RMSE FOR VARIOUS RADAR FILTERS AND WINDOW SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7 9*9 11*11 13*13 15*15 17*17 19*19 21*21 23*23 25*25 27*27 29*29
Mean 0.22 0.22 0.21 0.20 0.19 0.19 0.18 0.18 0.17 0 .17 0.17 0.16 0.16 0.16
Median 0.24 0.24 0.23 0.23 0.23 0.22 0.22 0.21 0.21 0.20 0.19 0.16 0.14 0.12
Lee-Sigma 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0 .23 0.23 0.23 0.23 0.23 0.23
Local Region 0.24 0.24 0.24 0.23 0.23 0.23 0.22 0.2 1 0.20 0.19 0.17 0.15 0.14 0.14
Lee 0.24 0.24 0.23 0.22 0.21 0.21 0.21 0.20 0.20 0. 19 0.19 0.18 0.18 0.18
Frost 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.23 0.22
Gamma-MAP 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0 .24 0.24 0.23 0.23 0.23 0.23

TABLE I(B)
PSNR FOR VARIOUS RADAR FILTERS AND WINDOW SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7 9*9 11*11 13*13 15*15 17*17 19*19 21*21 23*23 25*25 27*27 29*29
Mean 12.96 13.33 13.67 14.00 14.31 14.59 14.85 15.0 7 15.26 15.43 15.57 15.68 15.76 15.81
Median 12.46 12.52 12.61 12.71 12.83 12.98 13.18 13 .46 13.69 14.00 14.59 15.80 17.01 18.08
Lee-Sigma 12.87 12.83 12.80 12.78 12.76 12.74 12.72 12.69 12.68 12.66 12.64 12.62 12.61 12.59
Local Region 12.43 12.46 12.53 12.62 12.73 12.89 13 .13 13.47 13.88 14.60 15.45 16.30 16.80 16.99
Lee 12.19 12.50 12.80 13.07 13.38 13.38 13.60 13.81 14.02 14.25 14.47 14.69 14.88 15.05
Frost 12.43 12.43 12.43 12.45 12.47 12.50 12.54 12. 58 12.63 12.69 12.74 12.81 12.88 12.95
Gamma-MAP 12.34 12.32 12.30 12.30 12.32 12.35 12.38 12.42 12.46 12.50 12.56 12.65 12.74 12.83

TABLE I(C)
SSIM FOR VARIOUS RADAR FILTERS AND WINDOW SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7 9*9 11*11 13*13 15*15 17*17 19*19 21*21 23*23 25*25 27*27 29*29
Mean 0.57 0.51 0.47 0.45 0.44 0.44 0.44 0.44 0.45 0 .46 0.48 0.49 0.51 0.53
Median 0.58 0.55 0.53 0.51 0.50 0.50 0.50 0.50 0.50 0.51 0.52 0.54 0.56 0.58
Lee-Sigma 0.57 0.53 0.50 0.49 0.48 0.47 0.46 0.46 0 .46 0.46 0.45 0.45 0.45 0.45
Local Region 0.54 0.49 0.46 0.44 0.42 0.42 0.42 0.4 2 0.43 0.43 0.44 0.46 0.47 0.48
Lee 0.55 0.51 0.48 0.46 0.45 0.44 0.45 0.45 0.47 0. 48 0.50 0.52 0.54 0.56
Frost 0.57 0.55 0.54 0.53 0.53 0.53 0.54 0.54 0.54 0.55 0.55 0.56 0.56 0.56
Gamma-MAP 0.56 0.51 0.47 0.45 0.43 0.42 0.41 0.41 0 .41 0.42 0.43 0.45 0.47 0.49

TABLE II(A)
RMSE FOR VARIOUS MORPHOLOGICAL FILTERS AND WINDOW
SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 0.17 0.11 0.04 0.11 0.03 0.05
Close 0.17 0.11 0.04 0.11 0.04 0.06
Erode 0.20 0.17 0.14 0.17 0.11 0.14
Dilate 0.20 0.17 0.14 0.17 0.11 0.14
Note: The use of ‘.’ Represents sequential application of a filter i.e.
3.3.3 is a 3*3 window filter applied sequentially t hrice.

TABLE II(B)
PSNR FOR VARIOUS MORPHOLOGICAL FILTERS AND WINDOW
SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 15.28 19.33 27.71 19.20 29.41 25.63
Close 15.27 19.31 27.56 19.14 28.71 25.10
Erode 13.77 15.26 16.99 15.22 18.98 16.84
Dilate 13.77 15.25 16.97 15.20 18.88 16.77
Note: The use of ‘.’ Represents sequential application of a filter i.e.
3.3.3 is a 3*3 window filter applied sequentially t hrice.

TABLE II(C)
SSIM FOR VARIOUS MORPHOLOGICAL FILTERS AND WINDOW
SIZES ON SIMULATED LENA IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 0.76 0.85 0.92 0.84 0.92 0.88
Close 0.76 0.85 0.92 0.83 0.92 0.88
Erode 0.69 0.76 0.80 0.75 0.83 0.78
Dilate 0.69 0.75 0.80 0.74 0.82 0.78
Note: The use of ‘.’ Represents sequential application of a filter i.e.
3.3.3 is a 3*3 window filter applied sequentially t hrice.

TABLE III
RMSE, PSNR, AND SSIM FOR VARIOUS CONVOLUTION FILTER S
AND WINDOW SIZES ON SIMULATED LENA IMAGE
Function Window Size RMSE PSNR SSIM
Low
Pass 3*3 0.22 12.95 0.57
5*5 0.22 13.31 0.51
7*7 0.21 13.65 0.47
High
Pass 3*3 0.29 10.66 0.23
5*5 0.47 6.57 0.08
7*7 0.47 6.57 0.08

TABLE IV
RMSE, PSNR, AND SSIM FOR SELECTED RADAR FILTERS FOR
DIFFERENT WINDOW SIZES ON SIMULATED LANDSAT SLC-OFF
IMAGE
Window
Size Median Local Region
RMSE PSNR SSIM RMSE PSNR SSIM
3*3 0.18 14.91 0.74 0.18 14.90 0.73
5*5 0.18 15.00 0.75 0.18 15.01 0.72
7*7 0.17 15.15 0.75 0.17 15.20 0.71
9*9 0.17 15.35 0.75 0.17 15.47 0.72
11*11 0.16 15.61 0.76 0.16 15.84 0.72
13*13 0.16 15.96 0.77 0.15 16.35 0.73
15*15 0.15 16.42 0.78 0.14 17.04 0.74
17*17 0.14 17.02 0.80 0.13 17.96 0.76
19*19 0.13 17.82 0.82 0.11 19.22 0.78
21*21 0.11 18.92 0.84 0.09 21.07 0.80
23*23 0.09 20.59 0.86 0.06 23.86 0.82
25*25 0.07 23.64 0.88 0.05 26.61 0.84
27*27 0.03 30.24 0.90 0.04 28.45 0.85
29*29 0.03 31.30 0.91 0.04 28.70 0.86

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For Review Only
TABLE V(A)
RMSE FOR SELECTED MORPHOLOGICAL FILTERS FOR
DIFFERENT WINDOW SIZES ON SIMULATED LANDSAT SLC-OFF
IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 0.12 0.06 0.03 0.06 0.03 0.03
Close 0.12 0.06 0.03 0.06 0.04 0.03
Erode 0.15 0.12 0.09 0.12 0.06 0.09
Dilate 0.15 0.12 0.09 0.12 0.06 0.09
Note: The use of ‘.’ Represents sequential application of a filter i.e.
3.3.3 is a 3*3 window filter applied sequentially t hrice.

TABLE V(B)
PSNR FOR SELECTED MORPHOLOGICAL FILTERS FOR
DIFFERENT WINDOW SIZES ON SIMULATED LANDSAT SLC-OFF
IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 18.54 24.67 30.33 24.65 29.17 30.14
Close 18.54 24.65 30.26 24.61 29.04 29.88
Erode 16.51 18.54 21.15 18.54 24.68 21.13
Dilate 16.51 18.53 21.12 18.52 24.54 21.08
Note: The use of ‘.’ Represents sequential application of a filter i.e. 3.3.3 is a 3*3 window filter applied sequentially t hrice.

TABLE V(C)
SSIM FOR SELECTED MORPHOLOGICAL FILTERS FOR
DIFFERENT WINDOW SIZES ON SIMULATED LANDSAT SLC-OFF
IMAGE
Function Window Size
3*3 5*5 7*7
3 3.3 3.3.3 5 5.5 7
Open 0.85 0.93 0.98 0.93 0.97 0.96
Close 0.85 0.93 0.98 0.93 0.97 0.96
Erode 0.79 0.85 0.90 0.85 0.93 0.89
Dilate 0.79 0.85 0.90 0.85 0.93 0.89
Note: The use of ‘.’ Represents sequential application of a filter
i.e. 3.3.3 is a 3*3 window filter applied sequentia lly thrice.

TABLE VI
BRIGHTNESS TEMPERATURE (K) ESTIMATED FROM ORIGINAL LANDSAT IMAGERY AND RECONSTRUCTED IMAGERY USING
VARIOUS APPLICATIONS OF OPEN MORPHOLOGICAL FILTER
Location Latitude Longitude Brightness Temperature (K)
Original
Landsat
image Open Morphological filter
3.3.3 5.5 7
A 35° 05.338' N 118° 57.131' W 284.07 284.07 284.07 284.07
B 35° 14.053' N 118° 43.358' W 286.87 287.17 287.17 287.48
C 34° 56.781' N 118° 36.267' W 272.45 272.80 272.10 272.10
D 35° 02.804' N 118° 13.177' W 289.59 289.59 289.59 289.59
E 35° 17.878' N 117° 28.411' W 285.94 285.94 285.94 285.94
F 34° 56.570' N 117° 49.385' W 284.39 284.39 284.39 284.39
G 34° 42.301' N 117° 45.045' W 289.89 289.89 289.89 289.89
H 34° 39.251' N 117° 24.946' W 289.59 289.59 289.59 289.59
I 34° 37.676' N 118° 01.651' W 280.88 280.88 280.88 280.88
J 34° 41.097' N 118° 10.694' W 287.48 287.48 287.48 287.48
K 34° 35.143' N 118° 22.884' W 280.88 280.88 280.88 280.88
L 34° 12.293' N 118° 32.620' W 292.83 292.83 292.83 292.83
M 33° 51.773' N 117° 34.870' W 291.37 291.37 291.37 291.37
N 33° 55.709' N 118° 16.881' W 290.78 292.25 290.48 289.88
O 33° 57.845' N 118° 27.338' W 287.48 287.48 287.48 287.48
P 33° 59.700' N 118° 51.488' W 286.87 286.87 286.87 286.87
Q 34° 00.468' N 119° 25.409' W 296.84 297.12 296.27 295.42
R 34° 15.954' N 119° 21.117' W 286.25 286.56 286.56 286.25
S 34° 26.325' N 119° 02.902' W 282.81 282.81 282.81 282.81
T 34° 53.283' N 117° 19.639' W 290.19 290.48 290.48 290.48

Page 8 of 13
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For Review Only

Fig. 1. (a) Original Lena image, (b) Corrupted Lena image, restored by the application of 3*3 moving window of (c) Mean filte r, (d) Median filter, (e) Lee –
Sigma filter, (f) Local Region filter, (g) Lee filter, (h) Frost filter, (i) Gamma -MAP filter, (j) Open Morphological filter, (k) Close Morphological filter, (l)
Erode Morphological filter, (m) Dilate Morphological filter, (n) Lo w Pass filter and, (o) High Pass filter.

Fig. 2. Model design used for construction of corrupted image g( x,y) by introduction of noise
(x,y) into uncorrupted image f( x,y).

0 0 0 90 3 0 0 0
8 5 0 0 67 200 189 78
0 0 0 23 108 0 0 0
134 45 2 99 101 89 56 89
0 0 0 101 44 0 0 0
80 170 169 12 8 32 0 0
0 0 0 78 10 0 0 0
3 165 78 65 13 56 99 134
234 67 8 90 3 34 44 12
8 5 0 0 67 200 189 78
56 4 5 23 108 54 23 90
134 45 2 99 101 89 56 89
47 21 56 101 44 76 7 45
80 170 169 12 8 32 0 0
11 90 23 78 10 34 4 0
3 165 78 65 13 56 99 134
0 0 0 1 1 0 0 0
1 1 1 1 1 1 1 1
0 0 0 1 1 0 0 0
1 1 1 1 1 1 1 1
0 0 0 1 1 0 0 0
1 1 1 1 1 1 1 1
0 0 0 1 1 0 0 0
1 1 1 1 1 1 1 1
= +
g(x,y) f(x,y)
(x,y) (a) (b) (c) (d) (e)
(f) (g) (h)
(m) (l) (k) (j) (i)
(o) (n) Page 9 of 13
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For Review Only

Fig. 3. Histograms showing efficacy of various filters (a) 3*3 Radar, 3*3 Morphological and 3*3 Convolution filters, (b) 15*1 5 Radar, 5*5 Morphological
and 5*5 Convolution filters and, (c) 29*29 Radar, 7*7 Morphological and 7*7 Convolution filters applied to corrupted Lena image. Filters closely
following the pattern of original Lena image pixel distribution work best in restoring the corrupted Lena image.

01234
Pixel Intensity
Pixel IntensityNumber of Pixels (X 103)
0 50 100 150 200 250Original Lena Image (shaded)
Corrupted Lena Image
3×3 Mean Filter
3×3 Median Filter
3×3 Lee
Sigma Filter
3×3 Local Region Filter
3×3 Lee Filter
3×3 Frost Filter
3×3 Gamma
MAP Filter
3×3 Open Morphological Filter
3×3 Close Morphological Filter
3×3 Erode Morphological Filter
3×3 Dilate Morphological Filter
3×3 Low Pass Filter
3×3 High Pass Filter
01234

Pixel IntensityNumber of Pixels (X 103)
0 50 100 150 200 250Original Lena Image (shaded)
Corrupted Lena Image
15×15 Mean Filter
15×15 Median Filter
15×15 Lee
Sigma Filter
15×15 Local Region Filter
15×15 Lee Filter
15×15 Frost Filter
15×15 Gamma
MAP Filter
5×5 Open Morphological Filter
5×5 Close Morphological Filter
5×5 Erode Morphological Filter
5×5 Dilate Morphological Filter
5×5 Low Pass Filter
5×5 High Pass Filter
01234

Pixel Intensity
Number of Pixels (X 103)
0 50 100 150 200 250Original Lena Image (shaded)
Corrupted Lena Image
29×29 Mean Filter
29×29 Median Filter
29×29 Lee
Sigma Filter
29×29 Local Region Filter
29×29 Lee Filter
29×29 Frost Filter
29×29 Gamma
MAP Filter
7×7 Open Morphological Filter
7×7 Close Morphological Filter
7×7 Erode Morphological Filter
7×7 Dilate Morphological Filter
7×7 Low Pass Filter
7×7 High Pass Filter
Pixel Intensity(c) (c) (a) Page 10 of 13
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For Review Only
Fig. 4 . (a) Landsat SLC -on image (acquisition date February 3, 2003) with no dead pixels, (b) Simulated Landsat image corrupted with
dead pixels similar to Landsat SLC -off and, (c) zoomed in image showing introduced dead pixel gaps .

Fig. 5. (a) Original Landsat image, (b) Corrupted Landsat image, restored by the application of 3*3 moving window of (c) Median fi lter, (d) Local Region
filter, (e) Open Morphological filter, (f) Close Morphological filter, (g) Erode Morphological filter and, ( h) Dilate Morphological filter.

Fig. 6. (a) Original Landsat image, (b) Corrupted Landsat image, restored by the application of 15*15 moving window of (c) Me dian filter, (d) Local
Region filter, (e) Open Morphological filter, (f) Close Morphological filter, (g) Erode Morphological filter and, (h) Dilate Morphol ogical filter.

(a) (b) (c)
(a) (b) (c) (d)
(e) (f) (g) (h)
(a) (b) (c) (d)
(e) (f) (g) (h) Page 11 of 13
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Fig. 7. (a) Original Landsat image, (b) Corrupted Landsat image, restored by the application of 29*29 moving window of (c) Median filter, (d) Local
Region filter, (e) Open Morphological filter, (f) Close Morphological filter, (g) Erode Morphological filter and, (h) Dilate Morphological filter.

00.51.01.52.0
Pixel IntensityNumber of Pixels (X 106)

0 50 100 150 200 250Original Landsat Image (shaded)
Corrupted Landsat Image
3×3 Median Filter
3×3 Local Region Filter
3×3 Open Morphological Filter
3×3 Close Morphological Filter
3×3 Erode Morphological Filter
3×3 Dilate Morphological Filter
00.51.01.52.0
Pixel IntensityNumber of Pixels (X 106)

0 50 100 150 200 250Original Landsat Image (shaded)
Corrupted Landsat Image
15×15 Median Filter
15×15 Local Region Filter
5×5 Open Morphological Filter
5×5 Close Morphological Filter
5×5 Erode Morphological Filter
5×5 Dilate Morphological Filter(a) (b) (c) (d)
(e) (f) (g) (h)
(a)
(b) Page 12 of 13
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Fig. 8. Histograms showing efficacy of selected filters (a) 3*3 Radar and 3*3 Morphological, (b) 15*15 Radar and 5*5 Morpholo gical and, (c) 29*29 Radar
and 7*7 Morphological applied to corrupted Landsat image. Filters closely following the pattern of original Landsat image pixel distribution work best in
restoring the corrupted Landsat image.

Fig. 9. Brightness Temperature (K) estimated from (a) Original Landsat image and from corrected Landsat image by the applicat ion of (b) 3*3 open
morphological filter applied sequentially thrice, (c) 5*5 open morphological filter applied sequentially twice and (d) 7*7 open morphological filter applied
once.

00.51.01.52.0

Pixel IntensityNumber of Pixels (X 106)
0 50 100 150 200 250Original Landsat Image (shaded)
Corrupted Landsat Image
29×29 Median Filter
29×29 Local Region Filter
7×7 Open Morphological Filter
7×7 Close Morphological Filter
7×7 Erode Morphological Filter
7×7 Dilate Morphological Filter
(c)
(a)
(c) (d) (b) Page 13 of 13
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