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QUICKBIRD-2 REMOTE SENSING IMAGE SUPER-RESOLUTION USING
POCS/DCT
Miguel Archanjo Bacellar Goes Telles Junior1,2,3, Antonio Nuno de Castro Santa Rosa1
de Brasília – Instituto de Geociências, Campus Universitário Darcy Ribeiro,
ICC-Sul, IG, 70910-000, Brasilia – DF, Brazil , [email protected], [email protected]
2 MD-Exército Brasileiro-COTER, QG Ex Bl H 1º piso – SMU, Brasília-DF, Brazil,70272-110,
[email protected]
3 Centro Universitário de Brasília-UniCEUB, SEPN 707/909 - Campus do UniCEUB - Asa
Norte, [email protected]
1Universidade
The objective of this research is to present the results and analysis of our research in
image super-resolution of Quickbird-2 image. The goal of super-resolution is produce a
high resolution image from a set of low resolution images. The resulting high resolution
image has spatial resolution of 0.30 meters to Quickbird-2 image. To achieve this we
use a modified POCS super-resolution method with DCT resampling and shifting. The
resulting images are subsampled at its original spatial resolution and compared with the
original ones. The resulting images and statistical analysis showed good results
regarding to the used method in the cases considered in this paper.
Introduction
The main objective of our research is to
presents the results of super-resolution method
POCS/DCT on remote sensing images mainly
in Quickbird-2 image.
Super-resolution (SR) is one of most recent
research theme in digital image processing
(DIP). It overcome the inherent limitations of
the image systems and enhances the
performance of the most DIP applications. The
challenge of these set of techniques is to
improve spatial resolution, and with that, to
obtain a better interpretation and identification
of the targets in the images, preserving the
original information, without increasing false
targets to the image obtained.
The super-resolution method used in this paper
is based on the method of the projections onto
convex set (POCS) [1], modified by using sinc
interpolator [2], instead of the traditional
interpolators used, to know, nearest neighbor,
bilinear and cubic convolution.
The discrete cosine transform (DCT) is used
also to produce a displacement of the image in
the frequency domain to generate a different
frame. It aims to avoid aliasing.
Super-resolution
Super-resolution can be defined as the
obtaining of an image of better resolution
(HR) starting from multiple images of low
resolution (LR) [3] and [4], and it corresponds
to all those methods of DIP capable to increase
in a significant way the spatial resolution of an
image [4].
The super-resolution techniques combine LR
images of a same scene, in order to produce
one or several HR images. The LR images
represent the same geographic area, but they
possess differences among them, those are
characterized by: different acquisition dates,
different projections, small variations in the
spatial resolution and pixel displacements.
Most of the super-resolution methods consist
of three basic components: i. movement
compensation;
ii.resampling;
iii.focus
correction and noise removal.
The first of the three components refers to the
mapping of the movement of the different LR
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images to a grid of common reference, that
mapping can be modeled by vectors of
movements or affine transformations; The
second component, refers to the mapping of
the pixels manipulated by the first component
in the super-resolution grid; the third
component is necessary to remove the blur
effect caused by the sensor and its optics [4].
Fig. 1 presents a diagram of those stages.
y1
y2
...
...
yp-1
yp
Registro ou
Compensação
de
Movimento
Interpolação
na grade de
HR
Restauração
para correção
de foco e
remoção de
ruído
Imagem
SR
z
Fig. 1 Super-resolution scheme, adapted from
Chaudhuri (2001).
SR has been proving to be quite useful in
many cases, where it is possible to obtain
different images of a same scene, including
medical, remote sensing, video and forensic
images.
The interpolation algorithms, nearest neighbor,
bilinear and cubic convolution, differ from SR
because in the first ones, only one image is
used as source of information to produce an
image of larger resolution. Different that is
used to produce an image using SR.
Tsai and Huang [5] were the first ones to
develop research on the problem of the HR
image reconstruction starting from a sequence
of LR images. The model proposed by them
was based on the translation of movements
and it solved the problem of the registration
and restoration, but it didn't consider the
effects of the degradation of the signal and of
the noise. The method for them developed it
explores the relationship among fast cosine
transform and direct Fourier transform of the
subsampled frames.
Kim et al. [6] extended the method of Tsai and
Huang [5] and they considered the noise and
the blur effect in the LR images and developed
an algorithm based on the theory of pondered
least squares. Later on the method was
improved by Kim and Su [7] that considered
the blur effect in each one of the LR images.
The reconstruction of HR images starting
from a set of LR images was proposed initially
by Stark and Oskui [8], where they used the
formulation of the projection onto convex sets
(POCS) [1].
POCS Method
The POCS method uses a priori information of
the images to find a common point f that
satisfies a set of restrictions, each one of them
forming a convex set. The common point f
locates in the intersection of all the convex
sets.
im
f C    Ci
i 1
(1)
Where the ith convex set C i denotes the ith
restriction on f . The common point can be
found in an alternative way projecting onto the
convex set C i through the corresponding
projection operator P ci .
f (k 1)  Pcm Pcm 1 ...Pc1 f (k )  Pc f
(2)
The POCS algorithm is used in several superresolution and restoration methods.
Sinc Interpolation
Interpolation is a very common operation in
applications of DIP. These operations are
necessary when it is needed, in the domain of
the frequency of a larger resolution than that
corresponding to the sampling rate.
Yaroslavsky (2002).
The interpolation algorithms most used are:
nearest neighbor, bilinear and cubic
convolution. These algorithms are popular due
to its computational simplicity. This
simplicity, even so it takes to a low accuracy
and the production artifacts due to aliasing.
The most accurate method to represent
frequency with a monotonic decline of the
spectrum of its samples is the sinc
interpolation. In this interpolation, a
continuous signal a(x) is restored from its
samples that are taken with a sampling interval
x by its interpolation with the sinc function:

sin[  ( x / x  n)]
a ( x)   a n
 ( x / x  n)
n  

  an sin c[ ( x / x  n)]
n  
(3)
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where,
Results
sin x
sin c( x) 
x
(4)
Details about sinc interpolation can be
obtained in Yaroslavsky [9].
POCS/DCT Method
SR is processed band by band. In the proposed
method each one of the bands is an LR image.
Initially a new LR image is created and
displaced by 0.5 pixel in relation to the
original values of its lines and columns. This
procedure is accomplished, in order to reduce
the aliasing effect and to allow to the POCS
algorithm a better reconstruction of the HR
image.
After the displacement, the grid of high
resolution is created, that will be in this case
with twice the size of the original image.
The original LR image is resampled using the
sinc interpolator. This image and the displaced
LR image are processed then in the POCS
algorithm and the HR resultant image has a
spatial resolution of twice the original. The fig.
2 presents a schematic diagram of the POCS
method with sinc interpolator.
In the present paper only the panchromatic
band of the Quickbird-2 satellite is used.
The super-resolution method used in this paper
uses a cut of the panchromatic image of the
Quickbird-2 satellite acquired on July 17, 2005
and it cover the area of the Santos Dumont
airport at the Rio de Janeiro city in Brazil. Its
size is 256 x 256 pixels.
The original image was processed with the
following processing parameters:
a. Number of frames: 2;
b. Interpolator: sinc;
c. Number of interactions at POCS
algorithm: 2;
d. Frame displacement: 0.5 pixel
As the images LR and HR possess different
spatial resolution, to evaluate the results of SR,
the HR image was subsampled to the spatial
resolution of the original LR image, using the
nearest neighbor interpolator. This was
selected by preserve the spectral resolution of
the images better than others. Measures of the
correlation coefficient were accomplished and
the universal image quality index (Q) was used
as proposed by Wang and Bovik [11].
The universal image quality index (Q) is
given by:
4 xy .x. y
(5)
Q
( x2   2y )[( x ) 2  ( y ) 2 ]
Where x e y are the mean of LR original
image
and
subsampled
HR
image,
2
respectively;  x e  2y are de variances between
Fig. 2 Schematic diagram of the POCS method with
Sinc interpolator
x and y ; and  xy is de covariance between x
and y .
The Q index models the difference among two
images as a combination of three different
factors: the correlation loss, luminance
distortion and contrast distortion. The values
for Q are between -1 and 1.
In order to facilitate a better analysis of the
results is presented in the fig. 4(b) and fig. 4(c)
the original LR image resampled by the
nearest neighbor and bilinear interpolators,
respectively NN and Bi image.
The table 1 presents the qualitative measures
among the LR original image and the HR, NN
and Bi images. All the images were
subsampled to the size of the LR original
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image so that measured them qualitative
presented they were made.
The result of the qualitative measures among
the LR image and the HR image presents good
results so much for the correlation coefficient
as for the index Q.
significant alteration in the spectrum of the
images, but they degrade its high frequencies
that are related to the borders or details of the
images. The visual analysis confirms that
observation.
Fig. 4(a), 4(b) and (4(c) presents HR, NN and
Bi images, respectively. These figures have
512 x 512 pixels.
Table 1 – Qualitative measures of HR, NN
and Bi subsampled images
Images
CC
Q
0.976
0.882
HR
0.999
0.987
NN
0.999
0.987
Bi
Conclusions
(a)
In this paper we evaluate the potential of the
modified POCS/DCT method and its use for
SR of images with high spatial resolution, in
particular, the panchromatic band of the
Quickbird-2 satellite.
In spite of the presented results, our research
in SR will have continuity with the use and
developments of other methods of SR and of
better indexes for the results evaluation.
References
(b)
(c)
Fig 4 (a), (b) and (c) presents HR, NN and Bi images
The best results reached for the NN and Bi
images are due to the fact that in those
interpolation algorithms there isn't a
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