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Mapping without the sun
Zhang, Jixian

Pingxiang Li a, *, Jixian Zhang b, Huanfeng Shen c, Liangpei Zhang a
The State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan
University, Wuhan, Hubei, China, 430079-pxli@lmars.whu.edu.cn, zlp62@public.wh.hb.cn.
b Chinese Academy of Surveying and Mapping- zhangjx@casm.ac.cn
c School of Resource and Environmental Science, Wuhan University-shenhf@whu.edu.cn
KEY WORDS: Super resolution, Remote Sensing, Multi-temporal images, Registration, Joint framework, Maximum a posterior.
In this paper, we propose a super resolution (SR) image reconstruction algorithm to multi-temporal remote sensing images. The aim
is to reconstruct a high resolution (HR) image by fusing the non-redundant information among the low resolution (LR) remote
sensing images which captured on different dates by the same sensor. To increase the robustness of the image registration and SR
reconstruction, we combine the two processes together using the maximum a posterior (MAP) framework. In the solution procedure,
a cyclic optimization method is employed to solve the desired SR image, registration parameters and outliers which strongly depart
away from the observation model. We test the proposed algorithm using real multi-temporal MODIS images. The experimental
results and comparative analyses verily the effectiveness of this algorithm.
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Image fusion is the combination of two or more different
images to form a new image by using a certain algorithm. In the
field of remote sensing, image fusion technique is commonly
employed for sharpening low resolution (LR) images using one
or more high resolution (HR) images, such as the fusion of
multi-spectral images with SAR or panchromatic image. As a
special case of image fusion, super resolution (SR) image
reconstruction refers to a process that produces a HR image
from a sequence of LR images using the non-redundant
information among them. Generally, the non-redundant
information roots in the sub-pixel displacements among the
observed images.
The multi-frame SR problem was first formulated by Tsai and
Huang (Tsai and Huang 1984) in the frequency domain using
discrete Fourier transform (DCT) . Consequently, many kinds
of spatial domain approaches have been developed. Typical
spatial domain approaches include non-uniform interpolation
(Ur and Gross 1992), iterative back projection (IBP) (Irani and
Peleg 1991), projection onto convex sets (POCS) (Stark and
Oskoui 1989; Tekalp, Ozkan et al. 1992; Patti, Sezan et al. 1994;
Patti, Sezan et al. 1997), maximum likelihood (ML) (Tom and
Katsaggelos 1994), maximum a posteriori (MAP) (Schultz and
Stevenson 1996) (Hardie, Tuinstra et al. 1997), hybrid ML
/MAP/POCS (Elad and Feuer 1997), and adaptive filtering
(Elad and Feuer 1999).
Although the SR technique has been greatly developed in the
last decades, it has been applied to generic camera images,
medical images and video sequence much more commonly than
remote sensing images. Although some papers in the literature
provided the SR results of satellite images, most of them used
synthetic images and assumed known motion parameters. Shen
et al. (Shen, Ng et al. 2007, accepted) proposed a super
resolution image reconstruction algorithm to multi-temporal
remote sensing images. They implemented image registration
and SR reconstruction separately. This paper extends the
previous method by employing a joint MAP framework to
simultaneously estimate the image registration parameters and
the HR image. This algorithm reinforces the interdependence
among the motion estimates and HR image in a mutually
beneficial manner.
For the SR problem, a typical image observation model
assumes that imaging process involves warping followed by
blurring and down-sampling to generate LR images from a HR
image. Let us denote the underlying HR image in vector form
by Z- [z x ,Z 2 ....,Z LyN ^ LiNi f , where L x N x xL 2 N 2 is the HR
image size. Letting Lj and L 2 denote the down-sampling
factors in the horizontal and vertical directions respectively,
each observed LR image is of size A, x N 2 • Thus, the LR image
can be represented as g k =[g kA ,g kX ...,g k ^ N J <
where k = 1,2,.... P, with P being the number of the LR images.
The typical image observation model can be represented as
(Elad and Feuer 1997; Park, Park et al. 2003):
g k =DB k M k z + n k (1)
where M k is the warp matrix, B k represents the blur
matrix, D is a down-sampling matrix, and n k represents the
noise vector.
In remote sensing imaging, the sun zenith angle and
atmospheric absorption and scattering affect the amount of
radiance received by the sensor. These effects in many cases
can be simply modeled as a linear system (Conel 1985; Roberts,
Yamaguchi et al. 1985), with which the following image
observation model can be obtained
* Corresponding author.
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