IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 9, SEPTEMBER 2012 3453
A Bayesian Restoration Approach
for Hyperspectral Images
Yifan Zhang, Member, IEEE, Arno Duijster, and Paul Scheunders, Member, IEEE
Abstract—In this paper, a Bayesian restoration technique for
multiple observations of hyperspectral (HS) images is presented.
As a prototype problem, we assume that a low-spatial-resolution
HS observation and a high-spatial-resolution multispectral (MS)
observation of the same scene are available. The proposed ap-
proach applies a restoration on the HS image and a joint fusion
with the MS image, accounting for the joint statistics with the MS
image. The restoration is based on an expectation–maximization
algorithm, which applies a deblurring step and a denoising step
iteratively. The Bayesian framework allows to include spatial
information from the MS image. To keep the calculation feasible,
a practical implementation scheme is presented. The proposed
approach is validated by simulation experiments for general HS
image restoration and for the specific case of pansharpening.
The experimental results of the proposed approach are com-
pared with pure fusion and deconvolution results for performance
evaluation.
Index Terms—Bayesian, deconvolution, expectation–
maximization (EM), fusion, hyperspectral (HS) image,
restoration.
I. INTRODUCTION
I
N REMOTE sensors, usually, a tradeoff exists between
SNR, spatial and spectral resolutions due to physical limita-
tions, data-transfer requirements, and some other practical rea-
sons. In most cases, high spatial and spectral resolutions are not
available in a single image. Hyperspectral (HS) images employ
hundreds of contiguous spectral bands to capture and process
spectral information over a range of wavelengths, compared to
the tens of discrete spectral bands used in multispectral (MS)
images [1]. However, the spatial resolution of HS images is
usually lower than that of MS images [2]. In practice, many
applications require high accuracy both spectrally and spatially,
which inspires research on HS image spatial resolution en-
hancement techniques.
Manuscript received October 12, 2009; revised June 27, 2011; accepted
December 18, 2011. Date of publication March 5, 2012; date of current version
August 22, 2012. The work of Y. Zhang was supported in part by the National
Natural Science Foundation of China under Grants 60736007 and 61101188,
by the Natural Science Basic Research Plan in Shaanxi Province of China
under Grant 2011JQ8023, and by the Northwestern Polytechnical University
Foundation for Fundamental Research under Grant NPU-FFR-JC20100233.
Y. Zhang is with Shaanxi Key Laboratory of Information Acquisition and
Processing, School of Electronics and Information, Northwestern Polytechnical
University, Xi’an 710072, China (e-mail: yifanzhang@nwpu.edu.cn).
A. Duijster and P. Scheunders are with the Interdisciplinary institute
for BroadBand Technology Vision Lab, Department of Physics, University
of Antwerp, 2610 Wilrijk, Belgium (e-mail: arno.duijster@ua.ac.be; paul.
scheunders@ua.ac.be).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TGRS.2012.2184122
In the recent literature, different techniques were developed
for the spatial resolution enhancement of HS images [2]–[8].
When only one observation is available, one approach is image
restoration, in which the spatial resolution of the image is en-
hanced by inverting the imaging model based on the knowledge
of the image point spread function (PSF).
There exists a vast literature on grayscale image restoration.
Usually, the image degradation is described by a linear space-
invariant convolution (blurring) operator and additive Gaussian
noise. Inversion of the blurring operator is generally accom-
plished in Fourier domain, requiring regularization (denoising)
to avoid the singularities.
MS image (multiband) restoration has been performed as
well using similar strategies. A straightforward multiband
restoration approach is to transform the multiband image to
spectrally decorrelate the bands and restore the decorrelated
images in a single-band fashion [9]. This approach only works
when no spectral blurring is present. Multiband versions of
linear methods, such as Wiener filtering [10] and least squares
restoration [11], have been proposed. In [12], the authors
present a mathematical framework in frequency domain, allow-
ing a generalization of frequency-domain single-band decon-
volution techniques for multiband data processing. In [13], a
Bayesian maximum a posteriori (MAP) estimation has been
proposed, with a Gibbs prior over a Markov random field
constraining both spatial and spectral components as the image
model.
Restoration is known to be an ill-posed inverse problem,
since the deconvolution requires the inverse of the blurring
operator, which may be nearly singular or even not exist, re-
sulting in magnification of noise. A disadvantage of the Fourier
transform is that it does not efficiently represent image edges.
As a result, only small amounts of regularization are allowed
to avoid blurring of the edges in the image. In the wavelet
domain, on the other hand, this problem is avoided since
edges are represented by large coefficients which are better
retained after regularization. This property makes the wavelet
transform (WT) more suitable for image denoising, which has
been demonstrated in a countless number of effective denoising
schemes [14]. Therefore, for restoration, it is advantageous to
separate the deconvolution and the denoising problems.
In the recent literature, this strategy has been applied, and
several solutions for the deconvolution problem have been
formulated. In [15], a technique, referred to as ForWaRD,
applies a Wiener deconvolution followed by a wavelet shrink-
age. Several iterative deconvolution methods were proposed
based on the expectation–maximization (EM) algorithm [16]
or generalization of it [17], and the more recently developed
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