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NEW QUALITY REPRESENTATION FOR HYPERSPECTRAL IMAGES 
Emmanuel Christophe*, Dominique Léger*, and Corinne Mailhes* 
* CNES DCT/SI/AP Bpi 1219, 18 av E. Belin 31401 Toulouse Cedex 09 
emmanuel.christophe@cnes.fr 
* Optics Department of ONERA, 2 avenue E. Belin BP 4025, 31055 Toulouse Cedex 4 
* University of Toulouse, TESA - IRIT - ENSEEIHT, 14 port St Etienne 31000 Toulouse, FRANCE 
Commission VII/3 
KEY WORDS: Hyperspectral, quality criteria, evaluation, compression 
ABSTRACT: 
Assessing the quality of a hyperspectral image is a difficult task. However, this assessment is required at different levels of the 
instrument design: evaluation of the signal to noise ratio necessary for a particular application, determining the acceptable level of 
losses from compression algorithms for example. It has been shown previously that a combination of five quality criteria can provide 
a good evaluation of the impact of some degradation on applications, such as classification algorithms for example. This paper refines 
this concept, providing a representation of the degradation which allows predicting the impact on applications. 
1 INTRODUCTION 
Quality criteria should be easily applicable to measure the loss of 
information caused by compression or by any other forms of pro 
cessing. In the case of ordinary 2D images, a quality criterion has 
often to reflect the visual perception of a human observer. This 
is not the case for hyperspectral images, which are first aimed 
to be used through classification or detection algorithms. There 
fore, quality criteria have to be relevant to these corresponding 
applications. For example, some papers ( [Ryan and Arnold, 
1997], [Hu et al., 2004], [Qian, 2004]) address the problem of 
evaluating compression impact on specific hyperspectral applica 
tions. However, quality evaluations within the context of specific 
applications are heavy to conduct as they require in-depth knowl 
edge of these applications. 
Figure 1: Different hyperspectral images used during the experi 
ments. (a) and (b) are different parts from the f970620t01p02_r03 
run from AVIRIS sensor on Moffett Field site, (a) presents uni 
form spatial area with strong spectral features, (b) is mixed area 
with city (strong spatial frequency features), (c) is from the 
f010903t01p01_r03 AVIRIS run over Harvard Forest, it contains 
mostly vegetation whose spectrum contrasts with man-made ob 
jects. 
In a previous work [Christophe et al., 2005], different degrada 
tions were applied to hyperspectral images: additive white noise, 
smoothing (spectral and/or spatial) with a lowpass filtering of 
the data, Gibbs effect (ringing around sharp changes) and JPEG 
2000 compression [Taubman and Marcellin, 2002] using a mul 
ticomponent transform. Different images from the NASA/JPL 
AVIRIS hyperspectral airborne sensor were used for the exper 
iments (Fig. 1). Finally, five quality criteria have been selected 
to give a valuable representation of the degradations affecting the 
hyperspectral data and their impacts on three different classifica 
tion algorithms. These five quality criteria were found to be a 
good combination to discriminate between data degradation and 
appear to be almost orthogonal to each other. One advantage of 
this combination is the mix between local and global criteria for 
both spatial and spectral dimensions, thus enabling the detection 
of local and global degradations. 
2 QUALITY REPRESENTATION 
2.1 Efficient representation for five criteria 
The five quality criteria retained in [Christophe et al., 2005] were 
the MAD, MAE, RRMSE, F\ and Q( x , y ). Denoting I(x,y, A) 
the original image, I(x, y, A) the degraded image and ej = I — I 
(x, y being spatial dimensions and A the spectral one), these five 
quality criteria are defined as 
• Maximum Absolute Difference 
MAD = £oo(7 — I) = max {|ej-(a;, y, A) |} . (1) 
However, the way to use these measures was not detailed. The 
present paper proposes in the following section a graphic repre 
sentation of the chosen quality criteria. A numerical method is 
then derived in section 3 from this representation to provide a 
way to identify the degradation nature if unknown and to predict 
its impact on a specific application. The interest of the proposed 
representation is finally illustrated and compared with traditional 
SNR-based measure. 
• Mean Absolute Error 
MAE = 
Tlx Tly Tï\ 
l 
TixTlyTl X 
Y \e T (x,y,X)\. 
x,y,\ 
(2) 
where n x , n y and n\ are the number of pixels for each di 
mension.