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S ,IIS, Univ. of 
ADAPTIVE RECONSTRUCTION METHOD OF MULTISPECTRAL IMAGES 
Michal Haindl 
Institute of Information Theory and Automation 
Czech Academy of Sciences 
Czech Republic 
haindl@utia.cas.cz 
Stanislava Simberová 
Astronomical Institute 
Czech Academy of Sciences 
Czech Republic 
ssimbero@asu.cas.cz 
Commision lll, Working Group 2 
KEY WORDS: Image, Reconstruction, Multispectral, Theory, Application 
ABSTRACT 
A new adaptive method is introduced to reconstruct missing or corrupted lines in multi-spectral image data. The reconstruction 
uses available information from the failed pixel surrounding due to spectral and spatial correlation of multi-spectral data. 
Missing lines are assumed to be modelled with a multi-dimensional regression model but this model cannot be identified, so a 
special approximation is introduced. The reconstruction is based on two mutually competing adaptive approximations of the 
regression model from which the locally optimal predictor is selected. A directional forgetting concept is introduced to support 
parameter adaptation. 
1 INTRODUCTION 
There are several ways of reconstructing corrupted or missing 
image data. The simplest method is to replace the missing 
detector scan line by the scan line of the detector immediately 
above or bellow it (we will refer to this method further as A). 
This scheme can cause [Bernstein, 1984] very observable dis- 
tortions in the final image products, especially images of high 
contrast features. As a variant of mentioned method it has 
been suggested to linearly interpolate between the lines above 
and below the corrupted detector line - method B, or between 
six neighbouring pixels - method C. This does not solve the 
problem. Even interpolation with higher order curves, such 
as quadratic fit, is of no help see [Bernstein, 1984]. Three 
more sophisticated template-like methods were suggested in 
[Bernstein, 1984]: Template Replacement - D, Template Re- 
placement with Error Adjustment - E and Quadratic Verti- 
cal Fit with Template Data - F. The Template Replacement 
method directly substitutes a corrupted detector line with a 
detector line from a similar (well correlated) band, after scal- 
ing its output intensity so that its range is similar to the 
other lines of the failed line spectral band. The coefficients 
of the quadratic are determined by a least squares fit to the 
actual data in a five - pixel vertical slice centered around each 
bad detector pixel. The value used for the bad (center) pixel 
in the slice is calculated as in a D algorithm. Test results 
in [Bernstein, 1984] show in low contrast regions slightly off 
colour stripe after applications of algorithms D and E. The 
problem of algorithm F is that it produces a lower contrast 
value than expected in light contrast areas. 
These template-like methods cannot be used for reconstruc- 
tion of multi-spectral pixels with several spectral components 
missing, while the A,B,C methods can be used also in these 
cases. 
We have proposed the regression method [Haindl, 1992] , 
which clearly outperforms the above - mentioned recon- 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
struction methods. The regression method was improved in 
[Haindl, 1996] to select a locally optimal predictor from two 
mutually competing symmetrical adaptive predictors for each 
pixel to be reconstructed - G. In this paper we present further 
improvements of our reconstruction method. The regression 
model is generalised to reconstruct a multi-spectral line with 
all spectral components missing - H. Finally a modification 
of the method based on directional forgetting idea - method 
|, which improves parameter estimation is presented. 
Note that all the above mentioned methods, as well as our 
method, do not use any data from bad pixels, i.e. there is 
no difference between reconstruction of corrupted or missing 
data using these methods. 
The present paper is organized as follows. In Section 2, a 
proposed method general concept under a Bayesian frame- 
work is introduced. Section 3 completes the algorithm with 
a locally optimal model selection rule design. Section 4 deals 
with a multi-spectral line reconstruction and Section 5 intro- 
duces the concept of directional forgetting. Section 6 discuss 
numerical realization problems while Section 7 contains an 
application to radio-spectrograph observations of the solar 
radio emissions (mono-spectral case) and remote sensing im- 
agery data. 
2 MONO-SPECTRAL LINE REGRESSION MODEL 
Our method uses high spectral bands correlation and spa- 
tial correlation between neighbours of unusable pixels. We 
assume the mono-spectral line to be modelled as: 
Y; 2 3 aYL, b E; (1) 
ieT, 
with a multi-index £ = (m,n,d) ; Y; is a reconstructed 
mono-spectral pixel value, m is the row number, n the 
column number, d(d > 1) denotes the number of spectral 
bands and also the spectral band with line to be reconstructed 
809