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1 June, 1999
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3^J June, 1999
167
edener Verfahren
elliten-Bilddaten.
ition, No. 5, pp.
ASSESSMENT OF NOISE VARIANCE AND INFORMATION CONTENT
OF MULTI-/HYPER-SPECTRAL IMAGERY
Bruno Aiazzi 1 , Luciano Alparone', Alessandro Barducci 1 , Stefano Baronti 1 , Ivan Pippi 1
1 “Nello Carrara” Institute on Electromagnetic Waves IROE-CNR, Via Panciatichi, 64, 50127 Firenze, Italy, baronti@iroe.fi.cnr.it
-’Department of Electronic Engineering, University of Firenze, Via S. Marta, 3, 50139 Firenze, Italy, alparone@lci.die.unifi.it
KEYWORDS: Multispectral Images, SNR, Parametric Estimation, Bit Planes, Lossless Compression, Entropy Modelling.
ABSTRACT
This work focuses on reliably estimating the information conveyed to a user by multi-spectral and hyper-spectral image data. The goal
is establishing the extent to which an increase in spectral resolution can increase the amount of usable information. Actually, a trade-off
exists between spatial and spectral resolution, due to physical constraints of sensors imaging with a prefixed SNR. After reporting about
some methods developed for automatically estimating the variance of the noise introduced by multi-spectral imagers, an original and
effective data de-correlation algorithm designed for lossless compression of multi/hyper-spectral data is reviewed. Data compression
can be adopted to measure the useful information content of multi-spectral data. In fact, the bit rate achieved by the compression
process takes into account both the entropy the so called “observation” noise (i.e. information regarded as statistical uncertainty, but
whose relevance to a user is zero), and of the intrinsic information of hypothetically noise-free data. By defining a suitable model, once
the standard deviation of the observation noise has been preliminarily estimated, the code rate may be utilized to yield an estimate of
the true information content of the multi-spectral source, that is of one band of the multi-spectral image arranged in a causal sequence
in which the previous bands are known. Results show that the information content of multi-spectral Landsat TM images is superior to
that of hyper-spectral AVIRIS images, notwithstanding the latter are recorded with a 12 hit word length vs. the 8 bit of the former.
1. INTRODUCTION
Estimating noise and quantifying information are two tasks of
image analysis. Whereas several methods exist for assessments
of signal-to-noise ratio (SNR), e.g. for filtering (Aiazzi, 1998a,
1998b), actually the latter is still an open problem. Accurate es
timates of the entropy rate of an image source can only be ob
tained provided that data are uncorrelated. As a consequence,
data de-correlation must be considered in order to suppress or,
at least, largely reduce the correlation existing in natural images.
When multi-spectral images are concerned, de-correlation algo
rithms should take into account not only their spatial but also their
spectral correlation, to avoid over-estimating entropy (Amavut,
1998; Memon, 1994; Roger, 1996a; Ryan, 1997; Wang, 1995).
Actually, the entropy rate is a measure of statistical information,
that is of uncertainty of the source. Thus, any observation noise
introduced by the imaging sensor will result in an increase of the
entropy rate, without a corresponding enhancement of the (us
able) information content. Therefore, an estimation of the noise
must be preliminarily carried out in order to quantify its contri
bution to the overall source entropy rate.
If we assume that the noise is additive, on homogeneous areas
the variance of the observed signal will be equal to the variance
of the noise. This method, very simple indeed, suffers from being
supervised and from needing some knowledge about the presence
and location of homogeneous regions. It is possible, however, to
devise some quantities that are related to the noise of the data,
are based on local statistics and need no a-priori knowledge. A
viable approach refers to the bit-plane representation of bit-map
images. An image having L-bit word length is partitioned into
L 1-bit planes. Bit planes corresponding to bits that are more
significant exhibit a larger spatial correlation. By defining local
measurements on the bit-planes (average length of runs of zeroes
and ones, average difference between each pixel and its neigh
bours) it is possible to decide whether a bit-plane exhibits spatial
variations that entirely depend on the noise, or not. A different
approach consists of calculating the square root of local variance
on a sliding window of suitable size. The local standard devia
tion exhibits a unimodal distribution irrespective of the noisiness.
In fact, the presence of signal having nonzero variance tends to
spread the histogram towards high values, thereby increasing its
mean, but without affecting its mode. Therefore, the real valued
mode, which can be extrapolated from a smoothed version of the
histogram, will yield an estimate of the noise standard deviation.
Unlike the former, the latter method may be generalized to signal-
dependent noise, i.e. including as further parameter an exponent
ruling the dependence on the signal of the additive noise contribu
tion. Thus, histograms will become two-dimensional, i.e. scatter-
plots, and both parameters will be estimated (Aiazzi, 1999a).
The de-correlation algorithm (Aiazzi 1999c) consists of sub
tracting from each pixel its space/spectral-varying prediction.
Context-based classification of prediction errors is also included
in order to further improve the de-correlation. Prediction for a
pixel is obtained from thefuzzy-switching of a set of linear regres
sion predictors. Pixels both on the current band and on previously
encoded bands may be used to define a causal neighbourhood.
The coefficients of each predictor are calculated so as to minimize
the mean-squared error for those pixels whose intensity level pat
terns lying on the causal neighbourhood, belong in a fuzzy sense
to a predefined cluster. Size and shape of the causal neighbour
hood and number of predictors may be chosen by the user and
determine the trade-off between coding performance and compu
tational cost. The method exhibits impressive results, thanks to
the skill of predictors in fitting multi-spectral data patterns, re
gardless of differences in sensor responses.
Once the standard deviation of the observation noise, supposed
to be independent of the signal, has been measured, the bit rate
produced by the proposed reversible encoder will be utilized to
yield an estimate of the true information content of the multi
spectral source. Experimental results demonstrate that the infor
mation content of multi-spectral Landsat TM images is superior
to that of hyper-spectral images, notwithstanding the latter are
recorded with a 12 bit word length vs. the 8 bit of the former.
