International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-^ June, 1999 
173 
(b) 
Fig. 7. 512 x 512 details from (a) Band 1 and (b) Band 5 of the 
test Landsat TM image of Trento, in Italy. 
Fig. 8. Band 31 of AVIRIS Cuprite Mine ’89 test image. A 7 
correction of 2.5 was applied for displaying purposes. 
AVIRIS test data are a subset of 30 (12 to 41) from the 224 
bands of the 1989 image of the Cuprite Mine test site, having 
614 x 512 spatial size and 12 bit word length, one band of which 
is portrayed in Fig. 8 as a sample of the data set. Fig. 9 reports 
results obtained for 30 bands (12 to 41), each predicted from a 
couple of previous bands. The interval of bands considered com 
prises two different trends. In the former (bands 12 to 29), a 
decreasing noisiness appears, together with a larger and larger 
spectral predictability, since the inter-band coding scheme pro 
duces decaying bit rates. Between band 19 to 29 the plots of r 
and h u turn out to be swapped, resulting in an undefined multi- 
spectral entropy h s , which is set to zero. According to the model 
proposed, h s = 0 indicates that the bands are spectrally over 
sampled, i.e. that the spectral resolution is lower than the 10 nm 
wavelength sampling step. Thus, one band can be exactly pre 
dicted from the previous ones, apart from the noise, resulting in 
zero information. A way to obtain nonzero information would be 
to discard e.g. one band every two. An abrupt change in spec 
tral behaviour occurs at band 30: the last bands (30 to 41) are 
more difficult to be spectrally predicted, as proven by the large 
amounts of information. Notice that the plots of SNR and h s in 
Fig. 9(a) and (b), respectively, are almost opposite to each other, 
thus indicating that spectral oversampling may lead to an SNR 
improvement, which is not an indicator of spectral information. 
Band 
O u 
~ 2 
O u 
SNR (dB) 
r{k) 
h u (k) 
hs(k) 
TM-1 
1.39 
1.93 
34.5 
3.63 
3.33 
2.85 
TM-2 
0.67 
0.45 
40.8 
1.96 
1.46 
1.46 
TM-3 
0.73 
0.53 
40.1 
2.78 
1.59 
2.62 
TM-4 
5.08 
25.8 
23.2 
4.44 
4.38 
2.61 
TM-5 
4.43 
19.6 
24.4 
4.19 
4.18 
1.10 
TM-7 
1.58 
2.50 
33.4 
3.44 
2.70 
3.12 
Table 2. Noise parameters (a u , &u and SNR) and information 
parameters (r(k), h u (k) and h s (k), in bit/pel) mea 
sured on the six 30 m bands of the test TM image. 
As expected, the SNR is larger in the visible than in the infrared 
wavelengths; thus, notwithstanding the larger code rates of the 
latter, the former are slightly more informative, on the average. 
Bands 2 and 5 are the least informative, in the sense that they may 
be (bidirectionally) predicted to a larger extent than the others. 
6. CONCLUDING REMARKS 
A number of fully automatic methods have been proposed to 
identify and assess noise models from observed images. An 
extremely powerful scheme for lossless compression of multi- 
spectral images is reviewed as providing bit rates very close to 
the entropy rate of the image regarded as an information source. 
From the code rate and the estimated noise variance, a model 
was suggested to assess, or better to upper bound, the amount of 
usable information, i.e. the one not due to noise, of multi-/hyper- 
spectral images. Preliminary results indicate that bands coarsely 
sampling wavelengths (e.g. Lansat TM) convey more informa 
tion to a user than finely sampling bands (e.g. AVIRIS). In the 
latter case, depending on the characteristics of spectral resolution 
and on the 10 nm sampling step, spectral oversampling may oc 
cur which would explain the diminished amount of information 
per wavelength unit, although the SNR follows opposite trends.