Improved Grouping and Noise Cancellation for Automatic Lossy Compression of AVIRIS Images - Advanced Concepts for Intelligent Vision Systems - page 265

compression of the data with setting the quantization step individually for each
sub-band image as QS ( n )=4 . 5 σ n . This method is simple but it in no way
exploits the inter-band correlation inherent for hyperspectral data [2]-[6]. Note
that the accounting for the spectral redundancy of HSI results in a considerable
increase of CR. Taking this into account, a method called M2 has been also
proposed in [16]. For this method, the grouping of sub-band images is to be
carried out using two main rules. The first rule is that each the k -th group
should contain 4, 8, or 16 sub-bands. The second rule is that the grouping is
started from the first sub-bands and is performed depending upon the variation
of the noise variance. The main condition checked is

σ 2
n,k max
σ 2
n,k min

≤ 2 (1)

G k , σ 2
n,k max

, σ 2
n,k min

where n are the maximal and the minimal noise vari-

ances, respectively, in a group G k .Foreach k -th group, the quantization step
QS k =4 . 5 σ n,k min for compressing a given group of sub-band images. The com-
pression is carried out by the 3D AGU coder [16] based on the discrete cosine
transform that performs both the spectral and the spatial decorrelation of the
data. The smallest σ n,k min in a group is used for calculating QS k to avoid the
oversmoothing of the compressed images (see Section 2). Note that the method
M2 produces about twice larger CR than the method M1 with smaller intro-
duced distortions. Fig. 5 presents an example of the estimated noise standard
deviations σ n , n =1 ,..., 224 and the set quantization steps for the methods M1
and M2. As it is seen, the group sizes for the method M2 are different and they
are small (4 sub-bands) for subsequent sub-bands with a high variation of σ n .
The method M2 described in [16] has a certain shortcoming. If a group size is
small (e.g., 4 sub-bands), this does not allow exploiting the spectral redundancy
in full extent (note that the spectral decorrelation in many modern coders in
HSI is carried out for all sub-bands [5] although such approach might lead to
undesirable effects [28]). The reason why for some groups their size is small is the
use of the condition given in Eq. 1. However, there is a quite simple opportunity
to overcome the limitations on the group size as well as the problems of the
variation of the noise variance and the sub-band image undersmoothing.
Theideaistomakeall σ 2
n

∈

G k equal to each other before the compression.
This can be easily done by the following normalization:

, n ∈

= I ij,n
σ n

I norm
ij,n

, n =1 ,..., 224 (2)

where I ij,n is an original image value at ij -th pixel of n -th sub-band. Such
normalization allows providing the additive noise variance in all images close to
the unity (with taking into account the accuracy of the blind estimation).
After the normalization given in Eq. 2, the lossy compression is applied to
the sub-band images collected into groups with the size Q> 4. For all these
groups, QS is the same and, since the standard deviation of the additive noise
in all images after the normalization becomes about 1 . 0, we recommend using