=Paper=
{{Paper
|id=Vol-1638/Paper39
|storemode=property
|title=Interpolation for hyperspectral images compression
|pdfUrl=https://ceur-ws.org/Vol-1638/Paper39.pdf
|volume=Vol-1638
|authors=Mikhail V. Gashnikov
}}
==Interpolation for hyperspectral images compression==
https://ceur-ws.org/Vol-1638/Paper39.pdf
Image Processing, Geoinformatics and Information Security
INTERPOLATION FOR HYPERSPECTRAL IMAGES
COMPRESSION
M.V. Gashnikov
Samara National Research University, Samara, Russia
Abstract. The comparative research of the different interpolators for hierar-
chical compression of hyperspectral images is performed. The compression
method based on a hierarchical grid interpolation is considered. Standard inter-
polation schemes are described and the rank interpolator is proposed as a part of
this compression method. The computational experiments are performed on real
images of 16-bit hyperspectrometers. The results of the interpolators’ compari-
son are considered in the coordinates "error - compression ratio."
Keywords: interpolation, digital image compression, hyperspectral image,
maximum error.
Citation: Gashnikov MV. Interpolation for hyperspectral images compression.
CEUR Workshop Proceedings, 2016; 1638: 327-333. DOI: 10.18287/1613-
0073-2016-1638-327-333
Introduction
Research areas related to the processing of hyperspectral images attract more and
more attention in recent years [1-3]. Remote sensing data of this type are increasingly
used in various applications [4-10]. However, one of the main problems that disturb
the use of hyperspectral images is the size of this data. One such image includes sev-
eral hundred channels of two-dimensional size of several thousands of pixels in each
coordinate, and these images are used immediately.
The growth of capacity of communication channels and data storage devices currently
not keep pace with the growth of hyperspectral data sets, so the only possible practical
solution is the use the images compression [11-12]. The problem is compounded by
the fact that hyperspectral data are often 16-bit, with the result that most of the popu-
lar implementations of the compression methods are not applicable.
One of the most perspective methods of hyperspectral image compression is the
method [13-14], based on a hierarchical grid interpolation (HGI), which uses hierar-
chical image decimation and interpolation of pixels of more decimated image based
on pixels of less decimated image. Advantages of this method:
1. The high efficiency at a low computational complexity.
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2. Access speed to image fragments is independent of the required resolution due to
the hierarchical representation of the compressed data.
3. The possibility of strict error control [15], including mean square error and maxi-
mum error, which is especially important when processing the unique hyperspec-
tral data (including the possibility of compression without error).
4. The ability to stabilize the rate of compressed data flow, particularly relevant for
real-time systems, including on-board compression systems.
5. Possibility of using of spectral bands relationships, allowing the use of extremely
high correlation of the spectral components to improve compression efficiency.
6. The possibility of compression of 16-bit spectrometers data without significant loss
efficiency.
One of the key stages of the HGI method is the interpolation stage, so the task of
comparative research of the interpolators’ effectiveness for method HGI is actual.
This problem is not researched in the published literature. In this study, we perform a
comparative research of different interpolation schemes for HGI method, and propose
a "rank" interpolator which has not previously been used as a part of this method.
1 Hierarchical compression
Compression method based on HGI uses a special representation of image
F f m, n in the form of a nonredundant quadrotree [13] from L scale levels.
Let I l 2l m, 2l n is an index set of pixels, taken with 2 step. The index set I
l
L 1
of pixels of «senior» scale level of image is simply a grid with a step 2 . The index
L-1
set I l of pixels of any remaining scale level l number is a grid with the step 2l, from
which the pixels with the step 2l+1 are excluded:
I L1 I L1 , I l I l \ I l1 , 0 l L .
We can see that the index set I m, n of the image is covered by the sets of scale
levels indexes, and this representation is nonredundant:
L 1
I Il , Ij Ik k j .
l 0
When compression the scale levels are processed sequentially, starting with the «sen-
ior» level (L – 1) number. The proportion of «senior» level pixels in the total data size
is negligibly small, so any trivial algorithm can be used to compress it. Common dia-
gram of compression of any «non-senior» scale level number l is shown in Fig. 1 and
includes the following steps.
1) Pixels interpolation. An interpolated value is calculated for each pixel f m, n of
scale level number l on the basis of already processed pixels f m, n :
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fˆ m, n P f j, k , j, k I , m, n I .
l 1 l
Interpolation is based on recovery, rather than the original pixels values in order to
ensure the identity of the interpolated values for compression and decompression.
2) Calculation of difference signal (post interpolation residues):
m, n f m, n fˆ m, n , m, n I l .
This operation reduces the signal correlation; as a result the efficiency of compression
is improved
Source
image
Pixels interpolation
Calculation of difference signal
Archive file or
communication channel
Fig. 1. The scheme of compression of any «non-senior» scale level of image by HGI method
3) Quantization of difference signal by uniform scale:
m, n max
m, n sign m, n , m, n I l ,
2max 1
where ... is the symbol of integer part calculation. This quantization provides the
control [16] of maximum error max :
max f m, n f m, n .
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4) Packaging of quantized signal m, n , m, n I l to the archive file or commu-
nication channel.
5) Pixels restoring:
f m, n fˆ m, n m, n 2 max 1 , m, n I l .
These recovered values are used for interpolation during compression of the next
scale level number l 1 . In this description of the compression procedure is com-
pleted.
When decompressing the quantized signal m, n , m, n I l is extracted from the
archive file (or link) and unpacked. Next, reconstruction and interpolation steps iden-
tical respective compression steps are performed.
2 Interpolation for hierarchical compression
For interpolation in HGI method the simple schemes [17] are usually used, based on
averaging the nearest already processed pixels of more decimated scale levels of the
image. These schemes are differed from each other in the number of referenced pixels
and interpolations sequence.
Formulas for a description of these schemes are cumbersome, but these formulas are
clear from Fig. 2, so there are only formulas for the interpolator is shown in Fig. 2c:
4 fˆ 2l 2m 1 , 2l 2n 1 f 2l 1 m 1 , 2l 1 n 1
f 2 m 1 , 2 n f 2 m, 2 n 1 f 2 m, 2 n ,
l 1 l 1 l 1 l 1 l 1 l 1
4 fˆ 2l 1 m, 2l 2n 1 f 2l 1 m, 2l 1 n 1
f 2 m, 2 n f 2 m 1 , 2 2n 1 f 2 m 1 , 2 2n 1 ,
l 1 l 1 l 1 l l 1 l
4 fˆ 2l m 1 , 2l 1 n f 2l 1 m 1 , 2l 1 n
f 2 m, 2 n f 2 2m 1 , 2 n 1 f 2 2m 1 , 2 n 1 .
l 1 l 1 l l 1 l l 1
Also listed in Fig. 2 interpolators in this paper we propose to use as "rank" interpola-
tor within a hierarchical compression. Location of the reference pixels and sequence
of interpolations are used in it are the same as that of the interpolator "Two crosses"
(see Fig. 2c). Actually interpolation algorithm consists in constructing the ordered
sample [6] of reference pixels, dropping his two extreme elements and averaging the
remaining. Described truncation of ordered sample reduces the effect of noise which
usually falls on the edge of ordered sample and discarded.
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(a) (b) (c)
Fig. 2. Location of reference pixels and the processing sequence for the interpolators:
(a) «Diagonal cross», (b) «Straight cross», (c) «Two crosses»
3 Experimental researches
All of the algorithms were implemented in software by author. The developed soft-
ware was used to perform the computational experiments on the series of real images
of 16-bit hyperspectrometers SpecTIR [18] and AVIRIS [19]. Fragments of the spec-
tral bands of hyperspectral image are shown in Fig. 3 (we specially selected examples
of very different components of weak and strong noise). Charts of the relationship
between the compression ratio and compression error are shows in Fig. 4-5. Based on
thise results, the following conclusions were reached:
1. Interpolators "two crosses" and "rank" showed the greatest efficiency in compres-
sion of hyperspectral images by HGI. Interpolators "diagonal cross" and "straight
cross" significantly lose.
2. Linear interpolator "two crosses" and the non-linear “rank” interpolator showed
almost identical results. Consequently, the key characteristics of the interpolator
are the location of the reference pixels and the sequence of interpolations, not the
kind of interpolation function.
3. “Ranked” interpolator proposed in this paper for use in a hierarchical compression,
showed results close to the best. This leads to the conclusion about the prospects of
non-linear interpolation scheme for the HGI method.
Fig. 3. The fragments of spectral bands №70, №119 of image «Gulf of Mexico Wetland Sam-
ple» of hyperspectrometer SpecTIR
Conclusion
Comparative research of different interpolation schemes for hyperspectral images
compression is carried out in this paper. As a method of hyperspectral images com-
pression we consider HGI method. Researches the effectiveness was carried out on
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the real images of the 16-bit hyperspectrometers. The dependence the compression
ratio of the compression error is obtained when using different interpolators. Compar-
ison of the three averaging interpolation schemes, as well as proposed for use in the
method of the ISI «rank» scheme is performed. Key features of interpolators that
affect the efficiency of compression are revealed.
In the future, we plan to develop the non-linear interpolation scheme, showing its
effectiveness in a hierarchical compression of hyperspectral images. Also the adaptive
selection of different interpolation schemes for different spectral components is per-
spective, as the characteristics of these components are substantially different.
Кс
15
13
11
9 Interpolators:
7 “Two crosses”, rank
5 “Straight cross”
“Diagonal cross”
3
0 1 2 3 4 5 6 7 8 9 max
Fig. 4. Relationship between the compression ratio Kc and maximum error max
for HGI method when using different interpolators
Кс
25
20
15
Interpolators:
10 “Two crosses”, rank
“Straight cross”
5 “Diagonal cross”
0
0 10 20 30 50 60 70
Fig. 5. Relationship between the compression ratio Kc and square error 2
for HGI method when using different interpolators
Acknowledgements
This work was financially supported by the Russian Scientific Foundation (RSF),
grant no. 14-31-00014 “Establishment of a Laboratory of Advanced Technology for
Earth Remote Sensing”.
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