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Airborne and spaceborne acquired hyperspectral images are used to recognize objects and to classify materials on the surface of the earth. The state of the art compressor for lossless compression of hyperspectral images is the Spectral oriented Least SQuares (SLSQ) compressor (see [
Hyperspectral remote sensing obtains information from the visible and the nearinfrared spectrum of reflected light. Agriculture, mineralogy, physics, surveillance, and so on are just some examples of applications of the hyperspectral images.
This technology is continually in evolution and it is gradually becoming available to the public.
In military and civilian applications the remote acquisition of high definition electrooptic images has been increasingly used. Moreover, these airborne and spaceborne acquired data are used to recognize objects and to classify materials on the surface of the earth.
It is possible to recognize the materials pictured in the acquired threedimensional data by analysis of the spectrum of the reflected light.
NASA and other organizations have catalogues of various minerals and their spectral signatures. The new technologies for hyperspectral remote sensing acquisition allow the recording of a large number of spectral bands, over the visible and reflected infrared region. The obtained spectral resolution is sufficient for an accurate characterization of the spectral reflectance curve of a given spatial area.
Higher resolution sensors will be available in the near future that will permit to increase the number of spectral bands. In fact, the increase in the number of bands,
The volume of data generated daily by each sensor is in the order of many gigabytes and this brings an important need for efficient compression.
Example of data cube for a hyperspectral image.
We focus our attention on visualization, band ordering and compression of hyperspectral imagery.
A hyperspectral image is a collection of information derived from the electromagnetic spectrum of the observed area. Unlike the human eye that can only see visible light,
Each material has an unambiguous fingerprint in the electromagnetic spectrum (spectral signatures). The spectral signature allows the identification of different types of materials.
There is a wide range of real life applications where hyperspectral remote sensing plays a very important role. For example, in geological applications the ability of hyperspectral images to identify the various types of minerals makes them an ideal tool for oil and mining industries, and hyperspectral remote sensing is used to search for minerals and oil. Other important fields of application are ecology, surveillance, historical research, archeology,
The hyperspectral sensor for the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) [
The AVIRIS system measures and records the power level of the radiance of the instrument.
In the rest of this paper we have tested our approach on six hyperspectral images provided freely by NASA JPL:
The
The
The
The hyperspectral image denoted as
We have implemented a tool to visualize single bands of a hyperspectral image or to visualize the combination of three bands. For the visualization of a single band, each signal level is converted to a grayscale tone. Therefore, the resulting image is a grayscale bitmap ([
In the second case, our tool permits the selection of three bands, and each band is assigned to a RGB component. The resulting image is a falsecolor visualization, where each signal level of the first band is converted to the red component, the second band is converted to the green component and the last one is converted to the blue component. The bands can be assigned to the RGB components according to their wavelength into a spectrum (as proposed in [
For example, the spectral band of the red color (wavelength from 620 nm to 750 nm) is assigned to the red component of the RGB, the spectral band of the green color (wavelength from 495 nm to 570 nm) is assigned to the green component of the RGB and the spectral band of the blue color (wavelength from 450 nm to 475 nm) is assigned to the blue component of the RGB.
Lunar Lake Scene 01, Band 120.
The accuracy of the hyperspectral sensors is typically measured in spectral resolution, which indicates the bandwidth of the spectrum that is captured. If the scanner picks up a large number of “images” with relatively small bandwidth, then it is possible to identify a large number of objects even if they are located in a relatively small area of pixels.
The JPL (Jet Propulsion Laboratory–NASA) AVIRIS sensor has a spatial resolution that covers an area of 20 × 20 meters per pixel.
The spectral components are obtained via a 12 bits ADC (AnalogtoDigital Converter). The elements of the spectrum, after the necessary calibration and geometric correction, are represented with a16bit accuracy.
Lunar Lake Scene 03, with band 125 assigned to the red RGB component, band 70 to the green and band 30 to the blue.
Yellowstone Scene 11, with band 125 assigned to red component, band 70 to green and band 30 to blue.
In the last few years, mobile devices, such as tablets, smartphones,
Therefore, we have realized a novel implementation of a tool for the visualization of hyperspectral images, similar to the one discussed above. This tool runs on Google Android OS (1.5 or later) ([
Yellowstone Calibrated Scene 01 on Google Android SDK Emulator in portrait mode and landscape mode with a HVGA screen resolution.
Yellowstone Calibrated Scene 18 on Google Android SDK Emulator in portrait mode and landscape mode with a HVGA screen resolution.
This tool might be helpful in many kinds of applications, as for example the visualization of a hyperspectral image directly on the field.
Moreover, the portability of smartphone devices is certainly important in real application (for example in mineralogy, physics,
The builtin OS allows some features on touchscreenbased portable devices, such as gestures, pinchtozoom,
Compression algorithms that provide lossless or nearlossless quality are generally required to preserve the hyperspectral imagery often acquired at high costs and used in delicate tasks (for instance classification or target detection).
Low complexity compression algorithms may allow onboard implementation with limited hardware capacities, therefore it is often desirable to use this typology of algorithms, for example when the compression process has to be carried out in an airplane or on board a satellite, before transmitting data to the base.
Hyperspectral data presents two forms of correlation:
–
–
Spectral correlation is much stronger than spatial correlation. For this reason standard image compression techniques, as for instance the spatial predictor of LOCOI used in JPEGLS [
Spectraloriented Least Squares (SLSQ) [
Others approaches are, for example, EMPORDA [
The SLSQ approach is based on an optimized linear predictor. SLSQ determines for each sample the coefficients of a linear predictor that is optimal with respect to a three dimensional subset of the past data.
The intraband distance is defined as:
The interband distance is defined as:
The enumerations obtained by using these distances allow the indexing of the pixels from the current pixel.
Similar to the Euclidean distance, the intraband distance defines the distance of the current pixel with respect to other pixels in the current bands.
The interband distance defines the distance of the current pixel with respect to other pixels in the current band and in the previous one. When
The pixels that have the same distance are considered in clockwise order for both types of distance.
The resulting context for intraband and interband enumerations.
As we can see from
In the following,
The
The coefficients
We can write
where,
The optimal predictor coefficients are the solution of the linear system, defined as:
which is obtained by taking the derivative with respect to α of
The prediction error, defined as
Spectral oriented Least SQuares (SLSQ) block diagram (from [
A selector of predictors (as is possible to see in SLSQ block diagram in
A standard median predictor is selected if the band of the current sample is in the IntraBand (IB) set. Otherwise, the SLSQ predictor described above is selected.
Each band in a hyperspectral image can be seen as a twodimensional image. By visualizing the content of each band it becomes clear that the spectral correlation is high between many bands, but it is also clear that a few consecutive bands are not strongly spectrally correlated.
In
Lunar Lake Scene 01, Band 160.
If we compare
If we are able to analyze the band correlation and if we can reorder the bands, this can lead to improvements to the SLSQ algorithm.
The proposed approach can be subdivided into three step:
–
–
–
The first step consists of making a dependence graph G = (V, E), where each vertex denotes a band and each vertex
An edge (
Now, we are able to compute the Minimum Spanning Tree (MST) on the graph G.
MST allows us to associate each band
The last step consists into computing a Depth First Search (DFS) visit on M. This gives a band ordering, where M is a MST on graph G.
In some cases DFS does not work correctly for our purposes.
In the simple example below we see a case in which DFS does not work correctly for band ordering.
In
Incorrect band ordering given by DFS on MST M.
For these cases we need to modify our approach and introduce band ordering based on DFS and
In the previous example the band ordering given by a modified DFS visit is therefore
A correct band ordering given by DFS on MST M.
As we can see in
Others approaches of band ordering may be found in [
An important measure of dependence between two random distributions is Pearson’s Correlation [
where
When
The X axis refers to the
Correlation for continuous band for each scene of Lunar Lake.
Average scene correlation for continuous band for Lunar Lake.
Correlation for continuous band for each scene of Moffett Field.
Average scene correlation for continuous band for Moffett Field.
Correlation for continuous band for each scene of Low Altitude.
Average scene correlation for continuous band for Low Altitude.
By looking at the above figures we can see that there are many points where there is a discontinuity between continuous bands.
For example, consider the minimum peak in the graph of
The graph reports the trend of the correlation for continuous band (in green) and the trend of the correlation after the execution of the proposed band ordering (in red).
From the figure it can be seen that there are less points of discontinuity after the execution of band ordering.
Without band ordering, Pearson’s correlation assumes the minimal value of approximately 0.101975512 (very low correlation).
After band ordering, Pearson’s correlation assumes the value of approximately of 0.415955776 (that means that the bands are correlated).
We have also considered the Bhattacharyya distance [
When both the distributions are univariate and are assumed to follow normal distribution, the Bhattacharyya distance is defined as:
where
We have tested our Javabased implementation of the SLSQ algorithm on the test data set (a) without band ordering; (b) with Pearson’s correlationbased band ordering; and (c) Bhattacharyya distancebased band ordering.
Our test data set is composed by five NASA AVIRIS hyperspectral images (each one subdivided into scenes): Lunar Lake (3 scenes), Moffett Field (4 scenes), Jasper Ridge (6 scenes), Cuprite (5 scenes) and Low Altitude (8 scenes).
Each scene has 614 columns and 224 spectral bands.
Results (C.R. achieved for each scene of the hyperspectral imagery without band ordering).


















3.17 

3.14 

3.20 

3.22 

3.00 

3.20 

3.18 

3.21 

3.18 

2.98 

3.21 

3.26 

3.18 

3.21 

3.03 

3.11 

3.17 

3.18 

3.01  

3.22 

3.18 

2.99  

3.19 

3.03  

3.03  

3.02 
The columns indicate respectively the results achieved for Lunar Lake, Moffett Field, Jasper Ridge, Cupirte and Low Altitude.
The IB set used is IB = {1, 2, …, 8}, with M = 4 and N = 1.
Results (C.R. achieved for each scene of the hyperspectral imagery with Pearson’s correlationbased band ordering).


















3.22 

3.16 

3.23 

3.28 

3.03 

3.25 

3.20 

3.24 

3.22 

3.01 

3.26 

3.28 

3.21 

3.26 

3.07 

3.14 

3.20 

3.23 

3.05  

3.23 

3.23 

3.02  

3.22 

3.06  

3.06  

3.05 
Results (C.R. achieved for each scene of the hyperspectral imagery with Bhattacharyya distancebased band ordering).


















2.96 

2.71 

2.88 

3.07 

2.75 

3.02 

2.78 

2.86 

2.93 

2.72 

3.06 

2.94 

2.83 

3.00 

2.81 

2.65 

2.78 

3.01 

2.80  

2.89 

3.03 

2.76  

2.87 

2.81  

2.81  

2.78 
The following tables (
Results (BPP achieved for each scene of the hyperspectral imagery without band ordering).


















5.05 

5.09 

5.00 

4.96 

5.34 

5.00 

5.03 

4.99 

5.03 

5.36 

4.98 

4.91 

5.04 

4.98 

5.27 

5.14 

5.04 

5.02 

5.31  

4.99 

5.03 

5.35  

5.02 

5.28  

5.28  

5.30 
Results (BPP achieved for each scene of the hyperspectral imagery with Pearson’s correlationbased band ordering).


















4.98 

5.06 

4.95 

4.88 

5.28 

4.92 

5.00 

4.94 

4.96 

5.31 

4.90 

4.88 

4.99 

4.91 

5.22 

5.09 

4.99 

4.96 

5.25  

4.95 

4.95 

5.30  

4.97 

5.23  

5.22  

5.24 
Results (BPP achieved for each scene of the hyperspectral imagery with Bhattacharyya distancebased band ordering).


















5.40 

5.89 

5.56 

5.20 

5.83 

5.30 

5.76 

5.59 

5.45 

5.87 

5.24 

5.44 

5.66 

5.34 

5.69 

6.04 

5.76 

5.31 

5.72  

5.54 

5.28 

5.80  

5.58 

5.70  

5.71  

5.75 
The following table (
Average results in terms of C.R. for each hyperspectral image without ordering, with Pearson’s correlationbased band ordering and Bhattacharyya distancebased band ordering.





Lunar Lake  3.19  3.24  3.01 
Moffett Field  3.17  3.20  2.77 
Jasper Ridge  3.19  3.22  2.85 
Cuprite  3.19  3.24  3.00 
Low Altitude  3.01  3.04  2.78 




Average results in terms of C.R.–Histogram.
From the observation of the experimental results it is clear that band ordering based on Pearson’s Correlation improves the lossless compression of hyperspectral images.
Contrariwise, the results achieved with the band ordering based on Bhattacharyya distance are worst with respect to the results achieved without band ordering.
Therefore, in our experiments Bhattacharyya distance does not work correctly for our purposes.
In detail, the average improvement introduced with the Pearson’s correlationbased band ordering is in terms of 0.04 on C.R. (approximately +1.27%) with respect to the achieved results without band ordering.
Instead, the results achieved with band ordering based on Bhattacharyya distance are worst with respect to the results without band ordering in terms of −0.27 on C.R. (approximately −8.5%).
Visualization, band ordering and compression of hyperspectral data are topics of interest in the remote sensing field.
For visualization we consider the visualization of single bands of the hyperspectral data or a combined visualization of three bands, where each band is assigned to a separate RGB component.
We have shown how to perform this visualization and have implemented a visualization tool for portable devices.
We then studied the lossless compression of hyperspectral images and examined the Spectral oriented Least SQuares (SLSQ) algorithm.
SLSQ is an efficient and low complexity algorithm for the lossless compression of hyperspectral images, it is suitable for onboard implementation. We have proposed our Javabased implementation of SLSQ.
Finally we have considered band ordering for hyperspectral image compression.
We have proposed an efficient band ordering approach that leads to improvements to SLSQ performance. The proposed approach is based on two metrics: Pearson’s Correlation and Bhattacharyya distance.
The experimental results achieved by our Javabased implementation of the SLSQ algorithm respectively without band ordering, with band ordering based on Pearson’s Correlation and with band ordering based on Bhattacharyya distance have been examined.
The band ordering based on Pearson’s Correlation achieved the best experimental performance.
The results achieved by the band ordering based on Bhattacharyya distance instead are not good enough when compared to the results achieved without band ordering.
In the future we will also test the proposed approach with other distance measures.
Future work will also include improvements for the tool we have developed for the visualization of hyperspectral imagery.