VST-based Lossy Compression of Hyperspectral Data for New Generation Sensors

1. VST-based Lossy Compression of Hyperspectral Data for New Generation Sensors A. Zemliachenko1, R. Kozhemiakin, S. Abramov1, M. Uss2, V. Lukin1, B. Vozel3, K. Chehdi3 1 Department of Transmitters, Receivers and Signal Processing, 2Department of Radioelectronic Systems Design, National Aerospace University, Kharkov, Ukraine e-mails: lukin@ai.kharkov.com, ask379@mail.ru 3 Institute of Electronics and Telecommunications of Rennes UMR CNRS 6164, University of Rennes 1 - Enssat, Lannion, France e-mail: benoit.vozel@univ-rennes1.fr SPIE ERS, 23 - 26 September 2013, Dresden, Germany

2. Outline Introduction Lossy compression of hyperspectral images Problem statement Examples of noise characteristics in real-life hyperspectral data (Hyperion) Criteria of lossy compression efficiency for single-channel images Optimal Operation Point (OOP) How to attain this OOP in practice? WOVST approach: component-wise compression WithOut VST WVST approach: component-wise compression With VST Simulation results for both approaches Preliminary conclusions Component-wise compression of real-life hyperspectral data (Hyperion) Lossy compression with sub-band grouping CR for particular sub-bands Conclusions

3. Introduction Goal: design of lossy data compression methods able to take into account noise characteristics present in images (signal-dependent character of the noise). Images Noise Image processing Signal-independent Signal-dependent Impulse Compression Reason: Circuit (dark, thermal) and atmospheric noise Reason:insufficient observation interval, counting principle of sensors operation Reason: Transmitting and encoding/decodingerrors Edge detection, segmentation Filtering, classification Mixed Need in noise characteristics evaluation and taking into account while processing data

4. Problem statement • Lossless techniques of hyperspectral image compression do not provide appropriately high compression ratio (CR up to 4…5). • Modern methods for lossy compression of hyperspectral data often do not take into account noise properties and their variability in sub-band images. • Even those techniques that do this are based on assumption that noise is pure additive. • However, this is not true, especially for new generation of hyperspectral sensors for which the level of additive component (induced by circuitry) is considerably reduced. • Thus, the problem is to take into account noise statistics (individually in sub-band images) at different stages of hyperspectral data processing, in particular, at image compression stage.

5. Possible avenues of thought • First, it has been noticed that the use of a simple Anscombe transform applied to hyperspectral data reduces data amount practically twice and makes noise almost additive in all spectral sub-bands. • Second, lossy compression of data with applying standard or generalized Anscombe transforms has been earlier applied for astronomic images and other data corrupted by signal-dependent noise. • Third, the use of 3D compression techniques allows considerable increasing the CR due to exploiting high inter-channel correlation of hyperspectral data. But it should be done carefully with taking into account noise statistics since otherwise information in some sub-bands (with small dynamic range) can be severely distorted. • Fourth, optimal operation point can exist in lossy compression of noisy images and it is desirable to carry out lossy compression of images in the neighborhood of OOP or with slightly smaller CR.

6. Noise characteristics in real-life data Proposed mixed noise model: An appropriate model for the noise variance in a n-th sub-band image is where denote image indices in the spatial domain, is SI noise variance, is SD noise parameter, is the true image value in ij-th pixel of n-th sub-band image.

7. Examples of noise characteristics in real-life data Dependences of noise components’ parameters’ estimates for the Hyperion data EO1H1800252002116110KZ Note: there are several sub-bands in Hyperion data for which dynamic range is very small and which are usually not exploited in acquired image processing and analysis

8. Some important properties (observations) • The estimates of parameters for either SI or SD components are usually quite close for neighbor sub-bands • Both the estimates of SI and SD noise parameters are the largest at the edgesof sensor bands (recall that there are two sensors in Hyperion system, one basically operating in visible range and the second operating in infrared band) • The estimates of SI noise variance vary from approximately 10 to thousands whilst the estimates of SD noise parameter are from 0 to about 1 where mostly they are about 0.1 (few estimates are even negative). • The noise variance induced by SD noise component is usually considerably (up to 40 times) larger than SI noise variance at the upper margin of data dynamic range for all sub-bands, i.e., SD noise component is prevailing (for AVIRIS data contributions of SD and SI noise components are comparable).

9. Criteria of lossy compression efficiency for single-channel images In simulations: mixed noise added lossy compression compressed image noisy image true image • Most metricbecomes worse for any coder if CR increases. • Under certain value of a parameter that controls compression (PCC), a metric can exhibit an optimum • minimum for the standard mean square error (MSE) • maximum for such quality metrics as PSNR, MSSIM and PSNR-HVS-M.

10. Optimal operation point (OOP) • The optimum of a given metric is called Optimal Operation Point (OOP) and it is associated with the corresponding PCC (bppOOP, QSOOP or SFOOP). Five out of six curves have minima of the considered metric observed for QS about 50 (the DCT-based coder AGU has been used). A question is how to attain OOP in practice when true image is not available. Dependences of for six test images corrupted by signal-dependent noise with (largest value) and (lowest value)

11. Attaining OOP in practice • Several procedures to carry out lossy compression in the neighborhood of OOP have been already designed under assumption that noise type and parameters are a priori known or pre-estimated with appropriate accuracy. • The corresponding techniques exist and provide quite high accuracy. • These procedures are either iterative or not. • This depends upon a coder and PCC used. • If noise is not pure additive,homomorphic (variance stabilizing) image transformations can be exploited. • So, we have two possible options: • Compression without Variance Stabilizing Transform (VST) • Compression with VST What is better?

12. Component-wise compression without VST (WOVST approach) Method: • A coder is applied directly to noisy image. No additional operations are needed after decompression. • The lossy compression procedure can be fully automatic and it includes blind estimation of noise parameters, setting with taking into account the corresponding recommendations, and lossy compression with this . In practice: • Suppose that noise are known (or pre-estimated with high accuracy). Then, it is possible to pre-estimate equivalent noise variance as • Then, for coders with QS or SF used as PCC, these parameters for attaining OOP are to be set as where and are proportionality factors that depend upon a coder. For the coder AGU it is expedient to set

13. Component-wise compression with VST (WVST approach) Method: • Compression and decompression are also fully automatic. After blind estimation of noise parameters, an image is subject to VST and PCC is set for a chosen coder according to recommendations on setting QS or SF. In practice: • A noisy image is first subject to the VST, namely, the generalized Anscombe transform with obtaining the transformed image (if SI noise is supposed zero mean) • If noise parameters are estimated accurately, noise becomes purely additive and its variance equals to unity. This allows using coders with • After decompression and deblocking (if applied), a decompressed image has to be inversely transformed. • Main advantage: QS should be the same for all sub-band images.

14. Simulation results for both approaches Efficiency of compared approaches for compression in OOP neighborhood for the coder AGU

15. Preliminary conclusions From analysis of data in previous table: • A larger QSrec is used for the approach WOVST if k is larger and, respectively, σeq is larger; this leads to larger CRand MSEtc and smaller MSSIMtcand PSNR-HVS-Mtc, i.e. to worse quality of decompressed images; • Attained CR in OOP depends upon noise intensity and image complexity; • CR is larger if noise is more intensive (i.e., if is larger) and if a compressed image has a simpler structure (compare data for quite simple structure test image Peppers to data for textural test images Baboon and Airfield for a fixed k); • The considered approaches to lossy compression produce comparable performance; • For the WVST approach, the CR values are slightly smaller but MSEtc are smaller; • MSSIMtc and PSNR-HVS-Mtc are usually slightly larger for WVST than for the WOVST approach.

16. Component-wise compression of real-life hyperspectral data (Hyperion) Peculiarities of real-life data: Maximal and minimal (often negative) values of sub-band images • These effects might cause problems, especially for the second approach to lossy compression: • It might happen that argument in VST is negative and square root can not be determined. • If negative values are observed, carry out shifting the noisy image values of as • and apply • If k is smaller than 0, then normalization is applied instead of VST

17. Component-wise compression of real-life hyperspectral data (Hyperion) • In OOP, MSEnc is to be approximately equal to equivalent variance of the noise. • This is observed for that can be recommended for lossy compression with VST

18. Component-wise compression of real-life hyperspectral data (Hyperion) another image - HyperionEO1H2010262004157110KP Again, MSEnc in OOP is approximately equal to equivalent variance of the noise and this is observed for QS=3.5. Thus, recommendation is quite general.

19. Compression example Fragments of original (left) and compressed (right) image in the 220-th sub-band There is no essential difference except partial noise removal in homogeneous areas

20. Compression example Fragments of original (left) and compressed (right) image in the 145-th sub-band There is no visual differencebetween two images.

21. Lossy compression with sub-band grouping Basic idea: to incorporate sub-band image correlation to improve CR • The compression procedure based on VST has one favorable pre-requisite: • Noise is additive in all sub-bands after VST and has practically the same intensity. • This property can be exploited in several ways all dealing with setting fixed QS or SF for sub-band images formed into groups and/or pre-processed. In practice: • The first stage of the proposed procedure is the same as earlier, i.e., one determines parameters of the noise in all sub-bands and carries out pre-processing (VST and shifting if needed) as it is described earlier. • After this stage, we have a 3D data array. • This array is then divided into few sub-arrays (groups). • We used two groups where the first one contained sub-bands with indices from 13 to 57 and the second one contained sub-band images with n from 83 to 224.

22. Lossy compression with sub-band grouping • For each group, the first sub-band image has been considered as a reference. • For other images, the following operation with obtaining difference images has been carried out where q denotes sub-band image index in a group and Q is the number of sub-band images in this group. • Then, the reference image in the group is compressed with the QS recommended earlier whilst difference images are compressed with QS by about 15% larger than for the reference image (in fact, we used QS=3.5 for the reference images and QS=4.0 for the difference images). • This leads to increasing the CR for sub-bands where difference images are compressed. • The reason for this is that the difference images have considerably smaller dynamic range compared to the reference image

23. CR for particular sub-bands and the archiver RAR CR for particular sub-bands and the archiver RAR Dependences CR(n) on sub-band index for two proposed procedures and RAR (applied component-wise) Dependences CR(n) on sub-band index for two proposed procedures and RAR (applied component-wise) • Totally, CR increases by about two times compared to component-wise compression. • CR(n) varies within the limits from about 4.5 to 25, and it is about 6 for most sub-band images • Thus, it is possible to sufficiently increase CR by exploiting inter-channel correlation of the data. Lossy compression provides essential benefit in CR.

24. CR for particular sub-bands and the archiver RAR Dependences CR(n) on sub-band index for two proposed procedures and RAR (applied component-wise) another image EO1H2010262004157110KP

25. Conclusions • Two approaches to component-wise lossy compression of hyperspectral data that take into account prevailing influence of signal-dependent noise in sub-band images are proposed and compared. • One approach exploits VST whilst another one does not. It is shown that they produce approximately the same performance in the sense of decompressed image quality and reached CR. • One more approach to lossy compression that exploits inter-channel correlation in hyperspectral data by obtaining and compressing difference images after VST is put forward. • This approach provides essential benefit in CR compared to component-wise compression for approximately the same level of distortions introduced into sub-band images. To our opinion, this approach is worth using in practice. • All approaches provide compression in the neighborhood of OOP and are fully automatic. Thus, they can be used on-board of hyperspectral sensor carrier. This work has been partly supported by French-Ukrainian program Dnipro (PHC DNIPRO 2013, Project No 28370QL and M/8-2013) and by French-Lebanon program CEDRE (Project No 10SCI F21/L6)