Optics Communications 284 (2011) 4903–4909

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Optics Communications

j ourna l homepage: www.e lsev ie r.com/ locate /optcom

An adaptive OPD and dislocation prediction used characteristic of interferencepattern for interference hyperspectral image compression

Jia Wen a,b,⁎, Caiwen Ma b, Penglang Shui b

a The School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR Chinab The Photoelectric Measurement and Control Technology Research Department, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an, Shaanxi, 710119,PR China

⁎ Corresponding author at: The Photoelectric MeasurResearch Department, Xi'an Institute of Optics andAcademy of Sciences, Xi'an, Shaanxi, 710119, PR China.

E-mail address: b09033@opt.cn (J. Wen).

0030-4018/$ – see front matter © 2011 Elsevier B.V. Aldoi:10.1016/j.optcom.2011.06.061

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 April 2011Received in revised form 27 June 2011Accepted 28 June 2011Available online 13 July 2011

Keywords:Optical informationSpectrum compressionInterference patternLASISInterference hyperspectral image

According to the imaging principle and characteristic of LASIS (Large Aperture Static Interference ImagingSpectrometer), we discovered that the 3D (three dimensional) image sequences formed by differentinterference pattern frames, which were formed in the imaging process of LASIS Interference hyperspectralimage, had much stronger correlation than the original interference hyperspectral image sequences, either in2D (two dimensional) spatial domain or in the spectral domain. We put this characteristic into imagecompression and proposed an adaptive OPD (optical path difference) and dislocation prediction algorithm forinterference hyperspectral image compression. Compared the new algorithm proposed in this paper withDual-Direction Prediction [1] proposed in 2009, lots of experimental results showed that the prediction errorentropy of the new algorithm was much smaller. In the prediction step of lifting wavelet transform, thischaracteristic would also reduce the entropy of coefficients in high frequency significantly, which would bemore advantageous for quantification coding [2].

ement and Control TechnologyPrecision Mechanics, Chinese

l rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Combining optics with spectroscopy, electronic technology andprecision machinery, interference hyperspectral imaging was anadvanced technology appeared in the 1980s. As Fig. 1 [3] showed, itcould obtain both the space and spectrum information of themeasuredtargets, and had significant application value in many aspects, suchas the aero-remote and military sensing, the resources survey, theenvironmental monitoring as well as the agriculture and industry.LASIS (Large Aperture Static Interference Imaging Spectrometer) wasthe representative of the new generation interference hyperspectralimaging technology. Its application had received many scholars'attention and interest. As it had already been equipped on the “ChangE” for moon exploration, and would be used for exploration on Mars inthe future, the compression of LASIS interference hyperspectral imagehad become the focus in recent years [2,4,5].

2. Imaging principle of LASIS [2][3]

The schematic diagram of LASIS was shown in Fig. 2(a), which wasmainly composed offive parts: 1) fore-optics system; 2) interferometer;3) imaging system; 4) detector; and 5) computer.

The imaging principle of LASIS was shown in Fig. 2(b). Twodirectional lights with visual angle 0 andθ entered LASIS respectively.Through the Sagnac interference spectrometer, a bunch of light becametwo beams of parallel coherent lights. The interference phenomenonhappenedwhen the two beams of parallel coherent lights converging atthe same point of the imaging mirror's back focal plane.

In Fig. 2(b), d was the distance between two beams of lights,θ was the angle between the primary optical axis of the imaging lensand the direction of incident light passing through lateral shearinterferometer, f was the effective focal length of imaging lens, x wasthe distance between the imaging center and the lights convergingpoint. When the interference phenomenon happened, OPD on thedetector was:

δ = d sin θ ð1Þ

when the visual angle θ was very small,

sin θ≈ tan θ =xf

ð2Þ

δ = d sinθ = dxf

ð3Þ

LASIS would get the interference pattern of targets after pushingand sweeping a field of view along the shear direction of lateral shearinterferometer. In the ideal state, the detector units had the samedirection as the direction of pushing and sweeping. The column of

Fig. 1. Interference hyperspectral imaging [3].

4904 J. Wen et al. / Optics Communications 284 (2011) 4903–4909

detector units would output a line of interference pattern of a targetpoint after LASIS finished pushing and sweeping:

Ii xð Þ = ∫ v2v1

Bi vð Þ cos 2πvdxf

� �dv ð4Þ

Fig. 2. (a) Schematic diagram of LASIS. (b) Imaging principle of LASIS.

v1, v2 were the minimum and the maximal values of the wave numberrespectively, i was sequence number of spatial distinguishableunits, δm was the maximum distance of OPD, Bi(v) was the spectraldistributed function of the corresponding unit, Ii(x) was a line ofinterference pattern of the target point.

As different OPD corresponding to different positions of pixels,we could get the interference spectral distribution of the point byrecording the interference amplitude outputted by the detector whenthe pixel point was in different positions.

The data processing of LASIS interference hyperspectral image wasshown in Fig. 3. The data processing had two steps:

First choosing the same ground point from different OPD in theoriginal LASIS interference hyperspectral image sequences toform the interference pattern of point [5]. The interferencepatterns were formed by the corresponding columns of thesame targets chosen from different frames. So the number oforiginal interference hyperspectral image frames we neededto form an interference pattern was almost the same as thenumber of the columns in interference pattern, and every rowof pixels in interference pattern was formed by the sametarget point in different frames, so they would give the spatialinformation of that target point.

Second recovering the spectrum image by doing Fourier transformto the interference pattern of point:

Bi vð Þ = ∫ δm0

Ii xð Þ cos 2πxdvf

� �dx ð5Þ

As in the ideal state, Ii(x) and Bi(v) were both odd functions, sothey could be extended into the negative domain.

Ii xð Þ = ∫ Bi vð Þe j2πvdx= f3dv = F Bi vð Þf g ð6Þ

Bi vð Þ = ∫ Ii xð Þe−j2πvdx= f3dx = F−1 Ii xð Þf g ð7Þ

Fig. 3. Data processing of LASIS interference hyperspectral image.

4905J. Wen et al. / Optics Communications 284 (2011) 4903–4909

Where F was Fourier transform and F−1 was the inverse Fouriertransform. From formula (6) and (7), we could see the interferencepattern Ii(x)and the spectrum distributed functionBi(v) had therelation of Fourier transform and inverse transform.

3. New compression method using the characteristic ofinterference pattern

Suppose there were fframes of r×c LASIS image sequence as Fig. 4shows,r×c pixels in 2 dimensions, they could be shown as follows[1,3]:

X1 =

x1;1;1 x1;2;1 … x1;c;1x2;1;1 x2;2;1 … x2;c;1… … xi;j;1 …

xr;1;1 xr;2;1 … xr;c;1

2664

3775 ð8Þ

Xk =

x1;1;k x1;2;k … x1;c;kx2;1;k x2;2;k … x2;c;k… … xi;j;k …xr;1;k xr;2;k … xr;c;k

2664

3775 ð9Þ

Xf =

x1;1;f x1;2;f … x1;c;fx2;1;f x2;2;f … x2;c;f… … xi;j;f …xr;1;f xr;2;f … xr;c;f

2664

3775 ð10Þ

where i=1, 2, …, r;j=1, 2, …, c;k=1, 2, …, f.

As there was directional shift between frames of interferencehyperspectral image sequences, so in the ideal state, the inter-

ference pattern I1 was formed by

x1;c;1x2;c;1…xr;c;1

2664

3775,

x1;c−1;2x2;c−1;2

…xr;c−1;2

2664

3775,

x1;c−2;3x2;c−2;3

…xr;c−2;3

2664

3775…

x1;3;c−2x2;3;c−2

…xr;3;c−2

2664

3775,

x1;2;c−1x2;2;c−1

…xr;2;c−1

2664

3775,

x1;1;cx2;1;c…xr;1;c

2664

3775, these c columns of r pixels actually

corresponding to the same column of r pixels of actual targets,sothe correlation of these c columns should be very strong.

Step 1. Corresponding-columns-extracted to form interference patternsequences

We extracted the c columns corresponding to the same r points ofactual objects from c frames of interference hyperspectral image se-quences to form a new r×c matrix to form one frame of interferencepattern:

I1 =

x1;1;c x1;2;c−1 x1;3;c−2 … x1;c−2;3 x1;c−1;2 x1;c;1x2;1;c x2;2;c−1 x2;3;c−2 … x2;c−2;3 x2;c−1;2 x2;c;1… … … … … … …xr;1;c xr;2;c−1 xr;3;c−2 … xr;c−2;3 xr;c−1;2 xr;c;1

2664

3775 ð11Þ

Fig. 4. Interference hyperspectral image sequences.

4906 J. Wen et al. / Optics Communications 284 (2011) 4903–4909

Ii =

x1;1;c + i−1 x1;2;c + i−2 x1;3;c + i−3 … x1;c−2;i + 2 x1;c−1;i + 1 x1;c;ix2;1;c + i−1 x2;2;c + i−2 x2;3;c + i−3 … x2;c−2;i + 2 x2;c−1;i + 1 x2;c;i

… … … … … … …xr;1;c + i−1 xr;2;c + i−2 xr;3;c + i−3 … xr;c−2;i + 2 xr;c−1;i + 1 xr;c;i

2664

3775

ð12Þ

Ic =

x1;1;2c−1 x1;2;2c−2 x1;3;2c−3 … x1;c−2;c + 2 x1;c−1;c + 1 x1;c;cx2;1;2c−1 x2;2;2c−2 x2;3;2c−3 … x2;c−2;c + 2 x2;c−1;c + 1 x2;c;c

… … … … … … …xr;1;2c−1 xr;2;2c−2 xr;3;2c−3 … xr;c−2;c + 2 xr;c−1;c + 1 xr;c;c

2664

3775

ð13Þ

Fig. 5. Interference pattern after corresp

To form one frame of interference pattern, we required c framesof LASIS image sequences, so to form c frames of interferencepatterns, we required 2c-1 frames of LASIS image sequences. 3 groupsof 8 continuous interference patterns were shown as follows:

From Fig. 5, we could see that redundancy not only exists in inter-column in every frame of interference pattern, but also exists betweenadjacent frames of interference pattern. So in this paper we wouldeliminate the strong redundancy by the two following steps:

Step 2. Adaptive OPD (optical path difference) prediction method:

An adaptive OPD (optical path difference) prediction method wasproposed in this paper. We made the pixels in the same OPD as a

onding-columns-extracted method.

Fig. 6. Sketch map of forming interference pattern sequences.

Fig. 7. Sketch map of the proposed method for compression.

4907J. Wen et al. / Optics Communications 284 (2011) 4903–4909

channel, and we use pixels in this channel to predict pixels in thedifferent channels. The algorithm was shown as follows:

The pixels in the nth channel would be predicted by the pixels inthe m channels before this channel, that was,

Ik :;nð Þ = Ikmαn + e1k :;nð Þ; n = 1;2;…; c ð14Þ

k was the kth frame, e1 was 3D prediction error, e1kis the kthframe of e1, αn=[α1n, α2n … αmn]Twas the weighted value for the

Fig. 8. Raw data of interference hy

prediction of the nth channel, in order to minimize the error, αn

should be[3,6–8]:

αn = arg min jjIk :;nð Þ−Ikmαnjj2� �

; n = 1;2;…; c ð15Þ

|| • || was Euclid norm.Let

∂jjIk :;nð Þ−Ikmαnjj2∂αn

= 0; n = 1;2;…; c ð16Þ

We got

αn = ITkmIkm� �−1

ITkmIk :;nð Þ; n = 1;2;…; c ð17Þ

Ikm = Ik :;n−mð ÞIk :;n−m + 1ð Þ…Ik :;n−2ð ÞIk :;n−1ð Þ½ � ð18Þ

when nbm, m=n−1

e1k = Ik :;1ð Þ−Ikmα1 Ik :;2ð Þ−Ikmα2…Ik :; cð Þ−Ikmαc½ �; k = 1;2;…; c

ð19Þ

Step 3. Inter-framesprediction toeliminate the inter-frameredundancy:

After corresponding-column-extracted step, columns of pixels in thesame spectral dimension of the original interference hyperspectralimage data would be distributed into different frames, as Fig. 6 showed(pixels of the samecolors express pixels in thesamespectraldimension).After lots of experiments, we found that we could obtain much smallerentropy through doing dislocation prediction between inter-frames toprediction error sequences obtained after Step 2, than doing directlyprediction between inter-frames. The reason was that there was muchstronger correlation in the same spectral dimension of the originalinterference hyperspectral image than in different spectral dimensions.

So an algorithm of dislocation prediction was proposed in thispaper. According to the position as Fig. 6 shows, in order to get smallerinformation entropy, the algorithm of dislocation prediction betweeninter-frames was shown as follows:

e2i =

e1i 1;1ð Þe1i 2;1ð Þ

…e1i r;1ð Þ

e1i 1;1ð Þ−e1i + 1 1;2ð Þe1i 2;1ð Þ−e1i + 1 2;2ð Þ

…e1i r;1ð Þ−e1i + 1 r;2ð Þ

e1i 1;2ð Þ−e1i + 1 1;3ð Þe1i 2;2ð Þ−e1i + 1 2;3ð Þ

…e1i r;2ð Þ−e1i + 1 r;3ð Þ

…………

e1i 1; c−1ð Þ−e1i + 1 1; cð Þe1i 2; c−1ð Þ−e1i + 1 2; cð Þ

…e1i r; c−1ð Þ−e1i + 1 r; cð Þ

2664

3775

i = 1;2;…; c−1;

ð20Þ

Sketch map of the compression method proposed in this paperwas shown in Fig. 7.

4. Experiment and analysis

Compared the method proposed in this paper with the Dual-Direction Prediction method proposed in 2009[1], which also madeprediction in both spatial and spectral domain. Two groups of 8

perspectral image sequences.

4908 J. Wen et al. / Optics Communications 284 (2011) 4903–4909

frames of LASIS interference hyperspectral image sequences(Figs. 8and 10) had been chosen for experiment, define

Entropy = ∑pi⋅ log pið Þ ð21Þ

Experiment results were shown as follows in Figs. 9 and 11,Tables 1 and 2:

The results of experiments showed that, compared with themethod proposed in 2009, prediction error entropy generated by themethod proposed in this paper was much smaller, which would bemore advantageous for efficient realization of the transformation andquantization steps of image compression[2,9].

Fig. 10. Raw data of interference h

Fig. 11. Interference pattern of th

Table 1Prediction error entropy comparison.

Frame 1 Frame 2

Entropy of raw data (Fig. 8) 6.554 6.550Entropy of method proposed in this paper (Step 1) 6.330 6.321Entropy of method proposed in 2009 3.464 3.441Entropy of method proposed in this paper (Step 2) 3.239 3.241Entropy of method proposed in this paper (Step 3) 3.001 3.069

Table 2Prediction error entropy comparison.

Frame 1 Frame 2

Entropy of raw data (Fig. 10) 6.796 6.797Entropy of method proposed in this paper (Step 1) 6.732 6.720Entropy of method proposed in 2009 3.375 3.416Entropy of method proposed in this paper (Step 2) 3.403 3.406Entropy of method proposed in this paper (Step 3) 3.141 3.130

Fig. 9. Interference pattern of the

5. Conclusion

We discovered that either in 2D spatial domain or in the spectraldomain, the 3D image sequences formed by different interferencepattern frames had much stronger correlation than the originalinterference hyperspectral image sequences. As there was muchstronger correlation in the same spectral dimension of the originalinterference hyperspectral image than in different spectral dimen-sions, we could obtain much smaller entropy through doingdislocation prediction between inter-frames to different interferencepattern frames, than doing directly prediction between inter-frames.Compared the new algorithm proposed in this paper with Dual-Direction Prediction [1] proposed in 2009, lots of experimental resultsshowed that the prediction error entropy of the new algorithm was

yperspectral image sequences.

e same target point (Step 1).

Frame 3 Frame 4 Frame 5 Frame 6 Frame 7 Frame 8

6.555 6.556 6.560 6.559 6.546 6.5456.315 6.435 6.467 6.420 6.376 6.4343.386 3.282 3.486 3.385 3.472 3.6773.262 3.460 3.504 3.460 3.387 3.4593.216 3.236 3.218 3.206 3.184 3.218

Frame 3 Frame 4 Frame 5 Frame 6 Frame 7 Frame 8

6.798 6.792 6.794 6.793 6.797 6.7936.710 6.700 6.687 6.684 6.689 6.6963.363 3.501 3.449 3.450 3.477 3.3543.341 3.279 3.395 3.406 3.401 3.3953.133 3.130 3.131 3.117 3.123 3.126

same target point (Step 1).

4909J. Wen et al. / Optics Communications 284 (2011) 4903–4909

much smaller. In the prediction step of lifting wavelet transform, thischaracteristic would also reduce the entropy of coefficients in highfrequency significantly, which would be more advantageous forquantification coding [2].

Acknowledgement

National Natural Science Foundation issues (40805013) and theNational 863 support project (2009AA7080302) are acknowledged.

References

[1] Jing MA, Chengke WU, Yun song LI, Proceedings of IEEE DCC, 2009, p. 458.[2] Jia Wen, CaiwenMa, Penglang Shui, Optics Communications 284 (7) (April 1 2011)

1770.[3] Jing Ma, Chengke WU, “Research on Interferential Hyperspectral Image Compres-

sion Technology”. Xi'an University of Electronic Science and Technology doctoraldissertation, 2009.

[4] P.L. Dragotti, G. Poggi, A.R.P. Ragozini, IEEE Transactions on Geosciences andRemote Sensing 1 (38) (2000) 416.

[5] Xiangli Bin, Zhao Baochang, Xue Mingqiu, Acta Optica Sinica 18 (1) (1998) 18.[6] G.H. Golub, C.V. Loan, Matrix Computations, John Hopkins University Press, 1996.[7] S.H. Hsiesh, Proceedings of SPIE on Applications of Digital Image Processing XXVII,

2004, p. 664.[8] G. Motta, F. Rizzo, J.A. Storer, Proceedings of Data Compression Conference, 2003,

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Jia Wen, Aug 4, 1983, born in Tianjin, doctor of TheSchool of Electronic and Information Engineering, Xi'anJiaotong University, doctor of the Photoelectric Measure-ment and Control Technology Research Department,Xi'an Institute of Optics and Precision Mechanics, ChineseAcademy of Science, Research fields: digital image

processing.