On-Board Satellite Implementation of Wavelet-Based Predictive Coding of Hyperspectral Images

Transcription

1 On-oard Satellte Implementaton of -ased Predctve Codng of Hyperspectral Images Agneszka C. Mguel*, Alexander Chang #, Rchard E. Ladner #, Scott Hauck*, Eve A. Rskn* * Department of Electrcal Engneerng, Unversty of Washngton, Seattle # Department of Computer Scence and Engneerng, Unversty of Washngton, Seattle Abstract We present an algorthm for lossy compresson of hyperspectral mages generated by the MODIS nstrument. To greatly reduce the bt rate requred to code mages, we use lnear predcton between the bands. Once the predcton s formed, t s subtracted from the ncomng band, and the resdual (dfference mage) s compressed usng the Set Parttonng n Herarchcal Trees (SPIHT) algorthm. The proposed bt plane-synchronzed closed loop predcton smultaneously acheves hgh compresson rato, hgh fdelty, and smple on-board mplementaton. I. INTRODUCTION Moderate Resoluton Imagng Spectroradometer (MODIS) data are collected from the Terra satellte at a rate of 11 megabts/second. These data are transmtted to earth, stored, and analyzed by varous algorthms. Lossy compresson technques provde hgh compresson ratos that allow reducton n bandwdth and storage requrements. The compresson of hyperspectral mages was nvestgated n [1] and []. In [3], the nformaton content of hyperspectral data was studed and a lossless compresson technque was proposed. The effect of data compresson on cloud cover classfcaton of MODIS data was examned n [4]. In ths research, we use the Set Parttonng n Herarchcal Trees (SPIHT) algorthm [5], whch s a wavelet-based state-of-theart technque that codes mages wth both hgh compresson ratos and hgh fdelty. SPIHT can be parallelzed for mplementaton on FPGAs and therefore has a great potental for applcatons where the compresson s performed on the satellte. To reduce the bt rate requred to code hyperspectral mages, we use lnear predcton between the bands. Each band, except the frst, s predcted by a prevous band. Once the predcton s formed, t s subtracted from the ncomng band, and the resdual (dfference mage) s compressed usng SPIHT. The energy n the dfference band s low and therefore, the dfference band can be compressed wth only a small number of bts. All of the dfference mages are compressed to the same fdelty. To compute the exact dfference between the ncomng band and ts predcton from a prevous band, the encoder must have access to the decoded verson of the prevous band. Such a closed loop system however requres mplementaton of the decoder on the satellte, whch greatly ncreases the complexty of on-board applcatons. In the proposed bt plane-synchronzed closed loop system, both the encoder and the decoder smply use the same number of bt planes of the wavelet-coded dfference mage of the prevous band for predcton. Ths enables the encoder to be less complex because whle t must stll do an nverse wavelet transform, full decompresson on-board the satellte s not needed. In ths artcle we show the comparson between the open, halfopen, closed, and the bt plane-synchronzed closed loop systems. The proposed predcton method has very promsng performance n that for the same fdelty, the average bt rate s only slghtly hgher than for the closed loop system, yet t permts a smple encoder for mplementaton on the satellte. II. SET PARTITIONING IN HIERARCHICAL TREES SPIHT s a progressve mage coder, whch frst approxmates an mage wth a few bts of data, and then mproves the qualty of approxmaton as more nformaton s encoded. SPIHT creates an embedded bt stream n whch the later bts refne the earler bts. As shown n Fgure 1, the encoder frst performs a wavelet transform on the mage pxels. Then, the wavelet coeffcents are encoded one bt plane at a tme. To acheve compresson, the bt stream can be truncated at any tme (see Fgure ). Note that bt plane encodng and decodng takes sgnfcantly more tme than the wavelet transform. Ths work was supported by NASA.

2 mage (pxels) Encoder wavelet transform Decoder bt plane decodng transformed mage (coeffcents) transformed mage (approx coeffcents) bt plane codng nverse wavelet transform bt stream dstorted mage t rate [bpp] Usng predcton and SPIHT to compress hyperspectral data (target = 1) w/o predcton wth predcton Fgure 1. lock dagram of SPIHT.. 5 compressed bt planes: and number Fgure 3. Comparson of bt rates requred to code the hyperspectral data to =1 wth and wthout predcton. truncated compressed bt planes: Fgure. t plane codng. 1 bpp III. SPIHT ON HYPERSPECTRAL DATA We use predcton to take advantage of correlaton between bands. As shown n Equaton (1), frst, the current band s predcted from a prevous band. Then, the dfference D between the orgnal band and the predcted band P s computed. To recover the orgnal band, ts predcton P has to be summed wth the dfference band D. P D = = = a P P D b The predcton order of the bands has been optmzed to mnmze the overall dstorton D. The coeffcents a and b are computed to mnmze the norm of D usng least squares optmzaton. All dfference bands are coded to a target Mean-Squared Error (). Usng predcton sgnfcantly mproves the compresson rato. For example, as shown n Fgure 3, for the Cuprte mage (614x51, 4 bands, 16-bt nteger data), when all of the bands are coded to an of 1, usng predcton decreases the requred bt rate 5 tmes (from 8:1 to 43:1 compresson rato). (1) IV. PREDICTION IN SPIHT To predct the currently coded band, a prevous band s needed. The prevous band used for predcton can be the orgnal or the decompressed band. In ths research, we nvestgated four types of predcton: open loop, half-open loop, closed loop, and the proposed bt plane-synchronzed closed loop. A. Open Loop Predcton As shown n Fgure 4, n the open loop predcton, both the recever and the transmtter use the orgnal band for predcton. In the transmtter, the currently coded band s predcted from band usng the predcton coeffcents a andb. The predcted verson of, called Ps subtracted from to form the dfference band D. The dfference band D s then wavelet transformed nto W and bt plane encoded to a bt rate requred to acheve the target. The recever decompresses the truncated bt stream to Ŵ and then performs the nverse wavelet transform to compute the decompressed dfference band Dˆ. Ths dfference s summed wth P, the predcted verson of, to computeˆ. Note that P s predcted from the orgnal band. ecause n lossy compresson, the recever does not have access to the orgnal band, ths system cannot be mplemented. Therefore, n our research, we use the open loop only as a reference system to compare wth the results of other methods.

3 - D W t Plane Encodng average bt rate for the half-open case s 965 bpp, whle that for the open loop s.4 bpp. P Predcton Transmtter a b 5 Open and half-open loop results for target = 1 t Plane W D Decodng Open loop Half-open loop Recever P Predcton a b and number Fgure 4. Open loop predcton. Fgure 6. Results comparson for the open and half-open loops.. Half-open Loop Predcton Half-open loop predcton s a practcal alternatve to open loop predcton. In such a system, the transmtter uses the orgnal prevous band, whle the recever uses the prevous decompressed band for predcton (see Fgure 5). The transmtter s the same as n the open loop method. ecause the recever cannot use the orgnal band to predct band, t uses the decompressed verson of, that s ˆ. The predcted verson of, Pˆ, s summed wth the decompressed dfference band Dˆ to form ˆ. However, because the recever and the transmtter use dfferent bands for predcton, ths method leads to a lack of synchronzaton between the transmtter and the recever and thus large errors. C. Closed Loop Predcton In closed loop predcton, shown n Fgure 7, both the transmtter and recever use the decompressed band for predcton. It s the most accurate method, however t s also more complcated because t requres the transmtter to mplement the decoder, whch s computatonally complex. - D W Transmtter t Plane Encodng t Plane Decodng W Predcton P D a b - D W t Plane Encodng Predcton P t Plane W D Decodng a b Transmtter Recever P Predcton a b t Plane Decodng W D Recever Fgure 5. Half-open loop predcton. P Predcton a b Fgure 6 shows the bt rate requred to encode each band to the of 1 n two cases: open and half-open loop. The Fgure 7. Closed loop predcton. The transmtter uses the decompressed band ˆ to predct ˆ. The predcted verson of orgnal band to obtan the dfference, Pˆ, s subtracted from the D, whch s then wavelet transformed and encoded to a bt rate requred for the target. Then the dfference s decompressed agan to form Dˆ, whch s summed wth Pˆ to form ˆ. The decompressed band ˆ s stored n the transmtter so n the

4 future t can be used to predct some other band k. The recever s the same as n the half-open loop. In Fgure 8, we compare the results of the closed and open loops. The average bt rate to code all bands to the target of 1 s.4 bpp for the open loop and.55 bpp for the closed loop. As can be seen from Fgure 8b, the s always below or close to the target. such that the bt rate s stll less than the target rate. We desgnate the truncated verson of WbyŴˆ. The nverse wavelet transform s then performed to obtan Dˆ whch s summed wth the predcted verson of, that s Pˆ, to obtan ˆ. Ths s the truncated and decompressed verson of may be used later to predct some other band k. that t rate [bpp] Open and closed loop results for target = 1 Open loop Closed loop and number a) - D W t Plane Encodng Transmtter Predcton P Truncaton W D a b Open and closed loop results for target = 1 Open loop Closed loop t Plane Decodng W D and number b) Fgure 8. Comparson of open and closed loop predcton results. a) t rate. b). D. t Plane-Synchronzed Closed Loop Predcton As a soluton that s easer to mplement on-board the satellte, we propose the bt plane-synchronzed predcton shown n Fgure 9. oth the transmtter and recever use the same number of bt planes of the wavelet coded dfference mage of the prevous band for predcton. We take advantage of the fact that the SPIHT algorthm can be splt nto two steps: wavelet transform and bt plane codng. The transmtter performs the wavelet transform on the dfference band to get Wand encodes t to the bt rate requred to code the band to the target. Once the target bt rate s known, the transmtter truncates W to the hghest number of full wavelet bt planes Truncaton W D Fgure 9. t plane-synchronzed closed loop predcton. P Recever Predcton The recever n the bt plane-synchronzed loop predcton uses Ŵ to compute the decompressed band ˆ and Ŵˆ to compute the decompressed truncated band ˆ. The transmtter and recever are always synchronzed because they use the same data for predcton. Ths synchronzaton s acheved wth a smpler on-board transmtter: t has to perform an nverse wavelet transform, but not a full decompresson as part of the predcton process. In Fgure 1, we compare the closed and bt planesynchronzed loops. The average bt rate that s requred to code each band to the target of 1 s 1.1 bpp for bt plane-synchronzed loop and.55 bpp for closed loop. The average s smlar n the two cases and equals 87. a b

5 Closed and bt plane-synchronzed closed loop results for target = 1 t rate [bpp] Closed loop t plane-synch. loop and number R(W ) k R(Ŵˆ ) < T R(W ) k 1 R(Ŵˆ ) The results for the orgnal and the mproved bt planesynchronzed loops are shown n Fgure 11. The average bt rate for the mproved method s.65 bpp whch s ust slghtly over the bt rate requred n the closed loop predcton. In addton, the average n the mproved method s only 66, whle the of the orgnal loop s 87. Ths result shows that the mproved bt plane-synchronzed loop s a very promsng method to code hyperspectral data. It acheves a very good compresson rato wth a low and has a lower computatonal complexty compared to the orgnal closed loop predcton. () a) Closed and bt plane-synchronzed closed loop results for target = 1 Closed loop t planesynch. loop and number b) t rate [bpp] Improved bt plane-synchronzed closed loop results for target = t plane-synch. loop Improved bt plane-synch. loop and number a) Improved bt plane-synchronzed closed loop results for target = 1 Fgure 1. Results for the bt plane-synchronzed closed loop predcton. a) t rate. b). E. Improved t Plane-Synchronzed Closed Loop Predcton To mprove the bt plane synchronzed loop, we nvestgated computng new predcton coeffcents and mplementng rate control. Instead of smply truncatng the wavelet transformed dfference band, we can round up to the next number of bt planes. Our decson s presented n Equaton (), where R(W ) s the rate requred to code wavelet transformed dfference W to the target, and k R(W ) and k 1 R(W ) are rates requred to code k and k1 bt planes, respectvely. If the statement n Equaton () s true, k bt planes are selected for predcton. If t s false, k1 bt planes are selected for predcton. Note that when k1 bt planes are selected for predcton, the target rate has to be ncreased to that of the full k1 wavelet bt planes. T s a threshold wth typcal values on the order of t plane-synch. loop Improved bt plane-synch. loop and number b) Fgure 11. Results for the mproved bt plane-synchronzed closed loop predcton. a) t rate. b). V. CONCLUSION In ths research, we have nvestgated dfferent methods of usng predcton to code hyperspectral data. As expected, we saw that combnng predcton wth a state-of-the-art mage compresson algorthm sgnfcantly mproves the compresson rato. We have also compared dfferent methods of predcton (open, closed, and half-open loops) and proposed a new

6 method, the bt plane-synchronzed loop. We showed that under the constrants of a smple mplementaton on-board the satellte, bt-plane synchronzed loop predcton offers excellent performance. REFERENCES [1] Govann Motta, Francesco Rzzo, and James A. Storer, Compresson of Hyperspectral Imagery, Proceedngs of the Data Compresson Conference, pp , 3. [] CCSDS Lossless Data Compresson, [3] runo Aazz, Lucano Alparone, Alessandro arducc, Stefano aront, and Ivan Ppp, Informaton-Theoretc Assessment of Sampled Hyperspectral Imagers, IEEE Transactons on Geoscence and Remote Sensng, vol. 39, no. 7, July 1. [4] A. Lenharth, R.E. Ladner, S. Hauck, E.A. Rskn, A. Mguel. Compresson of MODIS Satellte Images, n NASA Earth Scence Technology Conference, 1. [5] A. Sad and W. A. Pearlman, A new, fast, and effcent mage codec based on set parttonng n herarchcal trees, IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 6, no. 3, pp. 43 5, June 1996.