SAR Interferometric phase noise reduction using wavelet transform

entire ensemble is affected immediately. In the steady state, however, only a portion of the molecules are in the signal generating portion of the photocycle. 3.0 [ -1.5 1 V I 0 2 4 time, ms a W’ 0.1 0.01 0.1 1 10 light intensity, mW/mm2 b 1798/21 Fig. 2 Mcasurvd photoresponse iwveform Io niodulured 630nm light for conduction ~icross ITO/bR/Au/GaAs under umbient humidity contlitions rind pcuk ~)hotorurriv~t acro,m .mmple us .firnetion of incident light intensity ri Photoresponse waveform Light intcnsity = 8ni\V/mm2 0 Peak photocurrent against incident light intensity The effect of aging of the bR is not revealed in our experiments. This is because the photoexdation has a wavelength (632nm) that is significantly different from the absorption peak wavelength (570nm) of the bR molecule. This results in a small absorption by the bR film and a small number of molecules being converted to the M photoinkmediate state, which does not seriously lower the lotdl available population of the bR ground stale. Acknowledgment: This work is supported by the Army Research Orlice (MURI program) under Grant DAADIY-99-1-0 198. Discussions with S. Datta and D. Janes are gratefully acknowledged. 0 IEE 2001 16 October 2000 Electronics Letters Online Not 20010426 Dot: 10.1049/el:20010426 J. Xu and P. Bhattacharya (Solid State Electroniu Laborcitory, Depurtment o/ Eleclricul Engineering rind Compulrr Science, Unii~ersity of Michigun. Ann Arbor, MI 48109-2122, USA) E-mail: pkbi&eecs.umich.edu D.L. Marcy, J.A. Stuart and K.K. Birge (W.M. Keck Center for Molwulur Electronics & lkpurtment of Chemistry, SjJrriczi.Pe Univer.ritv, Svrucuse, NY 13244, USA) K.K. Birgc: Present addrcss: Dcpartment of Chemistry and Molecular & Cell Biology. University of Connecticut. Storrs, CT 06269, USA References 1 HIKtiE, R.R., CilLLkSPlh, N.B., ILACiUIKKh. b.W., KUSNETZOW, A., I.AWRENCE. A.F., SINGH, D., SONG, Q.W., SCHMIDT, E, SIUAKI. J.A., SEETHARAMAN. s., and WISE, K.J.: ’Biomolecular electronics: proteinbased associative processors and volumetric memories’, J. Plzy.?. Clem. B, 1999, 103, pp, 10746 10766 LOZIER. R.H., BOGOLNI. R.A., and STOECKENIUS, w.: ‘Bacteriorhodopsin: a light-driven proton pump in Halobacterium halobium’, Biophj~. .I. 1975, 15, pp. 955-962 the proton pump of bacteriorhodopsin. Microwave cvidence for a cation-gated mechanism’, J. Phys. Chem., 1996, 100, pp. 999010004 HONG. F.T.: ‘Molecular sensors based on the photoelectric effect of bacteriorhodopsin: origin of diffcrcntial rcsponsivity’, Mtcteu. Sri. Eng., 1997, 4, pp. 267-285 MIYASAKA. T.K.. and ITOH, I.: ‘Quantum conversion and image delection by a bacteriorhodopsin-based artificial photoreceptor’, Science, 1992, 255, pp. 342-344 TAKEI. H., LEWIS, A., and NEBENZAHL, I.: ‘Implementing reccptive ficlds with excitatory and inhibitory optoelectrical response of bacteriorhodopsin films’, A,r+d. Opt., 1991, 30, pp. 500-509 bacteriorbodopsin measured with a tin-oxide electrode’, Biophys. J., 1995, 68, pp. 1507-1517 TIMASHEV. s.F.~ CHFKLJI.AEVA, I..N., and RURIN. A.B.: ‘Oriented purple-membrane film as a probe for studies of the mechanism of bacteriorhodospiii functioning 11. Photoelectric process’, Biochimica et Biophysics Acto. 1987, 892, pp. 56 61 BIRGE. R.R., DESHAN, , IZGI, K.C., alld TAN. E.H.L.: ‘Role Of caciUm in RORERTSOK, R., and LIJKASHEV, F.: ‘Rapid pH change due to KONONENKO, A.A., CIIAMOROVKSY. S.K., MAXIMYCHEV, A.V., SAR interferometric phase noise reduction using wavelet transform C.L. Martinez, X.F. CBiiovas and M. Chandra The problem of synthetic aperture radar interferometric phase noisc rcduction is addressed. A new technique based 011 discrctc wavelet transfoiin is presented. This technique guarantees high resolution phase estimation without using phasc image scpentation. Arcas containing only noise ai-e hardly processed. Tests with synthetic and real interferograms are reported. Introduction: Synthetic aperture radar interferometry (InSAR) has been successfully applied to obtain topographic information of the earth’s surface. Interferograms are fomied multiplying a synthetic aperture radar (SAR) image by the complex conjugate of a second SAR inrage taken from a slightly different position. The phase of the interferogram at each point is then proportional to its topographic height. Interferometric phase is wrapped in a 271 modulus making it necessary to unwrap the phase to derive topographic infomiation. The degree of coherence between SAR images determines interferometric phase quality. Factors such as system noise, terrain decorrelation (non-simultaneous surveys), image misregistration, geometric decorrelation, act as noise sources. The principal effect of phase noise are residues (phase points with nonzero rotational), as they make the unwrapping process dependent on the path through which the phase is integrated. To facilitate unwrapping the interferometric phase, it is necessary to remove phase noise. As coherence varies across phase image, phase noise is a non-stationary process. Therefore, any kind of phase noise reduction algorithm has to take into account this non-stationarity. A common way to reduce phase noise is to make use of a coherent averaging or multilook filter. Unfortunately, noise reduction is achieved at the expense of spatial resolution. Other existing techniques always make use of some kind of phase windowing to process it locally. For example, the technique presented in [l] despite outperforming a mean filter, also applies a windowing segmentation process. In this Letter, we present a new technique to remove SAR interferometric phase noise. This technique is based on discrete wavelet transform (DWT) [2]. The purpose of using DWT is to avoid a phase windowing process, perfom~ng a local phase analysis, and therefore, achieving phase noise reduction within the wavelet domain. The algorithm is not based on coefficient thresholding, as we have observed that these techniques present poor results in low coherence areas. The technique also minimises the loss of resolution suffered by techniques using the DWT duality property [2]; in addition, it does not require previous phase unwrapping. ELECTRONICS LETTERS 10th May 2001 Vol. 37 No. 10 649 Princble of operation: To maintain phase jumps, which contain information for phase unwrapping, interferometric phase is processed in the complex plane: tj = arg{T*(eJ*)} = arg{Td;(R(c”)) +j .T~/,(S(~$’)),) (1) where y~ and f~ are original and estimated interferometric phases. T,,,(.) represents the noise reduction process in the complex plane. DWT. using Daubechie’s orthogonal wavelet filters, is applied to the real and imaginary parts of the interferometric phase. In the wavelet domain, a complex wavelet coefficient: C,,, is defined, the amplitude and phase of which can be written as: lc?‘21 = IDT.t’T,{sR(eJ’i’)} +j .Drvz;,(3(e’*)}I (2) arg{C,} = arg{DIVT,(R(eJ*)) + j . D1.liTrL(S(eJ@))} where n indicates the number of scales of the DWT. Phase (eqn. 3) can be defmed as a wavelet intcrferometric phase. This phase has the same information as the interferometric phase y~, but split in the wavelet scales. The amplitude values (eqn. 2) depend on sigma1 and noise content, being inversely proportional to the noise content. Interferometric noise can be reduccd, decreasing the effect of complex wavelet coefficients with low amplitude (eqn. 2). Complex wavelet coefficients at different scales and giving infomation about the same area in the original image, can be related using hierarchical relationships between these scales [3]. Due to interferometric phase properties, wavelet complex coeffcients at low frequency scales are dominated by useful information, whereas thosc located at high frequency scales are dominated by noise, i.e. there is a signal concentration at low frequency scales. Wavelet hierarchies are defined over IC,,l, and then a signal model is defined within each hierarchy by taking the coefficient with the maxi” value, c,,, as the useful signal, the remaindcr being considered as noise. Noise standard deviation a, is calculated from the highest frequency scale coefficients. Then, for each hierarchy, a reduction parameter is defined as (3) (4) Results: To test the proposed technique, synthetic and real interferograms havc been used. An X-band interferogram of Mount Etna, taken with the German E-SAR, was employed. Synthetic interferograms of a ramp of 512 x 512 pixels, contaminated with phase noise covering the coherence range from 0.1 to 0.95, have been simulated. Fig. 1 shows a detailed image (150 x 150 pixels), making it evident that the proposed algorithm does not create artifacts in the processed image. Fig. 2 shows numerical results (using synthetic interferograms) obtained with the proposed algorithm and with a multilook filter using a 5 x 5 pixels window. For coherences greater than 0.45. thc proposcd algorithm outperforms the multilook phase filter. For lower coherences (areas with almost only noisc), despite obtaining worse numerical results than the multilook filter, the proposed algorithm has the advantage that il hardly alters these areas, avoiding the creation of artifacts or ghost fringes, while maintaining the original resolution. 35 r 19 r. 01 I I I 0.1 0.2 0.3 0.4 0.5 0:6 OT7 *E 2 I ” 0.8 0.9 1.0 coherence 1271/21 Fig. 2 Algorilhm pwformance 0 original interferometric phase residues (%) + denoised interferometric phase residues (YO) (multilook filter) & denoised interferometric phase residucs (“A) (proposed algorithm) r RMS (dB) between orininal and denoised interferometric phase - (multilook‘ filter) 0 RMS (dB) between original (proposed algorithm) and denoised interferometric phase where a is an adjustment constant (equal for the whole iniage).fird will depend on signal content, the higher this content the lower its value. Asfred will be applied only over IC,”l to those coeffcients considered as noise (i.e. coefficients with low amplitude) the effect is to reduce the amplitude of noise coefficients in areas with a signal, and without significantly altering areas dominated by noise. However, since the real and imaginary parts of the transfomied phase are processed by the same amount, the relation is maintained, with the consequence that phase is maintained. The result is that the phase of low amplitude coefficients (noise coefficients) will not be incorporated in the inverse transfonnation process, thereby reducing their contribution to the recovered phase. This reduction will be performed locally, due to DWT. Inverse DWT is applied lo the processed real and imaginary parts in the wavelet domain. Denoised phase is then obtained by taking the phase between the real and imaginary processed parts in the original domain. Fig. 3 Mount Etna interfiwgrum a Original interferometi-ic phase b Proccsscd interferometric phase with multilook filter c Processed interferometric phase with proposed algorithm a b Fig. 1 Synthetic interferogrum (coherence equal to 0.4) a Original interferometric phase b Interferometric phase denoised with proposed algorithm Fig. 3 shows detailed images (150 x 150 pixels) of the Mount Etna interfcrogram. It is shown that the proposed technique preserves areas containing only noise, and does not lose fringes of the original image. The results shown in Fig. 3 prove that the proposed technique clearly outperforms the multilook filter, overall in 650 ELECTRONICS LETTERS 10th May2001 Vol. 37 No. IO areas containing only noise, and that it almost completely preserves most of the original resolution. Retransmissions Data-drivcn Timcr-driven Total retransmissions Throughput Concluvions: A new technique for SAR interferometric noise reduction, based on the wavelet transform, has been presented. The technique is highly robust in the presence of noise, avoiding the loss of resolution, while preserving the original fringes. The proposed technique provides better results than those obtained using a multilook filter. Without Snoop With Snoop FH FH Snoop % Y" Y" 3.0 1.3 12.5 10.5 21.4 13.1 13.5 22.1 25.6 1.373Kbitis 1 .053Kbit/s 0 IEE 2001 Electronics Letter$ Onlinc No: 200 10438 DOI: 10.104Y/el:20010438 5 Murch 2001 C.L. Martinez and M. Chandra (Institute of Radio Frequency Technology and Rndur System., German Aerospace Center DLR, Muenchener strasse 20, 82230 Wessling, Gertnuny) E-mail: [email protected] X.F. Cinovas (Signol Theory and Communications Department) Technical University of Catalonia UPC, Jovdi Gironn 1-3, 08034 Barcelunu, Spain) References 1 LEE, J.s., PAPATHANASSIOU, K.P., AINSWOKI'H, I.L., GRUNES, M.R., and REIGBER, A.: 'A new tcchniquc ror noisc filtering of SAR interferometric phase images', IEEE Trans. Geosci. Remote Sens., 1998, 36, (5), pp. 1456-1465 MALLAT, s.: 'A wavelet tour of signal processing' (Academic Press, San Diego, CA, USA, 1999). 2dn edn. SHAPIRO, J.M.: 'Embedded image coding using zerotrees of wavelet coefficients', IEEE Trrms. Signal Process., 1993. 41, (l2), pp. 34453462 2 3 Analysis of Snoop TCP protocol in GPRS system J. Rendon, F. Casadevall, D. Serarols and J.L. Faner The General Packet Radio Service system provides an casy adaptation to bursty traffic generated by Internet applications, e.g. e-mail, WWW and FTP. These applications usc TCP as the transport protocol and therefore good interaction is necessaiy bctwecn the TCP and GPRS protocols. The pxfotmance of the Snoop TCP protocol in a GPRS network is analysed. Introduuctirin: The General Packet Radio Service (GPRS) is the packet switching data service for GSM. It provides an easy adaptation to the bursty traffic generated by Internet applications, e.g. e-md, WWW and FTP. All three of these applications use transmission control protocol (TCP) as the transport protocol. TCP is a protocol initially designed for working in fmed networks such as the Internet, where the main problem is congestion. The problems in wireless nctworks vary: bursty packet losses, high packet delays depending on the wireless network, variable throughput, etc. There have been some proposals which enhance the TCP performance in wireless networks. One of the most well known is the Snoop TCP protocol. The Snoop TCP protocol [l] consists of having an agent installed at the base station which makes locd retransmissions on the wireless paths depending on the type of acknowledgments (ACKs) received from the mobile host (MH) and on local timers. Snoop hides the TCP sender in the fixed host (FH) from losses in the wireless link. When the Snoop agent detects a loss, it retransmits the lost TCP segment to the MH, waits for the corresponding ACK and sends it to the FH before the FH realises there has been a packet loss. Snoop TCP is a protocol which has been proven to work well in a wireless LAN environment [2], but its performance in a mobile cellular network such as GPRS has not been analysed. In this Letter we analyse, with the use of a simulator, the behaviour of the Snoop TCP protocol under realistic conditions in GPRS. Simulator structure: The GPRS radio link simulation model has been created with the event driven simulator Cadence Bones ELECTRONICS LETTERS 10th May2001 Vol. 37 Designer. We simulate the FTP transmission of' a 512Kbytes data File from an FTP server attached to the Internet to a mobile host connected to the GPRS network. We have simulated the behaviour of all the main nodes that exist in the GPRS architecture. An FTP scrver, with the corresponding TCP and IF' layers, models the fixed host. TCP-Reno version is assumed. The Internet cloud is modelled by means of a loss packet probability and a delay. The dclay is statistically characterised as a Gaussian random variable. The GPRS backbone is characterised as follows: the gateway GPRS support node (GGSN) is represented with a router, whereas the serving GPRS support node (SGSN) is modelled as a fxed delay that represents the node process delay. The SGSN node contains the Snoop agent. The GGSN-SGSN and SGSN-BSS (base station subsystem) links are also modelled with fmed delays. which take into account the limited link capacities, i.e. 2Mbitis and MKbitls, respectively. In the radio link, a transmission at the logical link control (LLC) layer has been simulated. The LLC layer has becn simulated operating in unacknowledged mode. The RLCiMAC layer has been implemented in detail. The MAC layer uses the slotted Aloha access mechanism. A round robin scheduling method without priorities is assumed. The RLC layer uses a selective-repeat ARQ mechanism. In the GPRS radio interface we can vary the number of users, the coding scheme, the channel conditions (Cfl), the number of PDCHs, the type ol' service of'fered (WWW, FTP or e-mail), and the transmission direction (uplinkidownlink). Three types of bursty traffic have been considered in the radio interface, i.e. e-mail, WWW and FTP. We hwe distributed the type of users in the following form: 50% e-mail, 30Yn WWW and 20% FTP. Table I: Comparison of Ulroughput and retransmissions r simulation time, s 1415111 Fig. 1 RTT (FHj, TCP with Snoop 60 simulation time, s 1415121 Fig. 2 RTT (Snoop agent), TCP with Snoop No. 10 65 1