Baseline Combination for Insar Dem Atimetric Resolution Enhancement

Combination of several interferograms of a same area, each having its own ambiguity of altitude, allows producing a combined interferogram with either a better signal to noise ratio or a lower ambiguity of altitude, unreachable from a single interferometric pair. InSAR baseline combination by summation of interferograms allows reaching peculiar equivalent baselines while increasing signal to noise ratio in the resulting interferogram. Despite this drawback such combination revealed to be highly useful in atmospheric artifacts identification and localization. Choosing adequately the interferograms to combine allow to generate interferograms with very short baseline in which the topographic phase component can be neglected, revealing artifacts before going further in a then useless processing. Baseline combination by averaging can only be applied on unwrapped phases. Therefore, each interferogram must be unwrapped prior to combination. We thus implemented a three step phase unwrapping procedure allowing to take fully advantage of an interferometric data set containing several InSAR pairs of a given site. Phase averaging allows to lower substantially the phase standard deviation and thus to increase the altitude accuracy. Baseline combination process was developed in the frame of an ESA DUP project [1] and of a TELSAT IV project [2]. 1 BASELINE COMBINATION PROCESS DESCRIPTION The phase in a single interferogram may be expressed as follow: Dj + d l p + p + Dj = Dj e z n 4 h ha 2 p (1) Where: • the first term is the orbital phase term, • the second term is the topographical one, with ha the ambiguity of altitude, • the third term is the differential one, with ndz the optical path difference and n the refractive index, • the fourth term is the phase noise due to coherence losses between both considered wave fronts. We consider here that there is no differential phase term. Moreover, interferograms are combined after flat earth phase removal. Therefore, only the second and fourth terms are to be considered in eq. 1. 1.1 Combination by addition Two types of combination are possible. Either the interferograms are simply added or they are averaged. In case of combination by addition (or subtraction), the combined interferogram results in a phase expressed as: eq eq i i e h ha 2 e ha 1 h 2 Dj + p = Dj + p = Dj   (2) ____________________________________________________________ Proc. of FRINGE 2003 Workshop, Frascati, Italy, 1 – 5 December 2003 (ESA SP-550, June 2004) 31_derauw The first type of combination allows to get very short equivalent ambiguity of altitude haeq but with increasing phase noise, even if the signal to noise ratio is increased. Therefore, this first scheme may induce problems in the phase unwrapping process. In the same way, combination by simple addition (or subtraction) allows to obtain combined interferograms having very high ambiguity of altitude. This can be very helpful when the fringe rate is to high to allow reliable phase unwrapping in order to obtain a "first order" topographic phase. As it will be shown hereafter, some combination allows to generate interferograms having such a high equivalent ambiguity of altitude that no or few topographic phase is present. Such combinations are helpful for atmospheric artifact analysis. 1.2 Combination by averaging Phases from independent interferograms can also be averaged. In this case, the resulting phase is:   Dj + p = Dj i i e N 1 ha 1 N 1 h 2 (3) where N is the number of combined pairs. In this kind of combination, we can achieve an equivalent ambiguity of altitude with an averaged noise in the combined interferogram. The problem of averaging is that it is only applicable to unwrapped phase. Therefore, there is, a priori, no gain with respect to processing time nor with respect to noise induced difficulties since each interferogram must be unwrapped independently. 1.3 Advantages versus drawbacks From the foregoing, one may wonder what are the advantages of baseline combination since a priori; there is no gain in processing easiness. From one side, noise increases. On the other side, averaging can reduce noise but phase unwrapping is needed for each interferograms. In the next sections, we will see that, since we have several image pairs, a joint iterative phase unwrapping can be efficiently implemented. This joint phase unwrapping process allows us to obtain unwrapped phases better than those that can be independently generated. Therefore, baseline combination based on phase averaging keeps all its interest. Secondly, as it will be shown hereafter, baseline combination by addition (or subtraction) is a powerful tool to show and study atmospheric artifacts. 2 TEST SITE AND DATA SET Baseline combination process was implemented and validated on two distinct test sites: Brussels and Liège, Belgium area. These test sites offer a wide variety of land covers (urban, industrial, agricultural, forested,...) and landscape in a limited area. Moreover, a huge amount of ERS SAR data is available as well as exhaustive meteorological data and high resolution DEM to be used as reference for validation. For the Brussels area, we have chosen to use only ERS1 data acquired during the "Second Ice Phase" of the ERS1 mission (December 28, 1993 to April 9, 1994). This phase is characterized by a 3-day repeat cycle of acquisition above a given point. For the Liège area, two sets of 5 ascending and descending Tandem ERS1-ERS2 InSAR pairs were used. As far as possible, winter tandem acquisitions were chosen. Thanks to short lap between acquisitions, we can expect to keep a very good coherence between SAR scenes. Moreover, winter period ensures us to have a very low crop coverage and thus, to limit time decorrelation. Scenes were selected after analysis of meteorological data. Concerning the Brussels test site, we have chosen 5 image pairs whose main characteristics are given in table1. Validation was performed by measuring and comparing phase standard deviation evolution with respect to the number of combined interferograms as also by comparison with a high resolution provided by the National Geographic Institute (NGI) of Belgium (maximum error in height measurement of this reference is announced to be approximately 0.5 m). table 1. Selected data set Acquisition orbit Interferométric baseline Ambiguity of dates E1 E1 B// [m] B^ [m] altitude ha [m] January 3, 1994 & December 31, 1993 12914 12871 41 111 -86 February 5 &2, 1994 13387 13344 -46 -125 77 February 11 & 8, 1994 13473 13430 30 74 -130 February 17 & 14, 1994 13559 13516 -49 -134 -71 March 19 & 16, 1994 13989 13946 48 125 72 In order to ease nomenclature of the used scenes and generated interferometric products, we simply indexed the images chronologically from 0 to 9. Therefore, as an example, i10 refers to interferogram made from the scenes acquired the 3 of January 1994 and the 31 of December 1993. 3 BASELINE COMBINATION FOR ATMOSPHERIC ARTIFACTS ANALYSIS Looking to the altitude of ambiguity, we can deduce the usefulness of the following baseline combinations for atmospheric artifact analysis: table 2. Useful baseline combination by addition for atmospheric artifact analysis i10 i32 i54 i76 i32 i32 + i10 haeq > 730m i54 3 * i54 2 * i10 haeq > 5500m 2 * i54 + i32 haeq > 400m i76 i76 i10 haeq > 400m i76 + i32 haeq > 900m i76 2 * i54 haeq > 760m i98 i98 + i10 haeq > 440m i98 i32 haeq > 1100m i98 + 2 * i54 haeq > 660m i98 + i76 haeq > 5000m Knowing that the altitude of the covered area ranges between 0 and less than 250m, any of these combined interferograms must contain less than half a fringe. Moreover, some combinations have very large equivalent altitude of ambiguity. For these ones, the topographic phase must be nearly completely removed. The combined interferograms must show only the atmospheric component, baseline errors and local complex backscattering coefficient changes if present. All these combinations were tested and revealed that two pairs expected as good, contained in fact very important atmospheric artifacts. 3.1 Example: interferogram combinations i76 – i10 Fig. 1. shows the interferogram combination obtained from i76 and i10. The equivalent altitude of ambiguity is of about 400m. As a consequence, the topographical phase is not completely flattened but can only induce less than half of a fringe in the south and less than a tenth of fringe in the north of the scene. A vertical structure is clearly visible in the combination (fig. 1.). Since this structure is already visible in i76, it is suspected that this vertical structure is due to an atmospheric artifact contained in pair 76. It induces approximately a one-fringe step from left to right. It means that without this cross checking with other interferogram one may produce completely erroneous DEM from this sole SAR pair with local height bias up to 70m. Analysis of METEOSAT images showed nearly null cloud coverage for the 14 of February 1994 and a very low but apparently constant cloud cover for the 17 of February. This low cloud coverage seems sufficient to induce artifacts. Fig. 2. shows the METEOSAT images acquired the 17 of February 1994 at 21h30 and 22h00, thus 17 minutes before and 13 minutes after the SAR acquisition. When enhancing the contrast locally as shown in the figure, the cloud cover appears less continuous. A straight cloud front appears in the north of Belgium having the same orientation than the stripes observed in the interferogram. As a consequence, it appears that the characteristics of the atmosphere shown by the IR channel of METEOSAT have a strong influence on the phase in the generated SAR interferograms. Fig. 1. interferograms i10, i76 and i76 – i10 interferogram combination Fig. 2. Samples of METEOSAT IR images acquired just before and after the 17 February SAR acquisition 4 BASELINE COMBINATION BY AVERAGING Baseline combination by averaging can only be applied on unwrapped phases. Therefore, each interferogram must be unwrapped prior to combination. The simplest scheme is to unwrap each phase up to residue connection. Having connection maps corresponding to each interferogram, one must superimpose them in order to have a common connection map to unwrap each interferogram. Finally, we obtain unwrapped phases sharing the same connections, allowing us to combine them by averaging. This simple and say, classical procedure is not very efficient. Superimposing the connection maps of each interferogram gives a common connection map containing all the connection from each interferogram. There is thus no gain in the segmentation of the final combined phase. We thus implemented a three step phase unwrapping procedure allowing to take fully advantage of an interferometric data set containing several InSAR pairs of a given site. 4.1 Three step phase unwrapping From the analysis of the five SAR pairs of our data set, we chose the one that is the easiest to unwrap classically. This pair is characterized by the highest mean coherence level in order to ensure to have a minimum number of residues to be connected. The presence or absence of atmospheric artifact is not of prior importance since the aim is to obtain a first topographic phase approximation. On the other hand, the ambiguity of altitude must be chosen adequately because this first topographic phase approximation must be retrieved from the other interferograms. Therefore, in a second step, this phase shall be converted in the geometry of acquisition of each of the other pairs. This implies multiplication by factors that should be kept lower than 1 in order to avoid increasing the noise present in this first topographic phase approximation [3]. In our case, i10 corresponds to these characteristics. As an intermediate product during phase unwrapping process, we generate a biased coherence used to guide the residue connection process. Since all the images are observing the same scene, this biased coherence is considered as representative as the one that might be obtained in all the pairs. In other words, we suppose that, even if the other pairs show lower coherence, the low coherence guides should be mainly the same from one pair to another. After a classical phase unwrapping of i10 we obtain a first approximation of the topographic phase, which is then transposed in each of the acquisition geometry of each other pair. The first topographic phase approximation is used to flatten each remaining interferograms. The flattened interferograms are then strongly filtered. For each interferogram, a residual phase term is then calculated as the difference between the flattened interferogram and the filtered version of it. This residual phase term normally exhibits phases distributed along a sharp peak centered on zero. If the distribution curve falls to zero outside the [-p/2, +p/2] interval, then this residual phase does not need to be unwrapped. Generally, the distribution does not fall to zero outside these bounds, but these phase levels are very few populated. Moreover, these phases correspond to areas having very low coherence levels and for which, no valid topographic information can be obtained. Nevertheless, if the phase distribution is too far from an ideal one falling to zero outside the interval [-p/2, +p/2], one must simply use a less filtered version of the flattened interferogram to generate the residual one. The phase unwrapping process is then initiated on the filtered version of the flattened interferogram and stopped after the residues connections are generated. These connection maps show very few connections, since there are related to filtered and flattened interferograms. Next, all the connection maps are superimposed to get a common one that is used to unwrap each flattened and filtered interferograms similarly. We thus obtain a second phase component for each interferogram The third component of each unwrapped interferogram is given by the residual interferogram that does not need to be unwrapped as already explained. Finally, each unwrapped phase is obtained by the summation of the three components. After this three-step phase unwrapping, we obtain 5 topographic phases that can be averaged to generate the final DEM. 4.2 Advantages and drawbacks The main advantage of this three-step phase unwrapping is that it allows us to obtain N phases that are sharing a same connection map. This common connection map contains much less connections than the one obtained by a simple superimposition of the connection maps issued by independent phase unwrapping of each interferogram. As a consequence, the generated DEM is made of much fewer independently unwrapped zones than the one that should have been obtain using a classical averaging approach. Fig. 3. shows both connection maps obtained on a sample interferogram located around the Antwerp harbor (north border of our test site frame). The first connection map results from a simple superimposition of each connection map obtained from each interferogram individually. This is thus the connection map that would have been used in a classical averaging process. The second one is the one issued during the joined phase unwrapping procedure. The drawbacks of the methods are that this process is complex, not easily automatable and highly time consuming. Fig. 3. Connection map sample: left: Classical averaging process; right: Joint phase unwrapping process 4.3 Illustrative results After the joint phase unwrapping process, we obtain five phase surfaces that can be combined by averaging and converted in a combined DEM. In the case of the Brussels test site, the best combination we can generate is given by † 1 5 j10 j32 + j54 + j76 j98 ( ) which has an equivalent ambiguity of altitude of about 83m. Measurements of the phase standard deviation are represented on fig. 4. Phase standard deviation histogram of the combined topographical map is shown in comparison with the one of i10, the best intervening interferogram. Phase Standard Deviation [rad] Fig. 4. Phase Standard Deviation image measurement after 5 interferogram combination and corresponding histogram As can be seen, there is a clear gain in terms of phase accuracy. Low phase standard deviation levels are more populated in the combination than in the phase issued from the best intervening interferogram. In the combination, 90% of the unwrapped phase has a phase standard deviation below 0,37 radian which correspond to a height standard deviation below 4,9 meters. Most populated level corresponds to those having a height standard deviation of about 1,2 meter. While in the phase issued from interferogram i10, 90% of the topographic phase leads to a height standard deviation smaller or equal to 8,9 meters. Validation in comparison with the high resolution reference DEM of the Brussels area leads to similar results. In this area of moderately good coherence, the estimated phase standard deviation is of about 0,4 radian while the measured height standard deviation is below 5 meters.