Computer-implemented method for generating a data-driven model based on information from multiple interferometric single-pass SAR acquisitions.

Abstract

The invention relates to a computer-implemented method for generating a data-driven model based on information from multiple interferometric single-pass SAR acquisitions (IA), each comprising a pair of SAR images of the same predetermined area (AR) on the surface of a celestial body, acquired at the same time using a radar acquisition geometry (AG) with a different orthogonal baseline (B0), wherein the method comprises the following steps: a) Providing training data (TD) which for each interferometric single-pass SAR acquisition (IA) includes a training data set (TDS) which for each interferometric single-pass SAR acquisition (IA) includes at least one first parameter (PA1) and at least one second parameter (PA2), wherein the at least one first parameter (PA1) depends on the extent of volume scattering of radar waves and wherein the at least one second parameter (PA2) depends on the orthogonal baseline (B0) of the radar acquisition geometry (AG); b) Training a predetermined neural network (HAM) based on the training data (TD), wherein the training aims to ensure that the output (OU) of the predetermined neural network (HAM), which is generated for the at least one first parameter (PA1) of each training data set (TDS) input into the predetermined neural network (HAM), matches the at least one first parameter (PA1) of a specific training data set (TDS). ref ) corresponds to a specific radar acquisition geometry (AG).

Description

[0001] The invention relates to a computer-implemented method for generating a data-driven model based on information from multiple interferometric single-pass SAR acquisitions. Furthermore, the invention relates to a method for predicting one or more physical and / or biological variables from information from a given interferometric single-pass SAR acquisition using this data-driven model, as well as to a computer program product and a computer program.

[0002] Synthetic aperture radar (commonly abbreviated as SAR) is an established technique for remote sensing the surface of a celestial body, such as Earth. A radar system on a platform (e.g., a satellite or aircraft) flying over the surface of the celestial body transmits radar pulses and measures the radar returns from the pulses scattered by the surface of the celestial body. Using well-known SAR processing techniques, SAR images can be derived from the measured radar returns. These images include an amplitude value and a phase value for a large number of pixels corresponding to points on the surface of the celestial body.

[0003] SAR interferometry (often abbreviated as InSAR) is a well-known technique based on pairs of SAR images with different phase information from the same area (region) on the surface of a celestial body. From a corresponding pair of SAR images, a so-called SAR interferogram can be determined, which contains the phase differences of the radar echoes between the pair of SAR images. Using known methods, information about the terrain on the surface of the celestial body can be derived from SAR interferograms. For example, a digital elevation model (DEM) of the celestial body's surface, a classification of the terrain, and the like can be derived from SAR interferograms.

[0004] Interferometric SAR acquisitions are affected by decorrelation phenomena, which lead to noise contributions in the interferogram and affect the interferometric coherence, which is a known quantity. Documents [1] and [2] describe such decorrelation phenomena.

[0005] SAR interferometry can refer to both single-pass SAR interferometry and repeat-pass SAR interferometry. In repeat-pass SAR interferometry, the interferometric SAR image pair is acquired at different times, resulting in temporal decorrelation. In contrast, single-pass SAR interferometry is based on two SAR images acquired simultaneously, for example, by a bistatic SAR configuration comprising two radar receivers flying in formation over the surface of a celestial body, with one receiver also functioning as a transmitter for retransmitting the radar waves received by the receivers.

[0006] From single-pass interferometric SAR acquisitions that are not affected by temporal decorrelation, the decorrelation component caused by volumetric scattering can be precisely isolated from the interferometric coherence (see documents [1] and [2]). This decorrelation component, also called the volume decorrelation factor, describes the contribution of volumetric scattering caused by volumetric targets on the ground, such as vegetation, snow, ice, and sand. The volume decorrelation factor represents an extremely valuable source of information because it is related to the three-dimensional structure of the illuminated targets.

[0007] In addition to the radar frequency and the properties of the volumetric targets, the volume decorrelation also depends strongly on the radar acquisition geometry used for an interferometric single-pass SAR acquisition. The radar acquisition geometry is described, among other things, by the angle of incidence of the radar waves on the ground and the so-called height of ambiguity. The height of ambiguity represents the topographic height change corresponding to a complete 2π phase cycle in the SAR interferogram, which represents the phase differences between the SAR images of the SAR image pair forming an interferometric single-pass SAR acquisition. The height of ambiguity is inversely proportional to the distance (i.e.The distance (to the shortest connecting line) between the line of sight of one radar receiver and the position of the other of the two radar receivers used for interferometric single-pass SAR acquisition. This distance is a known quantity and is commonly referred to as the orthogonal baseline.

[0008] The dependence of volume decorrelation on acquisition geometry complicates the comparison of volume decorrelation between single-pass SAR acquisitions acquired with different acquisition geometries.

[0009] It is an object of the invention to provide a computer-implemented method for generating a data-driven model based on information from multiple interferometric single-pass SAR acquisitions, wherein the data-driven model compensates for the dependence of volume scattering effects on the radar acquisition geometry.

[0010] This object is achieved by the method according to claim 1. Preferred embodiments of the invention are described in the dependent claims.

[0011] The computer-implemented method according to the invention generates a data-driven model based on information from multiple interferometric SAR acquisitions. Each interferometric single-pass SAR acquisition comprises a pair of SAR images of the same predetermined region on the surface of a celestial body, acquired at the same time using a radar acquisition geometry of a radar system. Preferably, the celestial body is a planet, and the planet is preferably Earth.

[0012] The radar system comprises two radar receivers flying in formation and receiving radar waves scattered in the predetermined area on the surface of the celestial body. The two radar receivers are separated by an orthogonal baseline, which is the difference between the line of sight of one radar receiver and the position of the other radar receiver. Each interferometric single-pass SAR acquisition differs from the other interferometric single-pass SAR acquisitions of the multiple interferometric single-pass SAR acquisitions (exclusively) with regard to the orthogonal baseline of the radar acquisition geometry. In other words, the multiple interferometric single-pass SAR acquisitions are derived from the same radar system and are based on the same radar frequency, with the orthogonal baseline varying between the two radar receivers of the radar system.This is the case, for example, with the radar system of the well-known bistatic TanDEM-X mission.

[0013] In step a) of the method according to the invention, training data is provided, comprising a training data set for each interferometric single-pass SAR acquisition. The training data set for a respective interferometric single-pass SAR acquisition comprises at least one first parameter (i.e., one or more first parameters with corresponding values) that applies to the respective interferometric single-pass SAR acquisition, and at least one second parameter (i.e., one or more second parameters with corresponding values) that applies to the respective interferometric single-pass SAR acquisition.The at least one first parameter depends on the extent of volume scattering of radar waves occurring for the respective interferometric single-pass SAR acquisition within the predetermined area, and the at least one second parameter depends on the orthogonal baseline of the radar acquisition geometry used for the respective interferometric single-pass SAR acquisition.

[0014] In a preferred embodiment, at least part of the training data, and preferably all of the training data provided in step a), has already been calculated in advance. In other words, the step of providing this part of the training data means that the training data is read from a digital memory. Alternatively or additionally, at least part of the training data is not calculated in advance. For this training data, step a) refers to a step of calculating the training data from the multiple interferometric single-pass SAR acquisitions.

[0015] In step b) of the method according to the invention, a predetermined neural network is trained based on the training data described above, wherein the training has the goal that the output of the predetermined neural network generated for the at least one first parameter of each training data set input into the predetermined neural network corresponds to the at least one first parameter of a specific training data set from the training data. This specific training data set relates to a specific acquisition geometry and thus to a specific second parameter or specific second parameters (i.e., specific values ​​of these parameters). The neural network trained according to step b) is the data-driven model generated by the method according to the invention. Any suitable method known from the prior art can be used to carry out step b).

[0016] The inventive method maps volume scatter-dependent features from interferometric single-pass SAR acquisitions that differ in acquisition geometry to the same type of features with respect to a common radar acquisition geometry. In other words, the effects of volume scatter of radar waves derived from the respective interferometric single-pass SAR acquisitions no longer depend on the acquisition geometry. Consequently, the volume scatter-dependent features, such as the interferometric coherence and the volume decorrelation factor, resulting from different acquisition geometries can be directly compared. In other words, the trained neural network provides volume scatter data with respect to a predefined acquisition geometry.By using these data, the estimation of parameters related to volume dispersion can be facilitated by appropriate models.

[0017] In a preferred embodiment of the invention, the at least one first parameter comprises the interferometric coherence within the predetermined range. The interferometric coherence is a known quantity and refers to the normalized cross-correlation coefficient between the pair of SAR images of a respective single-pass interferometric SAR acquisition. A definition of this interferometric coherence can be found, for example, in document [2] (see equation (1) in this document). In a preferred embodiment, the interferometric coherence for each pixel or respective subgroups (subsets) of pixels within the respective SAR image pair is included in the first parameters. These interferometric coherence values ​​are given by equation (2) of document [2].

[0018] Alternatively or in addition to the above-mentioned interferometric coherence, the at least one first parameter comprises a volume decorrelation factor within the predetermined region, wherein the volume decorrelation factor quantifies the extent of volume scattering of radar waves within the predetermined region for a respective interferometric single-pass SAR acquisition. The volume decorrelation factor is a quantity known from the prior art and can be calculated based on equation (6) of document [2]. Preferably, the volume decorrelation factor is determined per pixel or per subgroup of pixels in the respective interferometric single-pass SAR acquisition.

[0019] In a particularly preferred embodiment, the at least one second parameter comprises the ambiguity level for a respective interferometric single-pass SAR acquisition. The ambiguity level is a known quantity and refers to the topographic height corresponding to a 2π phase cycle in the SAR interferogram of an interferometric SAR acquisition. The ambiguity level is closely related to the orthogonal baseline and thus to the radar acquisition geometry. As mentioned above, the ambiguity level is inversely proportional to the orthogonal baseline.

[0020] The predetermined neural network trained according to the invention can have any network structure known from the prior art. Preferably, the predetermined neural network is a convolutional neural network comprising multiple convolutional layers and / or a deep neural network comprising multiple hidden layers.

[0021] In addition to the method for generating a data-driven model described above, the invention relates to a method for predicting one or more physical and / or biological variables of a given region on a surface of a celestial body based on information from a given interferometric single-pass SAR acquisition. This interferometric single-pass SAR acquisition is typically not part of the multiple interferometric single-pass SAR acquisitions used to generate the data-driven model as described above. Furthermore, the given region can be a region that differs from the predetermined region used in the method for generating a data-driven model described above. Preferably, the celestial body is a planet, and the planet is preferably Earth.

[0022] The prediction method uses the data-driven model generated by the method described above. In other words, the data-driven model is the predetermined neural network that is or has been generated by the method described above. The step of generating the predetermined neural network can be part of the prediction method. However, the generation of the predetermined neural network can be performed in advance, so that this generation step is not part of the prediction method.

[0023] The specified interferometric single-pass SAR acquisition comprises a pair of SAR images of the specified area acquired simultaneously by a radar acquisition geometry of a radar array comprising two radar receivers flying in formation and receiving scattered radar waves in the specified area, the two radar receivers separated by an orthogonal baseline, which is the distance between the line of sight of one radar receiver and the position of the other radar receiver. The radar array may be a different radar array than the radar array in the data-driven model generation method. However, the radar array used in the prediction method may also be the same radar array used in the data-driven model generation method.The radar system in the data-driven model generation method and the radar system in the prediction method use the same radar frequency.

[0024] In a step i) of the prediction method, an output of the trained predetermined neural network is generated by supplying the at least one first parameter valid for the given interferometric single-pass SAR acquisition as input to the trained neural network.

[0025] In step ii) of the prediction method, one or more features applicable to the given interferometric single-pass SAR acquisition and comprising the output of the trained neural network generated in step i) are fed as model input into a model which determines as model output a prediction for the one or more biological and / or physical quantities.

[0026] In the method described above, the trained, predetermined neural network generated according to the invention is used in a preprocessing step for a suitable model that predicts biological and / or physical variables. Since the output of the predetermined neural network no longer depends on the acquisition geometry, the prediction of the biological and / or physical variables is improved.

[0027] In a preferred embodiment of the prediction method described above, the one or more biological and / or physical quantities comprise one or more of the following quantities: - the forest canopy height within the specified area; - the snow depth and / or snow structure within the specified area; - the penetration depth of radar waves within the specified area; - a terrain class of the given area; - the above-ground biomass within the specified area.

[0028] One or more of the above-mentioned quantities can be determined, for example, pixel-by-pixel or for subgroups of pixels within the specified area. Furthermore, one or more of the above-mentioned quantities can be determined for the entire specified area (e.g., as an average value). If the specified area includes regions without forest, the forest canopy height in these regions is zero. The same applies to the snow depth.

[0029] In a further preferred embodiment of the above prediction method, the one or more features supplied to the model comprise, in addition to the output of the trained predetermined neural network, one or more additional features. These one or more additional features preferably comprise the backscatter coefficient and / or the local angle of incidence of radar waves within the predetermined area with respect to one SAR image of the pair of SAR images of the predetermined interferometric single-pass SAR acquisition and / or a digital elevation map of the predetermined area. The backscatter coefficient and the local angle of incidence are preferably determined pixel by pixel or for subgroups of pixels within the predetermined interferometric single-pass SAR acquisition.The digital elevation map of the specified area provides elevation values ​​for each pixel or for subgroups of pixels within the specified single-pass interferometric SAR acquisition. The above-mentioned quantities are known to those skilled in the art and are described, for example, in document [3].

[0030] The model used in the above prediction method may be a model derived through machine learning. Alternatively, the model may be a model that analytically calculates the corresponding biological and / or physical quantities without using machine learning.

[0031] In a particularly preferred embodiment, the model used in the prediction method is a predetermined neural network, i.e., an additional neural network besides the above predetermined neural network. The predetermined neural network has been trained with predetermined training data. This predetermined training data differs from the training data used in the method for generating a data-driven model. The predetermined training data comprises predetermined training data sets, wherein each predetermined training data set refers to a different interferometric single-pass SAR training acquisition acquired with the same radar system for all predetermined training data sets. The predetermined training data sets comprise features from the interferometric single-pass SAR training acquisitions, but not the SAR acquisitions themselves.The interferometric single-pass SAR training acquisitions preferably differ with respect to the area on the surface of the celestial body covered by the corresponding interferometric single-pass SAR training acquisitions and / or with respect to the acquisition geometry. The radar system used for the corresponding interferometric single-pass SAR training acquisitions may differ from the radar system used for the interferometric single-pass SAR acquisitions of the training data in the method for generating a data-driven model. However, the radar system used for the corresponding interferometric single-pass SAR training acquisitions may also be the same radar system as the radar system used for the single-pass SAR acquisitions of the training data in the method for generating a data-driven model.

[0032] Each predetermined training data set comprises the one or more features described above that are valid for the respective interferometric single-pass SAR training acquisition, i.e., at least the output of the trained predetermined neural network generated for an input that includes at least one first parameter that is valid for the respective interferometric single-pass SAR training acquisition. Furthermore, each predetermined training data set comprises a pre-known value or pre-known values ​​of the one or more physical and / or biological quantities of the area on the surface of the celestial body covered by the interferometric single-pass SAR training acquisition of the respective predetermined training data set.

[0033] The training of the predefined neural network is based on the goal that the model output of the predefined neural network generated for the one or more features of each predefined training dataset corresponds to the known value(s) of the one or more physical and / or biological quantities of the area on the surface of the celestial body covered by the interferometric single-pass SAR training acquisition of the respective predefined training dataset. Any suitable method known in the art can be used to train the predefined neural network.

[0034] The predetermined neural network described above can have any structure known in the art. Preferably, the predetermined neural network is a convolutional neural network and / or a deep neural network.

[0035] In addition to the above-mentioned methods, the invention relates to a computer program product with program code stored on a machine-readable carrier for carrying out the method for generating a data-driven model according to the invention or one or more preferred embodiments thereof or for carrying out the method for predicting one or more physical and / or biological quantities according to the invention or one or more preferred embodiments thereof when the program code is executed on a computer.

[0036] Furthermore, the invention relates to a computer program with program code for executing the method for generating a data-driven model according to the invention or one or more preferred embodiments thereof or for executing the method for predicting one or more physical and / or biological quantities according to the invention or one or more preferred embodiments thereof when the program code is executed on a computer.

[0037] In the following, embodiments of the invention will be described with reference to the accompanying drawings, in which Fig. 1 is a diagram illustrating the training of a data-driven model based on an embodiment of the invention; and Fig. 2 is a diagram illustrating the use of the Fig. 1 trained data-driven model for predicting forest canopy height from single-pass interferometric SAR acquisitions.

[0038] Fig. 1 shows an embodiment of the method for generating a data-driven model according to the invention. In Fig. 1, the trained data-driven model is a neural network called HAM (Height of Ambiguity Alignment Model). The goal of this neural network is to align volume-decorrelation-dependent features of interferometric single-pass SAR acquisitions acquired with different acquisition geometries to a common reference geometry.

[0039] The neural network HAM is trained with training data stored in Fig. 1 are labeled TD. The training data TD comprises several training data sets TDS. Each training data set TDS refers to a different interferometric single-pass SAR acquisition IA. The interferometric single-pass SAR acquisitions are Fig. 1 as rectangles. Each interferometric single-pass SAR acquisition IA comprises a pair of SAR images of an area AR on the Earth's surface, where the SAR images are acquired simultaneously (i.e., in a single pass over the area) using a radar acquisition geometry AG of a SAR radar installation. The SAR radar installation comprises two radar receivers flying in formation and receiving radar waves scattered in the area AR. The two radar receivers are separated by an orthogonal baseline B0, which is the distance (i.e., the shortest connecting line) between the line of sight of one radar receiver and the position of the other radar receiver. The orthogonal baseline B0 is inversely proportional to the ambiguity height h amb (see, for example, equation (5) in document [2]).

[0040] In the embodiment described here, the radar receivers are arranged on different satellites that fly over the Earth. The radar system can, for example, be a bistatic SAR system, in which a radar receiver also functions as a transmitter for transmitting the radar waves received by both radar receivers. The bistatic SAR system can, for example, refer to the well-known bistatic TanDEM-X mission. In this mission, the two satellites with the corresponding radar receivers fly in formation over the Earth, with the satellites each moving in different orbits, so that the orthogonal baseline between the two radar receivers continuously changes. In other words, the interferometric single-pass SAR acquisitions are made by the same radar system, but refer to different radar acquisition geometries due to the varying orthogonal baseline.

[0041] The Fig. The interferometric single-pass SAR acquisitions IA shown in Figure 1 all cover the same area AR on the Earth's surface. Each interferometric single-pass SAR acquisition comprises a pair of SAR images acquired by the same radar installation, but with different acquisition geometries AG, which differ in the orthogonal baseline B0 and thus also in the ambiguity height h amb The first parameters PA1 and a second parameter PA2 are known in advance for each interferometric single-pass SAR acquisition IA and form the corresponding training data sets TDS. The first and second parameters (and not the SAR images of the acquisitions) are processed using the procedure described below.

[0042] The parameters PA1 refer to the interferometric coherence γ tot and the volume decorrelation factor γ volBoth parameters are known to the person skilled in the art, as mentioned above. In the embodiment described here, the interferometric coherence is calculated pixel by pixel for the respective interferometric single-pass SAR acquisition IA based on the formula (2) disclosed in document [2]. The volume decorrelation factor γ vol quantifies the extent of volume scattering of radar waves within the area AR for the corresponding interferometric single-pass SAR acquisition IA. This factor is calculated based on formula (6) in document [2]. The second parameter PA2 of a corresponding training data set TDS refers to the ambiguity height h described above. amb which differs between the interferometric single-pass SAR acquisitions IA.

[0043] The neural network HAM of Fig. 1 has the task of aligning the interferometric single-pass SAR acquisitions IA to a common acquisition geometry defined by the ambiguity height h ref which also specifies the second parameter PA2 of a reference training data set TDS ref which is one of the training data sets TDS. To solve the above task, the neural network HAM is trained in such a way that - for an input IN in the form of the first parameters PA1 of a corresponding training data set TDS - it calculates the first parameters PA1 of the reference training data set TDS ref as output. In other words, the neural network HAM is trained in such a way that the first parameters PA1 of each training data set TDS input to the neural network HAM produce the same output OU, i.e. the first parameters PA1 of the reference training data set TDS ref, generate. For this purpose, the training of the neural network HAM is configured so that the deviation between the output OU of the network HAM and the first parameters PA1 of the training data set TDS ref is minimized, regardless of which initial parameters of the training data sets (TDS) are fed to the HAM neural network. Known training techniques can be used to train the HAM neural network. Furthermore, any known architecture for the HAM neural network can be used. For example, the HAM neural network can be a convolutional neural network and / or a deep neural network.

[0044] The neural network HAM, which uses the method of Fig. 1 can be used in a preprocessing step for a model that predicts one or more biological and / or physical variables of an area on the Earth's surface from a single-pass interferometric SAR acquisition. Fig. Figure 2 shows the use of the HAM neural network for this purpose.

[0045] Fig. Figure 2 shows a model DN (DN = Downstream Network) for predicting a biological or physical quantity Q using, among other things, the first parameters PA1 described above (namely γ tot and γ vol ) an interferometric single-pass SAR acquisition IA' covering the area AR' on the Earth's surface. This area AR' does not have to be the same area AR used for training the neural network HAM. Preferably, however, the same radar system in the form of two radar receivers with different orthogonal baselines was used for the acquisition IA' and the acquisition IA, as in Fig. 1. In the embodiment described here, this biological quantity Q is the canopy height h caof a tropical rainforest captured by the interferometric single-pass SAR acquisition IA'. The model DN for predicting the biological variable Q is a neural network DN in the form of a convolutional neural network. In a particularly preferred embodiment, the neural network is based on the convolutional neural network described in document [3]. The variable Q forms the output OU' of the neural network DN.

[0046] The convolutional neural network described in [3] directly receives the first parameters PA1 of the single-pass interferometric SAR acquisition IA' as part of its input. In contrast, the network DN receives Fig. 2 as part of its input IN' first parameters PA1', which are preprocessed by the trained neural network HAM. In other words, in a preprocessing step, the trained neural network HAM receives as input IN the first parameters PA1 (γ tot , γ vol) of the interferometric single-pass SAR acquisition IA' and outputs corresponding parameters PA1', which relate to the interferometric coherence γ̂ tot and the volume decorrelation factor γ̂ vol adjusted to the level of ambiguity h ref These first parameters PA1' form part of the characteristics F that represent the input IN' of the downstream network DN.

[0047] In addition to the first parameters PA1', the downstream network DN receives additional features F' related to the interferometric single-pass SAR acquisition IA'. These additional features are the backscatter coefficient σ 0(preferably for a specific polarization, e.g., HH polarization) and the local angle of incidence of the radar waves at the corresponding pixels of a SAR image of the SAR image pair constituting the SAR acquisition IA', as well as a digital elevation map DEM of the area AR' covered by the SAR acquisition IA'. The above additional features F' are known to the person skilled in the art and correspond to the features used in document [3] (see Section IV.B. of this document). Based on the above features F (i.e., the parameters PA1' and the additional features F') input to the downstream network DN, this network generates the output OU', which represents the forest canopy height h ca which is determined pixel by pixel for the SAR training acquisition IA'.

[0048] The downstream network DN is trained with predefined training data TD', which comprises several training data sets TDS', each of which refers to an interferometric single-pass SAR training acquisition TIA. Each training data set TDS' contains the parameters PA1' and F' for the corresponding interferometric single-pass SAR training acquisition TIA, as well as previously known values ​​of the canopy height h. ca The training of the downstream network DN is carried out using a known method, as is the case for the neural network HAM. The goal of this training is for the parameters PA1' and F' of a corresponding training data set TDS', which is input to the downstream network DN, to generate the quantity Q contained in the corresponding training data set TDS' (i.e., the cabin roof heights).

[0049] The Fig. The network architecture shown in Figure 2 was evaluated based on single-pass interferometric SAR acquisitions, which were also used for training and testing the convolutional neural network disclosed in document [3] (see Fig.2 in this document). These single-pass interferometric SAR acquisitions include SAR images of rainforest areas in Africa obtained from the bistatic TanDEM-X mission. The downstream network DN is trained and tested based on these SAR acquisitions. The single-pass interferometric SAR acquisition used for training the HAM neural network refers to rainforest areas in the Amazon region obtained from the bistatic TanDEM-X mission. The prediction results of the DN network, which receives the output of the HAM network and has the same structure as the convolutional neural network described in document [3], were compared with corresponding results of the DN network without using the preprocessing step performed by the HAM network. The prediction results for the DN network in combination with the preprocessing of the HAM network are significantly better (i.e.more accurate) than for the DN network without using the HAM network preprocessing.

[0050] The model described above is based on the DN neural network trained by machine learning. However, the model can also refer to another type of model, i.e., a physical model that calculates the corresponding biological and / or physical parameters without the need for machine learning.

[0051] The invention, as described above, has several advantages. In particular, for interferometric single-pass SAR acquisitions with different acquisition geometries, a data-driven model in the form of a neural network is generated that adapts the interferometric single-pass SAR acquisitions to a reference geometry. In particular, the data-driven model compensates for the dependence of the volume decorrelation-dependent features of an interferometric single-pass SAR acquisition on the acquisition geometry. The data-driven model can be used in combination with a prediction model that predicts biological and / or physical quantities from interferometric single-pass SAR acquisitions. For this purpose, the output of the data-driven model is used as input for the prediction model.As described above, this combination of the data-driven model with the predictive model can achieve better prediction results for corresponding biological and / or physical variables. Literature list [1] Martone, M., Rizzoli, P., Krieger, G., 2016. Volume Decorrelation Effects in TanDEM-X Interferometric SAR Data, IEEE Geoscience and Remote Sensing Letters, 13(12), pp. 1812-1816 [2] Rizzoli, P., Dell' Amore, L., Bueso-Bello, J.-L., Gollin, N., Carcereri, D., Martone, M., 2022. On the Derivation of Volume Decorrelation from TanDEM-X Bistatic Coherence, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 15, pp. 3504-3518 [3] Carcereri, D., Rizzoli, P., Ienco, D., Bruzzone, L., 2023: Deep Learning for the Estimation of Forest Height from Bistatic TanDEM-X Data, IEEE Journal of Selected Topics in Applied Earth Observation and Remote Sensing, Vol. 16, pp. 8334-8352

Claims

[1] A computer-implemented method for generating a data-driven model based on information from multiple interferometric single-pass SAR acquisitions (IA), each interferometric single-pass SAR acquisition (IA) comprising a pair of SAR images of the same predetermined area (AR) on the surface of a celestial body, acquired at the same time using a radar acquisition geometry (AG) of a radar installation comprising two radar receivers flying in formation and receiving radar waves scattered in the predetermined area (AR), the two radar receivers being separated by an orthogonal baseline (B0), which is the distance between the line of sight of one radar receiver and the position of the other radar receiver,wherein each interferometric single-pass SAR acquisition (IA) differs from the other interferometric single-pass SAR acquisitions (IA) with respect to the orthogonal baseline (B0) of the radar acquisition geometry (AG), the method comprising the following steps: a) Providing training data (TD) containing a training data set (TDS) for each interferometric single-pass SAR acquisition (IA), wherein the training data set (TDS) for a respective interferometric single-pass SAR acquisition (IA) comprises at least one first parameter (PA1) that applies to the respective interferometric single-pass SAR acquisition (IA), and at least one second parameter (PA2) that applies to the respective interferometric single-pass SAR acquisition (IA), wherein the at least one first parameter (PA1) depends on the extent of volume scattering of radar waves that occurs for the respective interferometric single-pass SAR acquisition (IA) within the predetermined area (AR), and wherein the at least one second parameter (PA2) depends on the orthogonal baseline (B0) of the radar acquisition geometry (AG) used for the respective interferometric single-pass SAR acquisition (IA); b) training a predetermined neural network (HAM) based on the training data (TD), wherein the training has the objective that the output (OU) of the predetermined neural network (HAM) generated for the at least one first parameter (PA1) of each training data set (TDS) input to the predetermined neural network (HAM) corresponds to the at least one first parameter (PA1) of a specific training data set (TDS ref ) from the training data (TD), where the specific training data set (TDS ref ) refers to a specific radar acquisition geometry (AG), where the trained pre-defined neural network (HAM) is the generated data-driven model. [2] Method according to claim 1, wherein the at least one first parameter (PA1) is the interferometric coherence (γ tot ) within the predetermined area (AR), wherein the interferometric coherence (γ tot) is the normalized cross-correlation coefficient between the pair of SAR images of a respective interferometric single-pass SAR acquisition (IA), and / or wherein the at least one first parameter (PA1) is a volume decorrelation factor (γ vol ) within the predetermined area (AR), wherein the volume decorrelation factor (γ vol ) quantifies the extent of volume scattering of radar waves within the predetermined area (AR) for a respective interferometric single-pass SAR acquisition (IA). [3] Method according to claim 1 or 2, wherein the at least one second parameter is the ambiguity level (h amb ) for a respective interferometric single-pass SAR acquisition (IA), where the ambiguity height (h amb ) is the topographic height corresponding to a 2π phase cycle in the SAR interferogram of the respective interferometric single-pass SAR acquisition (IA). [4] Method according to one of the preceding claims, wherein the predetermined neural network (HAM) is a convolutional neural network and / or a deep neural network. [5] Method according to one of the preceding claims, wherein in step a) the training data (TD) are at least partially read out from a digital memory and / or wherein in step a) the training data (TD) are at least partially calculated from the plurality of interferometric single-pass SAR acquisitions (IA). [6] A method for predicting one or more physical and / or biological quantities (Q) of a given area (AR') on a surface of a celestial body from information from a given interferometric single-pass SAR acquisition (IA') by using a data-driven model, wherein the data-driven model is the trained predetermined neural network (HAM) generated or has been generated according to the method of any one of the preceding claims, wherein the given interferometric single-pass SAR acquisition (IA') comprises a pair of SAR images of the given area (AR') acquired at the same time by means of a radar acquisition geometry of a radar installation comprising two radar receivers flying in formation and receiving radar waves scattered in the given area (AR'), the two radar receivers being separated by an orthogonal baseline (B0),which is the distance between the line of sight of one radar receiver and the position of the other radar receiver, the method comprising the following steps: i) generating an output (OU) of the trained neural network (HAM) by supplying the at least one first parameter (PA1) valid for the given interferometric single-pass SAR acquisition (IA') as an input (IN) to the trained neural network (HAM); ii) feeding one or more features (F) applicable to the given interferometric single-pass SAR acquisition (IA') and comprising the output (OU) of the trained neural network (HAM) as model input (IN') to a model (DN) which determines a prediction of the one or more biological and / or physical quantities (Q) as model output (OU'). [7] Method according to claim 6, wherein the one or more biological and / or physical quantities (Q) comprise one or more of the following quantities: - the forest canopy height (h ca ) within the specified area (AR'); - the snow depth and / or snow structure within the specified area (AR'); - the penetration depth of radar waves within the specified area (AR'); - a terrain class of the given area (AR'); - the above-ground biomass within the specified area (AR'). [8] Method according to claim 6 or 7, wherein the one or more features (F) comprise one or more additional features (F') in addition to the output (OU) of the trained predetermined neural network (HAM). [9] The method of claim 8, wherein the one or more additional features (F') comprise the backscatter coefficient (σ 0) and / or the local angle of incidence of radar waves within the given area (AR') with respect to a SAR image of the pair of SAR images of the given interferometric single-pass SAR acquisition (IA') and / or a digital elevation map (DEM) of the given area (AR'). [10] Method according to one of claims 6 to 9, wherein the model (DN) is a predetermined neural network (DN) trained with predetermined training data (TD') comprising predetermined training data sets (TDS'), wherein each predetermined training data set (TDS') relates to a different interferometric single-pass SAR training acquisition (TIA) acquired with the same radar system for all interferometric single-pass SAR training acquisitions, and comprising one or more features (F) applicable to the respective interferometric single-pass SAR training acquisition and a previously known value or values ​​of the one or more physical and / or biological quantities (Q) of the area on the surface of the celestial body covered by the respective interferometric single-pass SAR training acquisition (TIA), wherein the training has the objective ofthat the model output (OU') of the predetermined neural network (DN) generated for the one or more features (F) of each predetermined training data set (TDS') corresponds to the previously known value(s) of the one or more physical and / or biological quantities (Q) of the area on the surface of the celestial body covered by the interferometric single-pass SAR training acquisition (TIA) of the respective predetermined training data set (TDS'). [11] Method according to claim 10, wherein the predetermined neural network (DN) is a convolutional neural network and / or a deep neural network. [12] Computer program product comprising program code stored on a machine-readable carrier for carrying out a method according to any one of the preceding claims when the program code is executed on a computer. [13] Computer program with program code for carrying out a method according to one of claims 1 to 11 when the program code is executed on a computer.

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