Detecting and suppressing ambiguities in synthetic aperture radar data and imagery.

Abstract

A method of detecting ambiguities in Synthetic Aperture Radar (SAR) image data is performed on SAR data including amplitude and phase values ​​for each pixel in an image. The method comprises the steps of calculating a phase derivative value for each pixel represented in the SAR data with respect to a spatial direction, determining a threshold for the phase derivative value, and determining pixels having phase derivative values ​​above the threshold to be ambiguous. A method of suppressing azimuth ambiguities in Synthetic Aperture Radar (SAR) single-look composite image data is performed on a Doppler spectrum obtained from a received SAR signal. The method comprises applying an amplitude threshold to the Doppler spectrum of the received SAR signal to exclude values ​​below the threshold due to ambiguity energy in the spectrum, replacing the excluded amplitude values ​​to produce a modified Doppler spectrum in which the ambiguity energy is suppressed, and using the modified Doppler spectrum to produce image data in which azimuth ambiguities are suppressed.

Description

[Technical field]

[0001] The present invention relates to the field of synthetic aperture radar and image processing. [Background technology]

[0002] Synthetic Aperture Radar (SAR) can be used to image areas on Earth, also known as target areas, by transmitting radar beams and recording the return echoes, or returning radar energy, from those transmitted beams. SAR systems can be installed on airborne platforms such as aircraft, as well as on satellites operated from space. Various modes of operating SAR (Scanning Synthetic Aperture Radar) can be used, such as Strip Map, Spotlight, and ScanSAR (Earth Observation by Progressive Scanning SAR).

[0003] SARs are typically mounted on moving platforms, such as satellites, and therefore move relative to the target on Earth being imaged. As the platform moves, the position of the SAR antenna relative to the target changes over time, causing the Doppler effect to change the frequency of the received signal. The received echoes therefore contain a spectrum of frequencies.

[0004] Typically, SAR systems transmit high frequency radiation in pulses and record the returning echoes. The data obtained from the returning echoes are sampled and stored for processing to form an image. Radar echoes from points outside the main target imaging area can cause ambiguities in the data and images. These ambiguities can arise due to the difficulty of directing the radar beam perfectly only at the target imaging area. In reality, the radar beam has side lobes that also illuminate areas outside the desired imaging area, causing radar echoes from these "ambiguous" areas to be mixed with reflections from "non-ambiguous" areas. Echoes from these undesired regions can be from previous and subsequent transmit pulses and can have ambiguities in both azimuth and range. Ambiguities can cause ground objects or features to appear at multiple locations in the image, only one of which is the true location. Although the amplitude of some of these ambiguity signals can be smaller than the non-ambiguity signals, they can still clutter the image and reduce image quality. It is therefore desirable to be able to detect and suppress ambiguities in SAR images.

[0005] First, one approach to reduce ambiguity is to design a SAR system with an appropriate selection of antenna size and pulse repetition frequency (PRF). For example, in the antenna design stage, the problem of azimuth ambiguity can be mitigated by appropriately setting the PRF based on the antenna length. Generally, an increase in PRF reduces the occurrence of azimuth ambiguity. However, an increase in PRF also causes an increase in range ambiguity. Therefore, there are trade-offs in the design and the two types of ambiguity must be balanced. Unfortunately, a suitable design may not match the requirements of modern SAR platforms such as small satellites. New SAR satellite constellations are equipped with smaller antennas compared to previous generations, imposing constraints on traditional methods to suppress ambiguity. Due to the physical nature of SAR and trade-offs, it is impossible to design a SAR system to completely eliminate ambiguity, especially for small SAR satellites, so other approaches have been developed to detect and suppress ambiguity.

[0006] One approach is to detect and remove ambiguities through post-processing of SAR data. For example, several algorithms have been proposed to estimate the local azimuth ambiguity-to-signal ratio (AASR). However, existing algorithms for ambiguity detection and suppression are unable to suppress large ambiguities, which may also cause a degradation of the azimuth resolution. Furthermore, some of the existing algorithms for ambiguity detection and suppression are based on the assumption that the ambiguity signal is located in a specific region of the signal spectrum depending on the antenna pattern. These proposed techniques use filters built based on the knowledge of the antenna design to identify the ambiguity spectrum, allowing the detection and selective suppression of ambiguities. The limitations of these suppression methods are their low sensitivity to weak and small ambiguities, and their specialization only for certain antenna designs.

[0007] Some embodiments of the present invention described below address some of these problems, however, the present invention is not limited to addressing these issues and some embodiments of the present invention address other issues. Summary of the Invention

[0008] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter.

[0009] Provided below are methods for detecting ambiguities in synthetic aperture radar (SAR) image data and methods for suppressing ambiguities. The detection and suppression methods can be used together or separately. For example, the detection method can be used to determine the effectiveness or quality of an ambiguity suppression method (either a known method or a method described below). Conversely, the suppression method can be used to improve the quality of an image after an ambiguity has been detected (either by the new method described herein or a known method).

[0010] Accordingly, in one aspect, there is provided a method of detecting ambiguities in Synthetic Aperture Radar (SAR) image data, the SAR data including amplitude and phase values ​​for each pixel in an image, the method comprising calculating at least one phase derivative value for each pixel represented in the SAR data with respect to a spatial direction, determining a threshold for the phase derivative value, and determining that a pixel having a phase derivative value exceeding the threshold is an ambiguity.

[0011] In another aspect, a method is provided for suppressing azimuth ambiguities in synthetic aperture radar "SAR" single-look complex image data, the data including a Doppler spectrum obtained from a received SAR signal, the method comprising applying an amplitude threshold to the Doppler spectrum of the received SAR signal to exclude values ​​below the threshold due to ambiguity energy in the spectrum, replacing the excluded amplitude values ​​to generate a modified Doppler spectrum in which the ambiguity energy is suppressed, and generating image data in which the azimuth ambiguity is suppressed using the modified Doppler spectrum.

[0012] Also, in an embodiment of the present invention, a computer readable medium is provided that includes instructions in the form of an algorithm which, when implemented in a computing system that forms part of a satellite operating system, causes the system to perform any of the methods described herein.

[0013] The features of the various aspects and embodiments of the invention may be combined as appropriate and in any combination with any aspect of the invention, as will be apparent to those skilled in the art. Embodiments of the present invention will now be described, by way of example only, with reference to the following drawings, in which: [Brief description of the drawings]

[0014] [Figure 1] 1 is a schematic perspective view of a satellite in orbit above the Earth; [Diagram 2] 1 is a schematic diagram of a satellite imaging an area on Earth; [Diagram 3] FIG. 1 is a schematic diagram of ambiguity generation due to range migration compensation. [Figure 4] 1 is a flow chart illustrating a Phase Variation Analysis (PVA) algorithm according to some embodiments of the present invention. [Diagram 5] 1 is an image showing one feature and two ambiguity images of the same feature. [Figure 6a]1 is a stripmap image illustrating ambiguities detected using the PVA method according to some embodiments of the present invention. [Figure 6b] 11 is a spotlight image illustrating ambiguities detected in a strip map using the PVA method according to some embodiments of the present invention. [Figure 7] 4 is a flow chart illustrating a method for detecting and suppressing azimuth ambiguity according to some embodiments of the present invention. [Figure 8] 1 shows an image of a ship containing ambiguities. [Figure 9a] 11 shows the Doppler spectrum of the image of FIG. 10 and after normalization according to some embodiments of the present invention. [Figure 9b] 11 shows the Doppler spectrum of the image of FIG. 10 and after normalization according to some embodiments of the present invention. [Figure 10] 1 shows a plot of the linear regression between inhibition rate and ambiguity coverage. [Figure 11a] 13 shows stripmap images with azimuth ambiguities before and after detection and suppression by the SDFS method. [Figure 11b] 13 shows stripmap images with azimuth ambiguities before and after detection and suppression by the SDFS method. [Figure 12a] A spotlight image with azimuth ambiguity before and after suppression by the SDFS method is shown. [Figure 12b] A spotlight image with azimuth ambiguity before and after suppression by the SDFS method is shown. [Figure 13] 1 is a flowchart illustrating the use of a PVA algorithm for detecting ambiguities in combination with a SDFS algorithm for detecting and suppressing ambiguities. [Figure 14] 1 is a block diagram of a computing system that may be used to implement any of the methods described herein.Common reference numbers are used throughout the drawings to denote like features. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Embodiments of the present invention are described below by way of example only. These examples represent the best ways of practicing the invention currently known to applicant, but are not the only ways in which this may be accomplished.

[0016] Some embodiments of the present invention provide systems and methods for processing SAR image data to detect and / or suppress ambiguities. For this purpose, the SAR may be mounted on a platform traveling relative to the surface of the Earth. For example, SARs are commonly mounted on satellites. However, the methods and systems described herein are not limited to data obtained from space, but may also be performed on data obtained using aircraft or any other suitable platform.

[0017] FIG. 1 is a perspective view of a satellite 100 in orbit above the Earth as an example of a platform that may be used with the methods and systems described herein. The satellite is comprised of a body 110 and "wings" 160. The satellite's wings may be fitted with one or more SAR antennas. The satellite 100 further includes a propulsion system 190, which is shown attached to the body 110 on the opposite side to the solar panels 150. The propulsion system may consist of thrusters 205, 210, 215, 220, which are part of a system for maneuvering and steering the satellite 100 to properly position it to take SAR images of the Earth. The satellite body 110 may house a computing system configured to perform some of the operations described herein. In some embodiments of the invention, a ground station and / or computing system 195 is also provided that is configured to post-process SAR data received from the satellite 110 and / or to perform some of the operations described herein.

[0018] As known to those skilled in the art, it periodically alternates between a transmit mode in which pulses of radiation are directed toward the Earth's surface, and a receive mode in which radiation reflected from the Earth's surface is received.

[0019] As is known in the art, a SAR image is created by transmitting successive pulses of radio waves to "illuminate" a target, and receiving and recording the echoes of each pulse. The pulses can be transmitted and the echoes received by a single beam-forming antenna. When a SAR is mounted on a mobile platform, such as a satellite, and moved relative to the target, the position of the antenna relative to the target changes over time, causing the frequency of the received signal to change due to the Doppler effect. Signal processing of the successively recorded radar echoes allows recordings from multiple antenna positions to be combined to form a synthetic antenna aperture, producing a higher resolution image.

[0020] The area captured by a SAR is currently known as its footprint. The direction along the SAR's flight direction is usually called azimuth or along track. The direction across the flight direction is usually called range, elevation, or cross track. The direction opposite the flight direction corresponds to the astern heading.

[0021] Ambiguities in SAR images are aliasing effects caused by the pulsed behavior of the radar system. The effect of ambiguity is that the image has artifacts that do not accurately represent the ground being imaged. For example, an image may contain features that appear multiple times. One example of an ambiguity is when a dense urban area appears in the correct location, but then an artifact of that area also appears elsewhere in the image, such as over a smooth body of water. This "ambiguity" reduces the quality of the SAR image.

[0022] Spaceborne systems can generate two types of ambiguities: azimuth or Doppler ambiguities, which are related to the motion of the satellite in the azimuth direction, and range ambiguities, which are related to the time delay of echoes from different distances in the range or cross-track direction of a side-looking SAR satellite. Ambiguities can be reduced by careful antenna design, such as by carefully selecting the antenna size and pulse repetition frequency (PRF). For example, increasing the PRF tends to reduce the occurrence of azimuth ambiguities. However, increasing the PRF also has the disadvantage of increasing the occurrence of range ambiguities. Therefore, a balance must be struck between reducing azimuth ambiguities and designing the system to generate less range ambiguities, and it is not possible to fully correct both types of ambiguities by the design of the SAR system alone. This is especially true for modern satellites, which require smaller antennas. In fact, the design constraints of smaller and lighter satellites tend to increase the occurrence of azimuth ambiguities, for example. Being able to detect ambiguities is important to access quality SAR images, and detecting and suppressing ambiguities is desirable to remove ambiguities from the images.

[0023] Embodiments according to the present disclosure teach a computer-implemented method for detecting either or both of azimuth and range ambiguities using a novel approach based on differential phase value (PDV).As an example, phase variation analysis is used to detect ambiguities by using specialized filtering and differential phase information.

[0024] Embodiments according to the present disclosure also teach novel computer-implemented methods for suppressing azimuth ambiguities. In one example, selective Doppler frequency suppression (SDFS), which selectively filters ambiguity frequencies in the Doppler spectrum, is used to detect and suppress azimuth ambiguity and detect ambiguous spectrum signals that have a joint azimuth and range dependency.

[0025] One source of ambiguity in SAR images is related to the pattern of the SAR antenna beam. Figure 2 shows an example of how such ambiguity can arise. A satellite 100 is shown moving along a flight trajectory 200 that defines the azimuth direction. The imaged area direction perpendicular to the flight trajectory 200 is the range direction or cross-track direction. The satellite is operating in a "side-scan" mode, where the area to be imaged is to the side of the satellite's flight path, rather than directly below the satellite. This is typical for SAR satellites, as bright specular returns from objects directly below the satellite, i.e. in the nadir region, make it difficult to form an image of that area. The shaded area 201 represents the area (strip) to be imaged.

[0026] FIG. 2 shows an example of a satellite 100 operating in a classic strip map mode, in which the SAR beam is swept along one swath (represented by the shaded area 201) along the Earth's surface as the satellite moves in orbit. In this mode, the SAR beam typically moves in azimuth at the same speed as the SAR platform. The time during which the radar beam collects data during a forward sweep is called the integration time. Many pulses may be recorded during the integration time. The embodiments according to the present disclosure are equally applicable to any SAR mode, including spotlight mode, ScanSAR mode, TOPSAR mode, etc. As an example, the satellite 100 shines a radar beam 210 orthogonal to the satellite's heading 200 and records radar echoes from a point 203 to determine information about the Earth's surface at that point. This information is formed into an image of the Earth's surface. However, due to the difficulty of forming a perfectly steered radar beam, there are typically side lobes to the main beam, represented in the azimuth direction by lines 211 and 212, which can cause echoes from points 204 and 205 to mix with the echo from point 203. This creates azimuth ambiguity in the signal, as a feature (e.g., a building) located at point 204 may appear in the SAR images of both points 203 and 204.

[0027] Similarly, range ambiguity can be caused by echoes returning from range side lobes, an example of which is represented by line 222, which mix with returns from the imaged target region 201 (where there is no ambiguity) due to differences in slant range distances. The shaded region 220 represents an area outside the imaged target region 201, sometimes referred to as the range ambiguous region. The slant range distance to the point being imaged is represented by line 210. The slant range distance to point 221 within the ambiguity region is represented by line 222. The two points have different slant range distances, which creates a time delay due to the difference in the time it takes the radar signal to travel to the two points. This time delay causes the echo return from the side lobe to mix with the echo return of a later pulse from the main lobe, causing range ambiguity. Although only one range ambiguity region 220 is shown as an example, in reality there are additional regions corresponding to various side lobes of the antenna beam in the range direction (e.g., closer to the satellite), all of which contribute to the occurrence of range ambiguity.

[0028] Figure 2 shows how ambiguities can be formed as a result of antenna beam patterns, although other ambiguities are possible as described below. As a result of ambiguities, an image may contain ambiguity and non-ambiguity pixels because a feature "appears" in multiple locations. In the following, the term "ambiguity pixel" refers to a pixel that contains signal data that may come from multiple locations.

[0029] The embodiments described in this disclosure provide improved methods for detecting ambiguities in SAR data and may include identifying regions in a SAR image that have ambiguities. Other embodiments describe improved methods for detecting and suppressing ambiguities in SAR data to enable the generation of high quality SAR images with fewer or reduced ambiguities. Referring again to FIG. 1, this data processing associated with these embodiments may be performed at the ground station 195 or at another location on Earth in communication with the ground station 195, for example. Alternatively, some or all of the operations described herein may be performed by an on-board computing system if sufficient processing power is available. Data processing may use all pulses transmitted during the integration time to focus the data in the azimuth direction.

[0030] As noted elsewhere herein, the methods described herein are particularly, but not exclusively, suited for implementation in conjunction with SARs carried onboard satellites.

[0031] In addition to ambiguities due to SAR antenna beam patterns, other sources of ambiguity in SAR images are related to the processing of SAR data. For example, ambiguities can arise due to errors in range migration correction (RMC) algorithms or Doppler centroid estimation. Unlike the first source of ambiguity, which is due to the physical properties of the antenna beam, these ambiguities arise due to the processing required to convert the raw SAR data into an image.

[0032] Figure 3 shows how azimuth ambiguities arise as a result of range migration correction algorithms performed on SAR data to account for differences in range to targets due to movement of the SAR platform. It should be noted that azimuth signals correspond to signals at different points along the satellite's direction of travel (azimuth direction), and these signals are time-tagged during acquisition creating "azimuth time." Range signals correspond to signals at different points substantially perpendicular to the direction of travel (range direction), and these signals are time-tagged during acquisition creating "range time."

[0033] The Y-axis shows the Doppler frequency shift of the SAR data, the X-axis shows the slant range, and the operation of the RMC algorithm. If the spectral signature of the target exceeds the azimuth bandwidth defined by the pulse repetition frequency (PRF) (in FIG. 3 this is shown by the curve 310 representing the slant range across the defined bandwidth by the dotted line), aliasing causes the part of the spectrum outside the PRF to wrap into the useful bandwidth (line 320, dotted line). The curvature of the solid parts of lines 310 and 320 represents a constant distance to the target, but in reality the slant range may change during the integration time due to the movement of the SAR platform moving in the azimuth direction during the integration time. The slant range is the straight-line distance between the satellite and a point on the ground (e.g. point 350).

[0034] As a result, the range shift is given by: TIFF2025511077000002.tif15153

[0035] D Transfer factor: TIFF2025511077000003.tif16150

[0036] In formula 1 and formula 2, f D is the Doppler frequency, and R0 is the slant range at zero Doppler. R0 represents the shortest direct distance between the satellite and the target point 350. V ris the relative velocity between the antenna and the target, and λ is the wavelength.

[0037] Range migration compensation techniques can apply techniques known in the art to compensate for this change in slant range distance as the satellite moves. For example, dotted line 330 is generated after applying the range migration compensation algorithm. The main part of line 330 is straight instead of curved, indicating that the change in slant range distance has been corrected. However, it can be seen that it still contains parts of the spectrum outside the PRF. The resulting (after RMC) image 340 consists of the target signal 350 and two ambiguities 360 formed by the parts of the spectrum outside the bandwidth.

[0038] Other sources of ambiguity in SAR images are known in the art. In embodiments according to the present disclosure, ambiguities in SAR images can be detected and pixels in the images affected by these ambiguities can be identified using a novel approach based on phase derivatives as described below.

[0039] SAR data is the sum of the main signal from the imaged area and signals generated by ambiguities. TIFF2025511077000004.tif12153

[0040] where M is the unambiguous signal, A is the ambiguity signal, s and t are the azimuth time and range time, respectively. After azimuth compression, the main signal is: TIFF2025511077000005.tif14153

[0041] Here, p rg andp az is the sinc-like amplitude of the impulse response function in range and azimuth, and f dc is the Doppler centroid.

[0042] The phase of M consists of a linear term representing the residual phase due to the non-zero Doppler centroid, and a constant phase due to the target position: TIFF2025511077000006.tif17153

[0043] An additional phase term Φ appears in the ambiguity signal shown below. For range ambiguities, Φ depends only on azimuth time, while for azimuth ambiguities, it depends on both range and azimuth time: TIFF2025511077000007.tif16153

[0044] The derivative of phase with respect to range and azimuth for the primary and ambiguity signals, referred to here as the phase derivative (PDV), is: TIFF2025511077000008.tif47153

[0045] It can be seen that the derivatives of the phase of the main signal with respect to azimuth and range are constant and zero, respectively, while the derivatives of the phase of the ambiguity signal vary with respect to azimuth and range.

[0046] In the example ambiguity detection method described below, the phase is analyzed to detect all ambiguities and distinguish azimuth ambiguity signals from the main signal. The presence of pixels in the image with a phase derivative different from zero suggests the presence of an ambiguity, while pixels with a phase derivative close to zero can be assumed to contain only the main signal. A threshold operation on the phase derivative can be used to distinguish between ambiguity and non-ambiguity pixels.

[0047] Thus, a method according to an embodiment of the present invention comprises calculating at least one phase derivative for each pixel represented by the SAR data, determining a threshold for the phase derivative, and determining that pixels having a phase derivative equal to or greater than the threshold are ambiguous. The phase derivative represents the rate of change of phase from one pixel to another and can be calculated based on a subset of the data. For example, in the method described below, the image data is divided into tiles and the phase derivative is performed for each tile. In principle, the phase derivative can be calculated for any spatial direction. In the following, only range and azimuth are considered. Equations 7 and 8 are calculated on the data using PDV, so that the main signal can be separated from the ambiguity signal on a pixel-by-pixel basis. PDV can be used to detect ambiguities and, for example, test the effectiveness of ambiguity suppression techniques. In the following, we disclose a method to determine PDV for both range and azimuth to distinguish between ambiguity and non-ambiguity pixels. However, PDV for any variable is useful to determine which pixels are ambiguous. Thus, for example, pixels can be identified using PDV for range only or azimuth only.

[0048] PDV can be used to detect ambiguities in SAR images. However, other factors can disrupt the signal phase, resulting in false alarms that lead to improper detection of ambiguities. For example, the motion of the imaged target can contribute to the phase term, resulting in false detection of moving objects such as ships or moving surfaces such as the ocean surface in the presence of wind and waves as ambiguities. Phase offsets can also occur if the target is not properly focused during processing of the raw SAR data. PDV results can also be sensitive to IRF sidelobes of strong targets.

[0049] In the following, an algorithm is presented for detecting ambiguities using phase derivatives while mitigating some of the limitations mentioned above. This algorithm is named Phase Variation Analysis (PVA). The PVA algorithm uses PDV together with a combination of dedicated filtering to reduce the aforementioned limitations. For example, reduction of IRF side lobes can be performed by applying filtering to the image data before calculating the phase derivatives. In particular, this can be achieved by using a smoothing window (e.g., band-pass filtering) of the Doppler signal spectrum. The use of a smoothing window or filter can reduce the side lobes, but at the same time, it reduces the sensitivity to detect ambiguity signals localized at the boundaries of the spectrum. In some examples of the present invention, dedicated adaptive filtering is then used to reduce the side lobes while preserving the spectral frequencies where the ambiguities are located (e.g., adaptive weighting to retain the spectral parts containing the ambiguities).

[0050] The algorithm described below is performed on single-look data, with optional weighting of the PDV by a factor that depends on the difference between range looks. Thresholding can then be performed on the weighted phase derivative values ​​(see Equation 27 below).

[0051] The operation, including an example of a PVA algorithm, is shown in FIG. 4. Note that in this example, the algorithm is applied to a portion of the data. The complete image data is divided into tiles, and the algorithm is run independently for each tile. In this example, we assume that the starting data 400 is SAR Single Look Complex "SLC" data. SAR data is complex data that contains both amplitude and phase. However, it is noted that the use of phase derivatives to detect ambiguities is not necessarily limited to single look data.

[0052] The PVA algorithm is based on the following steps: First, the complex data comprising the main signal and ambiguities is given by: TIFF2025511077000009.tif22164

[0053] Here, P rg and P az is the sinusoidal amplitude of the impulse response function (IRF) in range and azimuth, R0 is the minimum range to the target, f dc is the Doppler centroid, and φ(s,t) is an additional phase term that depends on the range time and azimuth time.

[0054] In step 410, a two-dimensional Fast Fourier Transform (FFT) is performed on the azimuth time and range time to generate a two-dimensional Doppler spectrum of the SAR SLC data in frequency space. Each pixel of the SAR SLC data contains the magnitude and phase of both the main and ambiguity signals.

[0055] Next, in operation 420, the SAR data spectrum is shifted to the Doppler centroid. This has the effect of providing a symmetric Doppler spectrum with the Doppler centroid at its center: TIFF2025511077000010.tif12153

[0056] The topology of the data is as follows: TIFF2025511077000011.tif26153

[0057] In operation 430, the shifted SAR SLC data is windowed or (filtered) to remove side lobes as described above. The Doppler spectrum can be windowed using a classical smoothing window function such as Hamming, Hanning, Kaiser or other suitable function to generate a windowed Doppler spectrum. An inverse fast Fourier transform (IFFT) is then applied to the windowed Doppler spectrum in range and azimuth (IFFT2) to obtain a Doppler spectrum spread out in time space. For example, a Kaiser window can be used to window the Doppler spectrum to generate a windowed Doppler spectrum as follows: TIFF2025511077000012.tif12153

[0058] Here, K(f dc ,f r ) defines a Kaiser window in the two-dimensional frequency domain, and f dc and f r are the Doppler and range frequencies, respectively. This windowing reduces the side lobes of the compressed IRF, reducing interference between targets, while preserving the Doppler frequencies with high energy corresponding to ambiguity signals to maintain high sensitivity to other ambiguities. This filtering is done because strongly reflecting targets can cause false ambiguity detections.

[0059] In operation 440, a normalization filtering operation is applied to the data. This filtering normalizes the Doppler energy of the azimuth-dependent spectral signatures, increasing the power of the ambiguity signals relative to the main signal. This normalization reduces the power of properly focused main signals of highly backscattering targets, but does not reduce the power of improperly focused ambiguity signals. Thus, the power of the ambiguity signals is effectively increased, making them easier to detect and filter. This operation is represented by: TIFF2025511077000013.tif21153

[0060] In operation 450, the phase derivatives are applied in azimuth in the following operation: TIFF2025511077000014.tif33153

[0061] The resulting phase derivative is given by: TIFF2025511077000015.tif23153

[0062] The phase derivatives are then averaged using an average convolution filter in an additional operation not shown. The phase derivative in azimuth is zero for the main signal and different from zero for the ambiguities. This term is sensitive to many signals that depend on azimuth, such as azimuth ambiguities, multiple reflections (especially in urban environments), range ambiguities, targets moving very fast in range or azimuth direction, IRF side lobes of strong targets, surfaces with complex geometries that change with time (such as the ocean surface in the presence of waves) and targets composed of different scatterers with complex geometries such as slopes. In this case, the slant range when the Doppler R0 is zero can vary in the pixel domain during the synthetic aperture and generate an additional contribution to the phase: TIFF2025511077000016.tif26153

[0063] In this case, the phase derivative in azimuth is: TIFF2025511077000017.tif16153

[0064] In operation 460, the phase derivative with respect to range is calculated for the normalized SAR SLC data as follows: TIFF2025511077000018.tif33153

[0065] The phase derivative with respect to range is: TIFF2025511077000019.tif17153

[0066] As in the previous case for azimuth, the phase derivative in range is averaged using an average convolution filter, so that the phase derivative in range is zero for the main signal and different from zero for the ambiguous signal. This term is sensitive to range-dependent signals such as azimuth ambiguities and fast moving targets moving in range. However, the phase derivative in range is less accurate than the phase derivative in azimuth, since the range dependence of azimuth ambiguities is less significant than the azimuth dependence. Note that the order of operations 450 and 460 is not important and they can also be performed in parallel.

[0067] In this case, after calculating two phase derivatives, one for azimuth and one for range, and optionally performing one or more of the shifting, filtering, and normalization as described above, the threshold used to determine whether a pixel is an ambiguity can be determined from a combination of the phase derivatives, e.g., a product of the phase derivatives.

[0068] In parallel with the above sequence of operations, in step 470, two symmetric sub-apertures within the range are generated by the following operations: TIFF2025511077000020.tif39153

[0069] Where: TIFF2025511077000021.tif12153 and TIFF2025511077000022.tif12153 are filters that select the first 50% of the spectrum and the last 50% of the spectrum, respectively, allowing the generation of two non-overlapping subapertures. The filters for the subaperture generation are implemented in the time domain and correspond to finite impulse response "FIR" filters that allow filtering of the desired bands: TIFF2025511077000023.tif22153

[0070] where B is the signal bandwidth. TIFF2025511077000024.tif11153 is the desired bandwidth, w is the weighting window to be applied (with the aim of reducing the Gibbs phenomenon), f ci is the center frequency of the lookup. Then, we apply an FFT to calculate the filter in the frequency domain. In this case, the sub-aperture filtering is achieved by multiplying the data spectrum with the frequency domain filter.

[0071] Due to their wavelength dependence, azimuth ambiguities are not collocated in different range looks, and the azimuth separation between two half-band range looks corresponds to half the indicated spread.

[0072] In operation 480, a normalized difference in range looks is generated by taking the difference (equation) between the two symmetric range sub-apertures as follows: TIFF2025511077000025.tif13153

[0073] The look difference is then normalized to produce the normalized look difference shown below: TIFF2025511077000026.tif18153

[0074] Range look difference is moderately sensitive to azimuth ambiguity. Its main advantage is its low sensitivity to strong targets in urban environments. The use of normalized range look difference is primarily intended to reduce false positives of strong targets with phase gradients, e.g. in urban areas.

[0075] The normalized difference of the range looks is then calculated as the phase differential value PDV by multiplying them together in operation 490. az and PDV rg to generate the final PDV map or Azimuth Ambiguity-to-Signal Ratio (AASR) map for each pixel by: TIFF2025511077000027.tif13153

[0076] In step 500, an azimuth ambiguity mask 401 is generated from the ambiguity map, for example by a segmentation or binarization process using an appropriate threshold. In this way, the map and / or mask are generated corresponding to all or part of the original image data. For the mask, the threshold can be selected depending on the way the image data was acquired or the imaging mode. The mask can be overlaid on the original image and used to highlight pixels with ambiguities. The ambiguity mask also allows the calculation of the percentage of the image affected by ambiguous energy.

[0077] Note that in this example the algorithm is applied to a portion of the data: the complete image is divided into tiles and the algorithm is run for each tile independently. The generation of the ambiguity map can be used to automatically generate a quality indicator in terms of the occurrence of ambiguities. Furthermore, the algorithm can be used to identify areas of the image where ambiguity suppression is required. In this example where the data comprises single look data, each phase derivative value is weighted with a factor that depends on the difference between the range looks, and a threshold is applied to the weighted phase derivative values.

[0078] In this particular example, the map has values ​​in radians. The stronger the ambiguity, the higher the absolute value in radians. Note that the value in radians depends on the amount of ambiguous energy, but is not an exact measure of the signal to ambiguity ratio. In general, any of the methods described herein in which phase derivatives are calculated can be used to generate a map of values ​​that allows identification of pixels affected by ambiguities.

[0079] The PVA algorithm described above can be used to identify regions containing ambiguities in an image formed from SAR SLC data. In addition, the algorithm is used to determine whether further processing of the SAR SLC data is required to suppress the ambiguities. In addition, the PVA map generation algorithm can be used to automatically generate a quality indicator for the occurrence of ambiguities. For example, a map of ambiguities generated with an appropriate threshold can be used to determine the percentage of an image that is affected by the energy of the ambiguities, which may be used to evaluate the effectiveness of image suppression techniques, some examples of which are given below.

[0080] The example PVA algorithm has been tested and validated using simulated and real data. Below we show the performance metrics calculated in the simulation and the results obtained with real data. A dedicated SAR SLC data simulator was used to generate simulated ambiguities to validate the algorithm. The SAR SLC data simulator generates raw data of the target using the full antenna pattern radiation including the side lobes which generate the unwanted received energy. The simulated data of the side lobes are inserted into the real scenario following a processing operation: -SLC data is defocused in range and azimuth to produce raw data. The simulated raw data of the ambiguities are summed to the actual raw data according to the overlap and sum principle. -This data is focused in range and azimuth to obtain simulated ambiguities in the real data.

[0081] The locations and signal-to-clutter ratios are defined randomly using uniform distribution. The SAR data simulator is a useful tool to reproduce realistic scenarios on demand to generate specific targets required for algorithm testing and validation. 50 simulated first-order and 50 second-order ambiguities were used to calculate the performance metrics. In this example, only strip map acquisition mode was used to calculate the metrics.

[0082] The PVA algorithm allows for the detection of ambiguities and the generation of an ambiguity map. Its performance has been measured using simulated data. The detection of ambiguities is considered successful when a minimal cluster of n ambiguity pixels is detected as an ambiguity and exhibits a differential phase higher than a threshold T used to quantify the AASR in operation 500. In the present simulations, n=15 pixels and T=0.6 radians.

[0083] Figure 5 shows an example of an image 550 generated from SAR SLC data using the SAR simulator described above. A simulated ship 560 is embedded in the data along with two realistic ambiguities associated with the ship. The SAR SLC data was processed using phase variation analysis as per the previous example and successfully detected both the right ambiguity 570 and the left ambiguity 580, as shown by the dark and light dots. Since ships are very small targets when imaged from space, this was suitable for testing the ability of the PVA method to detect ambiguities using the PDV approach.

[0084] Table 1 shows the ambiguity detection performance of the PVA algorithm. Table 1 TIFF2025511077000028.tif37153

[0085] Table 1 shows the detection rate (%) of ambiguities for orders 1 and 2. TOT is the average detection rate of the ambiguity orders. The missing detection of the algorithm is related to the level of simulated ambiguity energy. If the energy of the simulated target SCR (signal to clutter ratio) in the real background is too low, the ambiguities may go unseen and the algorithm may fail. Figure 6 also shows the PDV map of the image (produced in act 500 of Figure 4) identifying locations where the PDV value differs from zero.

[0086] The PVA algorithm has also been tested on real images. Figures 6a and 6b show the results of ambiguity detection (AASR or PDV map) in strip map and spotlight images, respectively, where the dark areas represent the mask of ambiguities indicating the detected ambiguities. In Figure 6a, a bright urban area 600 appears three times in the image (once at the corrected position of 600 and two more times at positions 610 and 620). Ambiguity 610 is clearly incorrect as it is above the water surface. Ambiguity 620 is partly above the water surface and partly above the land surface. The ambiguities were detected by the PVA algorithm and an ambiguity mask was created to highlight them by making them darker. Color can also be used in the ambiguity mask to highlight the ambiguities detected in the SAR images.

[0087] The algorithm has obtained very good results in simulations and real data. The implemented algorithm solves the problem of ambiguity detection with a light and simple technique. The algorithm also works in cases where the ambiguity signature cannot be easily separated from the main signal. Some advantages of the PVA algorithm over other ambiguity detection methods are the processing speed and its independence from specific models such as antenna patterns. Moreover, it can be used in parallel processing, which further increases the processing speed. Dedicated spectral filtering reduces the sensitivity of the algorithm to urban multipath, which generates many false positives, and the difficulty of separating azimuth and range ambiguities in the presence of strong range ambiguities.

[0088] In the examples described thus far, we have improved methods for detecting ambiguities in SAR images. It would also be desirable to have improved methods for detecting and suppressing ambiguities in SAR images. As noted in the background, existing methods for detecting and suppressing ambiguities suffer from a number of limitations.

[0089] Next, an improved method for suppressing azimuth ambiguity is described that overcomes some of the problems of known methods. This suppression method can be used by itself or in combination with the detection method described above that uses phase derivatives. For example, it can be used in conjunction with the PVA detection method of the present disclosure to determine when the azimuth ambiguity detection and suppression method is required and to evaluate the effectiveness of the azimuth ambiguity detection and suppression method.

[0090] The suppression method may include, for each SAR image, applying an amplitude threshold to the Doppler spectrum to detect ambiguity energy in the spectrum, and replacing the amplitude values ​​of the detected ambiguity energy to generate a modified Doppler spectrum in which the ambiguity energy is suppressed. The modified Doppler spectrum may then be used to generate image data for the affected pixels in which the azimuth ambiguity is suppressed. An example of this suppression method is described below in the form of an algorithm.

[0091] The proposed algorithm for suppressing azimuth ambiguities in SAR SLC data is named Selective Doppler Frequency Suppression (SDFS). It is based on the detection of ambiguous azimuth and range-variable energy that can be separated from the main signal in the Doppler spectrum. The algorithm can be used to perform a single pass to suppress azimuth ambiguities in SAR data, or iteratively to detect and filter all ambiguity signatures in the Doppler spectrum. For example, after the suppression algorithm is applied to the SAR SLC data, the data is used to generate image data, and then an ambiguity detection method, such as the PVA method described above, is applied. The ambiguity detection method is used to determine the effectiveness of the suppression, and if necessary, the suppression can be repeated until an acceptable level of ambiguity suppression is achieved (e.g., to a level that meets a predetermined criterion). For example, iterations of the suppression method may be performed on previously azimuth-ambiguity suppressed image data to improve the suppression.

[0092] In general, the suppression method may be performed on SAR image data in the form of a received Doppler spectrum for each image, also referred to herein as a “signature.” The Doppler spectrum is made up of amplitude values ​​corresponding to each frequency in the spectrum.

[0093] A specific example of how this can be achieved is described below. Let the Doppler spectrum of each pixel of the main signal and the ambiguity before RMC be: TIFF2025511077000029.tif37153

[0094] Where: TIFF2025511077000030.tif16153 is the azimuth antenna pattern, and f R is the Doppler rate, TIFF2025511077000031.tif12153 is the Doppler frequency corresponding to the side lobe of the antenna pattern that generated the ambiguity, k ∈ Z. After RMC and azimuth compression, which is performed by multiplying it by an azimuth reference function, which is TIFF2025511077000032.tif21153, the data is: TIFF2025511077000033.tif41153

[0095] TIFF2025511077000034.tif18153 represents the residual amplitude signal that depends on range time and azimuth frequency after range migration compensation, which is performed to compensate for the energy coming from the main beam of the antenna pattern, and R res is the residual range migration of the ambiguity. This term indicates that the ambiguity spectral signature is range and azimuth dependent, and that after focusing, the ambiguity is spread over several range cells. The SDFS algorithm detects the energy or amplitude of the ambiguity by thresholding the Doppler spectrum. This threshold may be an adaptive threshold that depends on the statistical parameters of the Doppler spectrum. This threshold allows: TIFF2025511077000035.tif21153 The azimuth-dependent spectral signature term of the main signal represented by the term, and the range- and azimuth-dependent spectral signature term of the ambiguity defining the energy skew in the range-Doppler domain represented by the term, It can be separated from the TIFF2025511077000036.tif22153 item.

[0096] An example of the selective Doppler frequency suppression method is shown in Figure 7. The process starts with SAR SLC data at 700. In step 710, the spectrum of the SAR data is shifted to the Doppler centroid, which results in data with a symmetric Doppler spectrum centered on the Doppler centroid. TIFF2025511077000037.tif12153

[0097] The resulting Doppler spectrum is: TIFF2025511077000038.tif18153

[0098] In step 720, a normalization filter is applied to the image data. This filtering normalizes the Doppler energy of the azimuth-dependent spectral signatures and increases the power of the ambiguous signals relative to the main signal. This normalization reduces the power of the properly focused main signal of a highly backscattering target, but does not reduce the power of the improperly focused ambiguity signals. Thus, the power of the ambiguity signals is effectively increased, making them easier to detect. This operation is represented by: TIFF2025511077000039.tif20153

[0099] In step 730, an azimuth ambiguity map AASR(s,t) is generated. This may be generated using the PVA algorithm. Also, other detection algorithms may be used in place of the PVA algorithm to generate an AASR map or other map that indicates where ambiguities exist in the image data. The amount of ambiguity energy in the image is quantified by the condition AASR(s,t)>T. As an example, a strip map image has T=0.62 2 A threshold of T=0.7 was used for the spotlight image. 2 A threshold of is used. Thus, the threshold may depend on how the image data was generated.

[0100] The generation of the ambiguity map is an optional step used in testing the effectiveness of the suppression method and does not necessarily form part of the suppression method.

[0101] In step 740, the Doppler spectrum of the normalized data is calculated using a Fast Fourier Transform: TIFF2025511077000040.tif12153

[0102] The normalized Doppler spectrum has the energy of the main target normalized, and only the ambiguous energy part remains unchanged. This makes it easier to detect ambiguous signatures. The normalized Doppler spectrum is obtained by normalizing the data in the image domain (only amplitude) and then calculating the Doppler spectrum. This operation can improve the detection of ambiguous signals in scenes with strong targets. Suppression can then be performed.

[0103] Next, in steps 750, 751, 752, 753, the absolute value of the normalized Doppler spectrum is analyzed, e.g., using an adaptive threshold depending on the spectral statistical parameters, to obtain the formula TIFF2025511077000041.tif18153 In the flow of FIG. 7, the amplitude is extracted in step 750 and the Doppler spectrum is averaged in step 751 using an average convolution filter: TIFF2025511077000042.tif12153

[0104] Here, the absolute value of the normalized Doppler spectrum can be convolved with an averaging filter h. In step 752, a statistical parameter, e.g., S(f d The mean μ and standard deviation of t are used to calculate the adaptive threshold: T s = μ + k.σ, where k is an empirically calculated constant. This can be used to generate a mask for a subsequent thresholding operation on the amplitude data. Statistical parameters can be calculated for the Doppler spectrum in the range TIFF2025511077000043.tif17153 B D is the Doppler spectrum used in this process. Azimuth ambiguity in the normalized Doppler spectrum can be detected using the following condition: TIFF2025511077000044.tif12153

[0105] In step 753, a thresholding operation is performed in which values ​​above the threshold determined in operation 752 are eliminated.

[0106] In step 755, for each azimuth sequence, a fit of the |Z(:,t)| values ​​may be calculated using a polynomial fit that excludes the ambiguous amplitude values. In other words, the ambiguity amplitude values ​​from the normalized Doppler spectrum may be replaced by the fitted function. This operation suppresses the energy of the ambiguities, producing a suppressed amplitude, which is multiplied by the phase of the SAR SLC data to obtain a suppressed or filtered Doppler spectrum: TIFF2025511077000045.tif12153

[0107] In step 760, the suppressed Doppler spectrum is inverse fast Fourier transformed with respect to azimuth time to obtain the suppressed or filtered SAR SLC data as follows: TIFF2025511077000046.tif14153

[0108] In step 765, an azimuth ambiguity map AASR(s,t) is generated based on the filtered SLC data. As in step 730, the AASR map may be generated using the PVA algorithm. Also, other detection algorithms can be used instead of the PVA algorithm to generate the AASR map or other map that indicates where ambiguities exist in the image data, from which the percentage of the image that contains ambiguities can be calculated.

[0109] In step 770, the filtered AASR map generated in step 765 is compared to the AASR reference map generated in step 730. If the comparison meets a predetermined criterion (e.g., a difference between the two), the filtering is continued until the filtering no longer results in a decrease in the AASR calculated by the PVA detection algorithm, or until a maximum number of iterations N max 7. The filtered SLC data from step 760 is sent back to step 720 until TIFF2025511077000047.tif12153 A detection and suppression algorithm can be iteratively performed on the filtered SLC data. At this point, the filtered SLC data is passed to step 780, completing the azimuth suppression algorithm according to this embodiment. The filtered SLC data can be formed into an image (with ambiguity suppressed) or used in other ways.

[0110] As with step 730, the generation of the ambiguity map in step 765, together with the comparison operation in step 770, is an optional step used to test the validity of the suppression method and does not necessarily form part of the suppression method. If no comparison is desired, the filtered SLC generated in step 760 can be passed as is to step 780 at the end of the algorithm.

[0111] In summary, the criteria for deciding whether to perform an iteration may be comparative, such as improved ambiguity suppression compared to the previous iteration, or absolute, such as meeting an ambiguity threshold, or a combination of these criteria. Other suitable quality criteria are known to those skilled in the art.

[0112] It should be noted that in the suppression method described with reference to Figure 7, a thresholding or segmentation operation may be performed for each iteration of the suppression method, whereas in the stand-alone detection method described with reference to Figure 4, it may be performed only once. In the specific example of Figure 7, the PVA algorithm (and associated thresholding) is performed multiple times to generate the AASR reference map (step 765) and to generate the AASR filtered map (step 730).

[0113] To illustrate how the SDFS algorithm works, Figure 8 shows an image of a vessel 810, with ambiguities 820 which can be seen on the right hand side of the image. Figure 9a shows the Doppler spectrum of the image data of Figure 8, with the main target represented by the straight line in the middle 910, and the energy of the ambiguities represented by the diagonal line on the right 920. Figure 9b shows the Doppler spectrum after normalization, which has the effect of reducing the power of the main target. Now the energy of the ambiguities 920, some of which were previously masked by the main target, are more visible and more easily detected.

[0114] The SDFS algorithm has been tested and validated using simulated and real data. Below we present the performance metrics calculated in the simulations and the results obtained on real data.

[0115] The SDFS algorithm provides a lightweight and efficient method of ambiguity suppression and has been demonstrated to work well even when the ambiguities are weak. It can fail when strong targets are present, such as in urban environments, when the ambiguity energy is masked by the target energy. The PVA algorithm is used to calculate the performance metrics. Performance is calculated on the simulated datasets that the PVA algorithm detects as ambiguities; ambiguities not detected by the PVA algorithm do not contribute to the performance calculation.

[0116] Table 2 shows the performance of ambiguity suppression. The suppression rate in frequency corresponds to the signature energy of the suppressed ambiguity spectrum, the false positive suppression rate in frequency refers to the falsely suppressed non-ambiguity spectrum, and the suppression rate in image is the amount of ambiguity suppressed in the image. Table 2 TIFF2025511077000048.tif42153

[0117] The difference between the results for first and second order ambiguities is mainly due to two factors. On the one hand, first order ambiguities have a higher SCR than second order ambiguities because of the lower energy of the second order sidelobes. On the other hand, second order ambiguities have a larger residual range migration, which leads to a higher sensitivity to detect range-azimuth dependent signatures. The fraction of spectrum falsely suppressed as ambiguities is less than 1% in both cases.

[0118] FIG. 10 is a graph showing the percentage of suppression rate and the percentage of ambiguity coverage rate in frequency. A linear regression between suppression rate and ambiguity coverage is shown. A low ambiguity coverage rate means that there are very small ambiguities and / or very few ambiguities in the image, while a high ambiguity coverage rate means that there are more ambiguities or larger ambiguities in the image. As can be seen from FIG. 10, the main contribution of the suppression rate is the ambiguity coverage rate in the image. If the ambiguity coverage rate is too low, it is difficult to accurately detect and suppress ambiguities. However, if the ambiguity coverage rate is higher than 0.1% of the analysis area, the performance of the SDFS algorithm is improved. If the ambiguity coverage rate is higher than about 0.3%, the suppression rate approaches 100%.

[0119] The SDFS algorithm has also been tested on real images. Figure 11a shows a SAR image of a city with a river running through it, taken using strip map imaging mode. An ambiguity 1110 is clearly visible in the river. Figure 11b shows the same image after the SDFS algorithm has been run on the SAR SLC data used to generate the image. It can be seen that some of the ambiguities at 1120 have been suppressed. Iteratively re-running the algorithm can help to further suppress the ambiguities, up to the point where no further improvement can be achieved.

[0120] Similarly, Fig. 12a shows a scene captured using spotlight mode with a large, well-defined ambiguity located at 1210. Fig. 12b shows the result of ambiguity suppression: as can be seen at 1220, the ambiguity is suppressed very effectively by the SDFS algorithm.

[0121] The SDFS algorithm for detection and suppression of azimuth ambiguities has achieved very good results in simulations and real data. The implemented algorithm solves the problem of ambiguity suppression in a light and simple manner. Ambiguity suppression is performed with an algorithm that does not reduce the resolution, preserves the phase and works even when the ambiguity signature is not easily separable from the main signal. The advantages of the SDFS algorithm are the processing speed and independence to a specific model. Moreover, the algorithm is able to suppress signals that are not well separated from the main signal, and the phase is preserved after suppression. Its limitations are its sensitivity to the configuration parameters and the suppression of useful signals in some conditions.

[0122] The Phase Variation Analysis (PVA) method of ambiguity detection and the Selective Doppler Frequency Suppression (SDFS) method of detecting and suppressing azimuth ambiguities described in this disclosure can both be used independently. However, they can also be used together in a synergistic manner. As previously mentioned, the effectiveness of SDFS suppression may be determined by detecting ambiguities in azimuth ambiguity suppressed image data using the PVA method.

[0123] As mentioned above, in an alternative example of determining the effectiveness of suppression, the suppressed SAR SLC data can be compared to a threshold in step 770 of FIG. 7. If the suppressed SAR SLC data is below the AASR threshold, e.g., a total energy threshold for the entire image, no further processing takes place. However, if the suppressed SAR SLC data exceeds the AASR, the SDFS algorithm is repeated on the azimuth ambiguity suppressed image data until the suppressed SAR SLC data is below the AASR. Alternatively, the maximum number of iterations N max Operations 720-770 may be repeated until , is reached.

[0124] FIG. 13 illustrates how the detection and suppression methods described herein, such as PVA and SDFS, can be used synergistically together to improve the quality of a SAR image. Starting with SAR data in step 1301, a PVA algorithm can be used in step 1302 to detect whether there are ambiguities in the image. If the level of ambiguity is low enough to meet a predetermined criterion, as indicated by the determination in step 1303, an image can be formed in step 1304. For example, the predetermined criterion can be a total ambiguity energy threshold determined using one or more phase derivative values ​​described herein. If the level of ambiguity is higher than the predetermined criterion, an SDFS algorithm can be used in step 1305 to detect and suppress azimuth ambiguities in the Doppler spectrum.

[0125] Once this process is complete, the new image with ambiguities suppressed may be fed back into the PVA algorithm in step 1302 to determine if the criteria are met. This process repeats until the image criteria are met, no further improvement is detected, or a certain maximum number of iterations is reached (checking the last two conditions is not shown in FIG. 13).

[0126] 13 may also be implemented using a PVA algorithm in step 1302 and a different suppression algorithm in step 1305. Similarly, in another embodiment, the method may be implemented using a different ambiguity detection method in step 1302 and the SDFS algorithm for detecting and suppressing ambiguities in step 1305.

[0127] Processing of the SAR data to detect and / or suppress azimuth ambiguities may be performed within the satellite or at a ground station, depending on available computing power. Additionally, the operations described herein may be performed in a distributed computing system that may or may not include a computing system onboard the satellite. Thus, some embodiments of the invention described herein provide a computing system configured to operate the SAR according to any of the methods described herein, an example of which is shown in FIG.

[0128] In any of the embodiments of the present invention, the satellite may travel in low Earth orbit or be configured to travel in low Earth orbit.

[0129] A computing system that may be used in implementing any of the methods described herein is illustrated generally in FIG.

[0130] Computing system 1400 may include a single computing device or component, such as a laptop, tablet, desktop or other computing device, or the functionality of system 1400 may be distributed across multiple computing devices.

[0131] Computing system 1400 may include one or more controllers, such as controller 1405, which may be any suitable processor or computing or calculation device, such as a central processing unit processor (CPU), chip, or FPGA as described above, an operating system 1415, memory 1420 that stores executable code 1425, storage 1430, which may be external to the system or incorporated into memory 1420, one or more input devices 1435, and one or more output devices 1440.

[0132] One or more processors in one or more controllers, such as controller 1405, may be configured to perform any of the methods described herein. For example, one or more processors in controller 1405 may be connected to memory 1420 that stores software or instructions that, when executed by the one or more processors, cause the one or more processors to perform methods according to some embodiments of the invention. Controller 1405 or a central processing unit within controller 1405 may be configured to perform some of the operations illustrated in Figures 4, 7, and 8, for example, using instructions stored in memory 1425.

[0133] The SAR data may be received by a processor configured within the controller 1405, which controls the subsequent operations of Figures 4, 7, and 8 according to one or more algorithms that may be stored as part of the executable code 1425.

[0134] The input devices 1435 may be or may comprise a mouse, a keyboard, a touch screen or pad, or any suitable input device. It will be appreciated that any suitable number of input devices may be operably connected to the computing system 1400, as indicated by block 1435. The output devices 1440 may comprise one or more displays, speakers, and / or any other suitable output devices. It will be appreciated that any suitable number of output devices may be operably connected to the computing system 1400, as indicated by block 1440. The input and output devices may be used, for example, to allow a user to select information to be displayed, such as images and graphs as shown herein.

[0135] Any of the computing systems described herein may be combined into a single computing system with multiple functions. Similarly, the functionality of any computing system described herein may be distributed across multiple computing systems.

[0136] Some operations of the methods described herein may be performed by software, for example in a machine-readable form, for example in the form of a computer program including computer program code. Thus, some aspects of the present invention provide a medium readable by a computing system that, when implemented in a computing system, causes the system to perform some or all of the operations of any of the methods of the present invention. The computer-readable medium may be in a transitory or tangible (or non-transitory) form, such as a storage medium, such as a disk, thumb drive, memory card, etc. The software may be adapted to run on a parallel or serial processor such that the method steps can be performed in any suitable order or simultaneously.

[0137] This application recognizes that firmware and software are separately tradable commodities of value. It is designed to include software that operates or controls on "dumb" or standard hardware to perform a desired function. It is also intended to include software that "describes" or defines the configuration of hardware, such as HDL (Hardware Description Language) software for designing silicon chips or configuring general purpose programmable chips to perform a desired function.

[0138] The above embodiments are largely automated: in some instances, a user or operator of the system may manually direct some of the method actions to be performed.

[0139] In the described embodiment of the invention, the ground station may comprise a computing and / or electronic system such as that described with reference to FIG.

[0140] As used herein, the term "computing system" is used to refer to any device having processing capability capable of executing instructions. Those skilled in the art will appreciate that such processing capability may be incorporated into many different devices, and thus the term "computing system" includes PCs, servers, smart cell phones, personal digital assistants, and many other devices.

[0141] It should be understood that the benefits and advantages described above may relate to one embodiment or to several embodiments, and the embodiments are not limited to those that solve any or all of the described problems or that have any or all of the described benefits and advantages.

[0142] Any reference to an "item" or "piece" refers to one or more of those items unless otherwise specified. As used herein, the term "comprising" means including the specified method operations or actions or elements, but such operations or actions or elements do not constitute an exclusive list and the method or apparatus may include additional operations or actions or elements.

[0143] Further, to the extent the term "comprising" is used in the detailed description or claims, it is intended that the term have the same inclusiveness as the term "comprising," as the term "comprising" is interpreted as a transitional term within the claims.

[0144] The accompanying figures illustrate exemplary methodologies. Although the methodologies are shown and described as a series of operations performed in a particular order, it is understood and should be understood that the methodologies are not limited by the order. For example, some operations may occur in a different order than described herein. Also, some actions may occur simultaneously with other actions. Furthermore, in some cases, not all operations may be required to implement the methodologies described herein.

[0145] Although the ordering of operations or actions of the methods described herein is illustrative, operations or actions may be performed in any suitable order, or simultaneously where appropriate. Further, operations or actions may be added or substituted, or individual operations or actions may be deleted from any method, without departing from the scope of the subject matter described herein. Aspects of any of the above embodiments may be combined with aspects of any of the other embodiments described above to form further embodiments.

[0146] The above description of the preferred embodiment is given by way of example only, and it should be understood that various modifications may be made by those skilled in the art. The above comprises one example of one or more embodiments. Of course, it is not possible to describe every possible modification and alteration of the above device or method in order to describe the above aspects, but those skilled in the art will recognize that many further modifications and arrangements of the various aspects are possible. It is therefore intended that the described aspects include all such changes, modifications, and variations that fall within the scope of the appended claims.

[0147] Aspects of the present disclosure are set forth in the following numbered clauses: 1. A computer-implemented method for detecting ambiguities in Synthetic Aperture Radar (SAR) image data, the SAR data including amplitude and phase values ​​for each pixel in an image, the method comprising: calculating at least one phase derivative for each pixel represented by the SAR data with respect to a spatial direction; determining a threshold value for the phase derivative; determining that pixels having a phase derivative value that exceeds the threshold are ambiguities. 2. The method of claim 1, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to azimuth. 3. The method of any one of clauses 1 to 2, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range. 4. The method of claim 1, 2 or 3, wherein calculating at least one phase derivative value comprises calculating phase derivative values ​​with respect to range and azimuth, and the threshold value is determined from a combination of the phase derivative values. 5. The method of claim 4, wherein the threshold is determined from a product of the phase derivatives. 6. The method of any of the preceding clauses, wherein the calculation of the at least one phase derivative is performed on a subset of the image data. 7. The method of any preceding clause, comprising filtering the image data to reduce side lobes before calculating the one or more phase derivative values. 8. The method of claim 6, further comprising generating a Doppler spectrum of the image data, and wherein the filtering is performed on the Doppler spectrum. 9. The method of any preceding clause, wherein the data comprises single look data. 10. The method of claim 8, further comprising weighting the one or more phase derivative values ​​with a coefficient dependent on the difference between range looks, and the threshold is applied to the weighted phase derivative values. 11. The method of claim 9, wherein the difference between the range looks is calculated using the first and second sub-apertures. 12. The method of claim 10, wherein the first and second sub-apertures are symmetric. 13. The method of claim 12, wherein the first and second sub-apertures select the first 50% of the SAR SLC data and the last 50% of the SAR SLC data, respectively, and the first and second sub-apertures are symmetric. 14. The method of any preceding clause, comprising shifting the data to a Doppler centroid prior to calculating the at least one phase derivative value. 15. The method of any preceding clause, comprising generating an ambiguity map corresponding to the image based on the at least one phase differential value. 16. The method of any preceding clause, comprising segmenting the phase differential values ​​to generate a mask corresponding to the image. 17. The method of any preceding clause, comprising normalizing the data to attenuate spectral signatures that depend only on azimuth before calculating the at least one phase derivative value. 18. The method of claim 16, wherein segmenting the phase differential values ​​to generate the mask comprises using a threshold. 19. The method of any of the preceding clauses, performed on data compensated for range migration. 20. The method of any of the preceding clauses, performed on data processed to form a SAR image. 21. The method of any preceding clause, further comprising suppressing ambiguities in the Synthetic Aperture Radar (SAR) image data. 22. Suppressing ambiguities in the synthetic aperture radar (SAR) image data includes: generating a Doppler spectrum of the image data; applying an amplitude threshold to the Doppler spectrum of the image data to eliminate values ​​below the threshold due to ambiguity energy in the spectrum; replacing the excluded amplitude values ​​to generate a modified Doppler spectrum in which ambiguity energy is suppressed; and and generating image data with azimuth ambiguity suppressed using the modified Doppler spectrum. 23. A computing system comprising one or more processors configured to perform a method according to any of the preceding clauses. 24. A computer-readable medium comprising instructions which, when executed on a computing system, cause the computing system to perform the method of any one of clauses 1 to 22. 25. A computer-implemented method for suppressing ambiguities in synthetic aperture radar (SAR) image data, the data including a Doppler spectrum obtained from a received SAR signal; applying an amplitude threshold to the Doppler spectrum of the received SAR signal to eliminate values ​​below the threshold that are due to ambiguity energy in the spectrum; replacing the excluded amplitude values ​​to generate a modified Doppler spectrum in which ambiguity energy is suppressed; and and generating azimuth ambiguity suppressed image data using the modified Doppler spectrum. 26. The method of claim 25, wherein the amplitude threshold is an adaptive threshold based on statistical parameters of the Doppler spectrum. 27. The method of claim 25 or 26, wherein the Doppler spectrum is obtained by amplitude-only normalizing SAR data in the image domain and calculating the Doppler spectrum based on the normalized data. 28. The method of claim 27, comprising shifting the data to a Doppler centroid, and wherein the normalizing comprises normalizing the shifted SAR SLC data to attenuate spectral signatures that are only dependent on azimuth. 29. The method of any of the preceding clauses, wherein the replacement is performed using a fitting function. 30. A method according to any one of the preceding clauses, comprising detecting ambiguities in azimuth ambiguity suppressed image data and, if the amount of ambiguity does not meet a predetermined criterion, performing the steps of any of the preceding clauses on the azimuth ambiguity suppressed image data. 31. The method of claim 30, wherein the predetermined criteria comprises an ambiguity energy threshold. 32. The method of claim 30 or 31, wherein the predetermined criteria comprises an improvement in ambiguity suppression compared to the SLC data on which suppression was performed. 33. Detecting the ambiguity includes calculating at least one phase derivative for each pixel represented in the SAR data with respect to a spatial direction; determining a threshold value for the phase derivative; and determining that pixels having a phase derivative value exceeding the threshold are ambiguities. 34. The method of claim 33, wherein calculating at least one phase derivative comprises calculating a phase derivative with respect to azimuth. 35. The method of any one of clauses 33 to 34, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range. 36. The method of any one of clauses 33, 34 or 35, wherein calculating at least one phase derivative value comprises calculating phase derivative values ​​with respect to range and azimuth, and the threshold value is determined from a combination of the phase derivative values. 37. The method of claim 36, wherein the threshold is determined from a product of the phase derivatives. 38. A method according to any one of clauses 33 to 37, wherein the calculation of the at least one phase derivative is performed on a subset of the image data. 39. The method of any one of clauses 33-37, comprising filtering the image data to reduce side lobes before calculating the at least one phase derivative value. 40. The method of claim 38, comprising generating a Doppler spectrum of the image data, wherein the filtering is performed on the Doppler spectrum. 41. A method according to any one of clauses 33 to 40, comprising weighting the one or more phase derivative values ​​with a coefficient responsive to a difference between range looks, and the threshold is applied to the weighted phase derivative values. 42. The method of claim 41, wherein the difference between the range looks is calculated using the first and second sub-apertures. 43. The method of claim 42, wherein the first and second sub-apertures are symmetric. 44. The method of clause 43, wherein the first and second sub-apertures select the first 50% of the SAR SLC data and the last 50% of the SAR SLC data, respectively, and the first and second sub-apertures are symmetric. 45. A method according to any one of clauses 33 to 44, comprising shifting the data to the Doppler centroid prior to calculating the at least one phase derivative value. 46. ​​A method according to any one of clauses 33 to 44, comprising generating an ambiguity map corresponding to the image based on the at least one phase differential value. 47. A method according to any one of clauses 33 to 44, comprising segmenting the phase differential values ​​to generate a mask corresponding to the image. 48. A method according to any one of clauses 25 to 47, wherein generating azimuth ambiguity suppressed image data using the modified Doppler spectrum comprises multiplying the modified Doppler spectrum by the phase of the input data and inverse transforming the Doppler spectrum with respect to azimuth. 49. A computing system comprising one or more processors configured to carry out the method according to any one of clauses 25 to 48. 50. A computer-readable medium comprising instructions that, when executed on a computing system, cause the computing system to perform the method of any one of clauses 25 to 48.

Claims

1. 1. A computer-implemented method for detecting ambiguities in synthetic aperture radar (SAR) image data, the SAR data including amplitude and phase values ​​for each pixel in an image, the method comprising: calculating at least one phase derivative for each pixel represented by the SAR data with respect to a spatial direction; determining a threshold value for the phase derivative; determining that pixels having a phase derivative value above the threshold are ambiguous.

2. The method of claim 1 , wherein calculating at least one phase derivative comprises calculating a phase derivative with respect to azimuth.

3. The method of claim 1 , wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range.

4. The method of claim 1 , wherein calculating at least one phase derivative comprises calculating a phase derivative with respect to range and azimuth, and wherein the threshold is determined from a combination of phase derivatives.

5. The method of claim 4 , wherein the threshold is determined from a product of the phase derivatives.

6. The method of claim 1 , wherein the calculation of the at least one phase derivative is performed on a subset of the image data.

7. The method of claim 1 , comprising filtering the image data to reduce side lobes before calculating the one or more phase derivative values.

8. The method of claim 7 , comprising generating a Doppler spectrum of the image data in frequency space, and wherein the filtering is performed on the Doppler spectrum.

9. The method of claim 1 , wherein the data comprises single-look data.

10. 9. The method of claim 8, comprising weighting the one or more phase derivative values ​​with a factor dependent on a difference between range looks, and wherein the threshold is applied to the weighted phase derivative values.

11. The method of claim 10 , wherein the difference between the range looks is calculated using the first and second sub-apertures.

12. The method of claim 11 , wherein the first and second sub-apertures are symmetrical.

13. 13. The method of claim 12, wherein the first and second sub-apertures select the first 50% of the SAR SLC data and the last 50% of the SAR SLC data, respectively, and the first and second sub-apertures are symmetric.

14. The method of claim 1 , comprising segmenting the phase derivatives to generate a mask corresponding to the image.

15. The method of claim 14 , wherein segmenting the phase derivative values ​​to generate the mask comprises using a threshold.

16. The method of claim 1 performed on data compensated for range migration.

17. The method of claim 1 , further comprising suppressing ambiguities in the synthetic aperture radar (SAR) image data.

18. Suppressing ambiguities in the synthetic aperture radar (SAR) image data includes: generating a Doppler spectrum of the image data and applying an amplitude threshold to the Doppler spectrum of the image data to remove values ​​below the threshold due to ambiguity energy in the spectrum; replacing the excluded amplitude values ​​to generate a modified Doppler spectrum in which ambiguity energy is suppressed; and and generating azimuth ambiguity suppressed image data using the modified Doppler spectrum.

19. A computing system comprising one or more processors configured to perform a method according to any one of claims 1 to 18.

20. A computer readable medium comprising instructions that, when executed on a computing system, cause the computing system to perform the method of any one of claims 1 to 18.

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