Detection and Suppression of Ambiguity in Synthetic Aperture Radar Data and Images

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 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 pixels having a phase derivative value exceeding the threshold are ambiguities. A method of suppressing azimuth ambiguities in Synthetic Aperture Radar (SAR) single-look complex 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 the azimuth ambiguities are suppressed.

Description

Technical Field

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

Background Art

[0002] Synthetic Aperture Radar (SAR) can be used to image an area on the Earth, also known as the target area, by transmitting radar beams and recording the return echoes, i.e., the return radar energy, from those transmitted beams. The SAR system can be installed not only on an airborne platform such as an aircraft but also on a satellite operated from space. Various modes of operating SAR (scanning synthetic aperture radar), such as stripmap, spotlight, and ScanSAR (Earth observation by progressive scan SAR), can be used.

[0003] SAR is typically mounted on a moving platform such as a satellite and thus moves relative to the target on the Earth being imaged. As the platform moves, the position of the SAR antenna relative to the target changes over time, and the frequency of the received signal changes due to the Doppler effect. Therefore, the received echo contains a frequency spectrum.

[0004] Typically, an SAR system transmits high-frequency radiation in pulses and records 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 ambiguity in the data and the image. These ambiguities can occur because it is difficult to direct the radar beam entirely towards only the target imaging area. In practice, the radar beam has side lobes that illuminate areas outside the desired imaging area, and the radar echoes from these "ambiguous" areas will mix with the reflections from the "non-ambiguous" areas. The echoes from these unwanted areas may be from previous and subsequent transmitted pulses and may have ambiguities in both the azimuth and range directions. Due to the ambiguities, ground objects and features may be displayed at multiple positions in the image, and only one of them will be the true position. The amplitude of some of these ambiguous signals may be smaller than that of the non-ambiguous signals, but they can cause confusion in the image and degrade the image quality. Therefore, it is desirable to be able to detect and suppress the ambiguities in the SAR image.

[0005] First, one approach to reducing ambiguity is to design the SAR system by appropriately selecting the antenna size and the pulse repetition frequency (PRF). For example, at 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 the PRF reduces the occurrence of azimuth ambiguity. However, an increase in the PRF also causes an increase in range ambiguity. Therefore, there is a trade-off in the design, and it is necessary to balance the two types of ambiguity. Unfortunately, in some cases, the appropriate design may not match the requirements of the latest SAR platforms such as small satellites. The new SAR satellite constellations carry smaller antennas compared to the previous generation, and the conventional methods for suppressing ambiguity are restricted. Due to the physical properties and trade-offs of SAR, especially in the case of small SAR satellites, it is impossible to design the SAR system to completely eliminate ambiguity. Therefore, other approaches for detecting and suppressing ambiguity have been developed.

[0006] One approach is to detect and remove ambiguity through post-processing of the SAR data. For example, several algorithms have been proposed for estimating the local azimuth ambiguity-to-signal ratio (AASR). However, existing algorithms for ambiguity detection and suppression cannot suppress large ambiguities and may cause a decrease in 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 according to the antenna pattern. These proposed techniques use filters constructed based on knowledge of the antenna design to identify the ambiguity spectrum and enable the detection and selective suppression of ambiguity. The limitations of these suppression methods are their low sensitivity to weak and small ambiguities and their specialization only to specific antenna designs.

[0007] Some embodiments of the present invention described below solve some of these problems. However, the present invention is not limited to solving these problems, and some embodiments of the present invention solve other problems.

Summary of the Invention

[0008] This abstract is provided to introduce, in a simplified form, a selection of concepts that are further described in the following detailed description. This abstract is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to determine the scope of the claimed subject matter.

[0009] In the following, a method for detecting ambiguity in synthetic aperture radar (SAR) image data and a method for suppressing ambiguity are provided. The detection method and the suppression method 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 (a known method or a method described below). Conversely, the suppression method can be used to improve the quality of an image after ambiguity has been detected (by either a new method or a known method described herein).

[0010] Accordingly, in one aspect, a method for detecting ambiguity in synthetic aperture radar (SAR) image data is provided below, where the SAR data includes amplitude and phase values for each pixel in the image, and the method includes calculating at least one phase derivative value for each pixel represented by the SAR data in the spatial direction, determining a threshold value for the phase derivative value, and determining that a pixel having a phase derivative value exceeding the threshold value is an ambiguity.

[0011] In another aspect, a method for suppressing azimuth ambiguity in synthetic aperture radar "SAR" single look complex image data is provided, 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 a threshold due to ambiguity energy in the spectrum, replacing the excluded amplitude values to generate a modified Doppler spectrum with suppressed ambiguity energy, and using the modified Doppler spectrum to generate image data with suppressed azimuth ambiguity.

[0012] Also, in an embodiment of the present invention, a computer-readable medium including instructions in the form of an algorithm for causing a computing system forming part of a satellite operating system to execute any of the methods described herein is provided.

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

Brief Description of the Drawings

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Best Mode for Carrying Out the Invention

[0015] Embodiments of the present invention are described below merely as examples. These examples represent the best mode known to the applicant for practicing the invention, but are not the only way to achieve it.

[0016] Some embodiments of the present invention provide systems and methods for processing SAR image data to detect and / or suppress ambiguity. For this purpose, the SAR may be mounted on a platform traveling relative to the Earth's surface. For example, the SAR is generally mounted on an artificial satellite. However, the methods and systems described herein are not limited to data obtained from space, and may be performed on data obtained using an aircraft or any other suitable platform.

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

[0018] As is known to those skilled in the art, the transmission mode in which a pulse of radiation is directed towards the Earth's surface and the reception mode in which the radiation reflected from the Earth's surface is received are periodically alternated.

[0019] As is known in the art, to create a SAR image, continuous pulses of radio waves are transmitted to "illuminate" a target, and the echoes of each pulse are received and recorded. Pulses can be transmitted and the echoes received by a single beamforming antenna. When SAR is mounted on a moving platform such as a satellite and moves relative to a target, the position of the antenna relative to the target changes over time, and the frequency of the received signal changes due to the Doppler effect. By signal processing of the continuously recorded radar echoes, recordings from multiple antenna positions can be combined to form a synthetic antenna aperture and create a higher-resolution image.

[0020] The area currently captured by SAR is known as the footprint. The direction along the flight direction of SAR is usually called azimuth or along-track. The direction across the flight direction is usually called range, elevation, or cross-track. The direction opposite to the flight direction corresponds to the backward azimuth.

[0021] The ambiguity in a SAR image is an aliasing effect caused by the pulsed operation of the radar system. The effect of ambiguity creates artifacts in the image that do not accurately represent the ground being imaged. For example, the image may contain features that appear multiple times. As an example of ambiguity, after a densely built-up urban area is displayed in the correct position, artifacts of that portion may also be displayed in another location within the image, for example, over smooth water. This "ambiguity" degrades the quality of the SAR image.

[0022] In a spaceborne system, two types of ambiguities can be generated: azimuth ambiguity or Doppler ambiguity related to the movement of satellites in the azimuth direction, and range ambiguity related to the time delay of echoes from different ranges in the range or cross-track direction of a side-looking SAR satellite. The ambiguities can be reduced by carefully designing the antenna, such as carefully selecting the antenna size and pulse repetition frequency (PRF). For example, increasing the PRF tends to reduce the occurrence of azimuth ambiguity. However, increasing the PRF also has the drawback of increasing the occurrence of range ambiguity. Therefore, it is necessary to strike a balance in designing the system so as to reduce azimuth ambiguity while not generating too much range ambiguity, and it is impossible to completely correct both types of ambiguities only by the design of the SAR system. This is especially true for the latest satellites that require miniaturization of the antenna. In fact, the design constraints of miniaturized and lightweight satellites tend to increase the occurrence of azimuth ambiguity, for example. The ability to detect ambiguities is important for accessing the quality of SAR images. Also, detecting and suppressing ambiguities is desirable for removing ambiguities from the images.

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

[0024] Embodiments according to the present disclosure also teach a novel computer-implemented method for suppressing azimuth ambiguity. In one example, selective Doppler frequency suppression (SDFS) is used to selectively filter ambiguity frequencies in the Doppler spectrum to detect and suppress azimuth ambiguity and to detect an ambiguous spectrum signal having a coupled dependence on azimuth and range.

[0025] One cause of ambiguity in SAR images is related to the pattern of the SAR antenna beam. FIG. 2 shows an example of how such ambiguity occurs. Satellite 100 is shown moving along flight trajectory 200 that defines the azimuth direction. The imaging target area direction orthogonal to flight trajectory 200 is the range direction or the cross-track direction. The satellite is operating in a “side-scan” mode, and the area to be imaged is not directly below the satellite but to the side of the satellite's flight path. This is common for SAR satellites because bright returns from objects in the directly below area, i.e., the specular reflection from objects directly below the satellite, make it difficult to form an image of that area. The hatched area 201 represents the area to be imaged (the strip).

[0026] FIG. 2 shows an example of a satellite 100 operating in a classical strip map mode, in which, as the satellite moves along its orbit, the SAR beam is swept along one swath (represented by the hatched area 201) along the earth's surface. In this mode, the SAR beam typically moves in the azimuth direction at the same speed as the SAR platform. The time during which the radar beam collects data while sweeping forward is called the integration time. During the integration time, many pulses may be recorded. Embodiments according to the present disclosure can be equally applied to any SAR mode, including spotlight mode, ScanSAR (scanning synthetic aperture radar) mode, TOPSAR (earth observation by progressive scan SAR) mode, and the like. As an example, the satellite 100 irradiates a radar beam 210 so as to be orthogonal to the traveling direction 200 of the satellite, records the radar echo from point 203, and determines information about the ground surface at that point. This information is formed into an image of the ground surface. However, since it is difficult to form a completely directed radar beam, typically there are sidelobes with respect to the main beam represented in the azimuth direction by lines 211 and 212, whereby echoes from points 204 and 205 may be mixed into the echo from point 203. As a result, features (e.g., buildings) located at point 204 may be displayed in the SAR images of both points 203 and 204, resulting in azimuth ambiguity in the signal.

[0027] Similarly, range ambiguities can be caused by echoes returning from side lobes in the range direction. An example is represented by line 222, which is mixed with the return from the imaging target area 201 (without ambiguity) due to the difference in slant range distance. The hatched area 220 represents an area outside the imaging target area 201 and may be referred to as the range ambiguity area. The slant range distance to the point being imaged is represented by line 210. The slant range distance to the point 221 within the ambiguity area is represented by line 222. The slant range distances of the two points are different, and a time delay occurs due to the difference in the time it takes for 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 the subsequent pulse from the main lobe, resulting in range ambiguity. Although only one range ambiguity area 220 is shown as an example, in reality, there are additional areas (e.g., closer to the satellite) corresponding to various side lobes of the antenna beam in the range direction, and all of these contribute to the occurrence of range ambiguity.

[0028] Figure 2 shows how ambiguities are formed as a result of the antenna beam pattern. However, as will be explained below, other ambiguities are also possible. Due to ambiguities, an image may contain ambiguous pixels and non-ambiguous pixels because a certain feature "appears" in multiple locations. Hereinafter, the term "ambiguous pixel" refers to a pixel containing signal data that may be from multiple locations.

[0029] The embodiments described in this disclosure provide an improved method for detecting ambiguities in SAR data and may include identifying regions having ambiguities in the SAR image. In other embodiments, an improved method is described for detecting and suppressing ambiguities in SAR data to enable generation of a high-quality SAR image with fewer or reduced ambiguities. Referring again to FIG. 1, this data processing related to these embodiments may be performed at the ground station 195, or at another location on Earth communicating with the ground station 195, for example. Alternatively, if sufficient processing power is available, some or all of the operations described herein may be performed on a mounted computing system. In data processing, all pulses transmitted during the integration time may be used to focus the data in the azimuth direction.

[0030] As also described elsewhere, the methods described herein are particularly suitable for implementation in connection with SAR mounted on a satellite, but are not exclusively so.

[0031] In addition to the ambiguities caused by the SAR antenna beam pattern, other factors that cause ambiguities in the SAR image are related to the processing of the SAR data. For example, ambiguities may occur due to errors in the range migration correction (RMC) algorithm or Doppler centroid estimation. Unlike the cause of the first ambiguity due to the physical characteristics of the antenna beam, these ambiguities occur due to the processing required to convert the raw SAR data into an image.

[0032] Figure 3 shows how azimuth ambiguity occurs as a result of the range migration correction algorithm executed on SAR data in order to account for the difference in distance to the target due to the movement of the SAR platform. The azimuth signal corresponds to signals at different points along the direction of travel of the satellite (azimuth direction), and since these signals are time-tagged during acquisition, it is necessary to note that an "azimuth time" is generated. The range signal corresponds to signals at different points that are substantially perpendicular to the direction of travel (range direction), and these signals are time-tagged during acquisition to create a "range time".

[0033] The Y-axis represents the Doppler frequency shift of the SAR data, the X-axis represents the slant range, and each operation of the RMC algorithm. When the spectral signature of the target exceeds the azimuth bandwidth defined by the pulse repetition frequency (PRF) (in Figure 3, this is shown by curve 310 representing the slant range crossing the bandwidth defined by the dotted line), the portion of the spectrum outside the PRF is wrapped into the useful bandwidth by aliasing (lines 320, dotted lines). The curvature of the solid line portions of lines 310 and 320 represents that the distance to the target is constant, but in reality, due to the movement of the SAR platform moving in the azimuth direction during the integration time, the slant range may change 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 migration is given by the following equation: TIFF0007700388000001.tif10158

[0035] D movement coefficient: TIFF0007700388000002.tif13158

[0036] In Equation 1 and Equation 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 speed 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 the slant range distance due to the movement of the satellite. For example, the dotted line 330 is generated after applying a range migration compensation algorithm. The main part of line 330 is a straight line rather than a curve, indicating that the change in the slant range distance has been corrected. However, it can be seen that it still contains the part of the spectrum outside the PRF. As a result (after RMC), the image 340 consists of the target signal 350 and two ambiguities 360 formed by the spectral parts outside the bandwidth.

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

[0039] SAR data is the sum of the main signal from the imaged area and the signal generated by the ambiguity. TIFF0007700388000003.tif9158

[0040] Here, M is the signal without ambiguity, A is the ambiguity signal, and s and t are the azimuth time and range time respectively. The main signal after azimuth compression is as follows: TIFF0007700388000004.tif12158

[0041] Here, p rg and p az are the amplitudes like sinc of the impulse response functions in range and azimuth, and f dc is the Doppler centroid.

[0042] The phase of M is composed of a linear term representing the residual phase due to a non-zero Doppler centroid and a constant phase due to the target position: TIFF0007700388000005.tif12158

[0043] In the ambiguity signals shown below, an additional phase term Φ appears. In the case of range ambiguity, Φ depends only on the azimuth time, and in the case of azimuth ambiguity, it depends on both the range time and the azimuth time: TIFF0007700388000006.tif12158

[0044] The differential values of the phase with respect to range and azimuth of the main signal and the ambiguity signal (here called the phase differential value (PDV)) are as follows: TIFF0007700388000007.tif39158

[0045] It can be seen that the differentials of the phase of the main signal with respect to azimuth and range are constant and zero respectively, while the differential of the phase of the ambiguity signal changes with respect to azimuth and range. In the example of the ambiguity detection method described below, in order to detect all ambiguities and distinguish the azimuth ambiguity signal from the main signal, the phase is analyzed. If there are pixels with a phase differential different from zero in the image, it suggests the presence of an ambiguity, and pixels with a phase differential close to zero can be assumed to contain only the main signal. A threshold operation on the phase differential can be used to distinguish between ambiguity pixels and non-ambiguity pixels.

[0046] Thus, the method according to an embodiment of the present invention includes calculating at least one phase derivative value for each pixel represented by SAR data, determining a threshold value for the phase derivative value, and determining that a pixel having a phase derivative value greater than or equal to the threshold value is an ambiguity. The phase derivative value represents the rate of change of phase from one pixel to another pixel 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 value is executed for each tile. In principle, the phase derivative value can be calculated with respect to any spatial direction. Hereinafter, only range and azimuth are considered.

[0047] Since Equations 7 and 8 are calculated on the data using PDV, the main signal can be separated from the ambiguity signal for each pixel. PDV can be used to detect ambiguities and, for example, to test the effectiveness of ambiguity suppression techniques. Hereinafter, a method for determining PDV with respect to both range and azimuth is disclosed to distinguish between ambiguous pixels and non-ambiguous pixels. However, any PDV with respect to a variable is useful for determining which pixels are ambiguous. Thus, for example, pixels can be identified using PDV with respect to only range or only azimuth.

[0048] PDV can be used to detect ambiguities in SAR images. However, the signal phase may be disturbed by other factors, resulting in false alarms that lead to inappropriate detection of ambiguities. For example, the movement of the target being imaged contributes to the phase term, and as a result, a moving object such as a ship or a moving surface such as a sea surface with wind and waves may be misdetected as an ambiguity. Also, if the target is not properly focused during the processing of the raw SAR data, a phase offset may occur. The results of PDV can also be sensitive to the IRF side lobes of strong targets.

[0049] The following shows an algorithm for detecting ambiguities using phase differential values while reducing some of the above limitations. This algorithm is named Phase Variation Analysis (PVA). The PVA algorithm uses PDV along with a combination of dedicated filtering to reduce the aforementioned limitations. For example, the reduction of IRF side lobes can be achieved by applying filtering to the image data before calculating the phase differential values. In particular, this can be accomplished 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 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 side lobes while preserving the spectral frequencies where ambiguities are located (e.g., adaptive weighting to retain the spectral portion containing ambiguities).

[0050] The algorithm described below is executed on single-look data and has an optional weighting of PDV by a coefficient that depends on the difference between range looks. Thresholding can then be performed on the weighted phase differential values. (See Equation 27 below)

[0051] An example of the operations that make up the 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 executed independently for each tile. In this example, it is assumed that the starting data 400 is SAR single-look complex "SLC" data. SAR data is complex data that includes both amplitude and phase. However, note that the use of phase differential values for detecting ambiguities is not necessarily limited to single-look data.

[0052] The PVA algorithm is based on the following steps. First, the complex data with the main signal and ambiguities is given by: TIFF0007700388000008.tif12158

[0053] Here, P rg and P az are the sine wave amplitudes 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 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 the frequency domain. Each pixel of the SAR SLC data contains both the magnitude and phase of both the main signal and the ambiguity signal.

[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: TIFF0007700388000009.tif9158

[0056] The phase of the data is as follows: TIFF0007700388000010.tif12158

[0057] In operation 430, the shifted SAR SLC data is windowed or (filtered) to remove sidelobes as described above. The Doppler spectrum can be windowed using a classical smoothing window function such as a Hamming, Hanning, Kaiser, or other appropriate function to generate a windowed Doppler spectrum. Then, an inverse fast Fourier transform (IFFT) is applied to the windowed Doppler spectrum with respect to range and azimuth (IFFT2) to obtain the Doppler spectrum in the time domain. For example, using a Kaiser window to window the Doppler spectrum, a windowed Doppler spectrum can be generated as follows: windowing in The Doppler spectrum is windowed using a Kaiser window, and a windowed Doppler spectrum can be generated as follows: TIFF0007700388000011.tif11158

[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 frequency and the range frequency, respectively. By this windowing, while reducing the sidelobes of the compressed IRF and reducing the interference between targets, it is possible to maintain the Doppler frequency with high energy corresponding to the ambiguity signal in order to maintain high sensitivity to other ambiguities. This filtering is performed because strongly reflecting targets may cause false detection of ambiguities.

[0059] In operation 440, a normalization filtering operation is applied to the data. This filtering normalizes the Doppler energy of the azimuth-dependent spectral signature and increases the power of the ambiguity signal relative to the main signal. By this normalization, the power of the properly focused main signal of the highly backscattering target decreases, but the improperly focused ambiguity signal does not decrease. Therefore, the power of the ambiguity signal effectively increases, facilitating detection and filtering. This operation is represented as follows: TIFF0007700388000012.tif12158

[0060] In operation 450, the phase differential value is applied in azimuth by the following operation: TIFF0007700388000013.tif21158

[0061] The resulting phase differential value is given by the following equation: TIFF0007700388000014.tif12158

[0062] Thereafter, the phase derivative values are averaged using an averaging 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 ambiguity. This term is sensitive to many signals that depend on azimuth, such as azimuth ambiguity, ambiguity of the multiple reflection (especially in urban environments) distance, targets moving very fast in the range or azimuth direction, IRF side lobes of strong targets, surfaces with complex geometric shapes that change with time (such as the sea surface when there are waves), and targets composed of different scatterers with complex geometric shapes such as slopes. In this case, the Doppler R0 The slant range when the Doppler is zero changes within the pixel area in the synthetic aperture and can generate an additional contribution to the phase: TIFF0007700388000015.tif21158

[0063] In this case, the phase derivative value in azimuth is as follows: TIFF0007700388000016.tif13158

[0064] In operation 460, the phase derivative value with respect to range is calculated as follows for the normalized SAR SLC data: TIFF0007700388000017.tif21158

[0065] The phase derivative value with respect to range is as follows: TIFF0007700388000018.tif12158

[0066] Similar to the previous case regarding azimuth, the phase differential values in range are averaged using an average convolution filter, and the phase differential values in range are zero for the main signal and different from zero for the ambiguous signal. This term is sensitive to range-dependent signals such as azimuth ambiguity and fast-moving targets moving within the range. However, since the range dependence of azimuth ambiguity is less important than the azimuth dependence, the phase differential in range is less accurate than the phase differential in azimuth. Note that the order of operations 450 and 460 is not important and they can also be executed in parallel. In this case, after calculating two phase differential values for azimuth and range respectively, optionally, after performing one or more of shifting, filtering, and normalization as described above, the threshold used to determine whether a pixel is ambiguous can be determined from a combination of phase differential values, for example, the product of phase differential values.

[0067] In parallel with the above series of operations, in step 470, two symmetric sub-apertures within the range are generated by the following operations: TIFF0007700388000019.tif21158

[0068] Here, F subapertur and F サブアパーチャ2 are filters that select the first 50% and the last 50% of the spectrum respectively. This enables the generation of two non-overlapping sub-apertures. The filter for sub-aperture generation is implemented in the time domain and corresponds to a finite impulse response "FIR" filter that enables filtering of the desired band: TIFF0007700388000020.tif11158

[0069] Here, B is the signal band, B look is the desired band, w is the weight window to be applied (for the purpose of reducing the Gibbs phenomenon), f ciis the center frequency of the look. Next, apply the FFT to calculate the filter in the frequency domain. In this case, the filtering of the sub-aperture is realized by multiplying the data spectrum by the filter in the frequency domain.

[0070] Due to its wavelength dependence, the azimuth ambiguity is not placed at the same position for different range looks, and the azimuth separation between two half-band range looks corresponds to half of the indicated spread.

[0071] In operation 480, the normalized difference of the range look is generated by taking the difference (equation) between two symmetric range sub-apertures as follows: TIFF0007700388000021.tif11158

[0072] Then, the look difference is normalized, and the normalized look difference is generated as shown below: TIFF0007700388000022.tif12158

[0073] The range look difference is moderately sensitive to azimuth ambiguity. The main advantage is its low sensitivity to strong targets in the urban environment. The use of the normalized range look difference is mainly aimed at reducing false detections of strong targets with phase gradients, such as in urban areas.

[0074] Next, the normalized difference of the range look is used to weight the phase differential values PDV az and PDV rg by multiplying them together in operation 490, and generating the final PDV map or a map of the azimuth ambiguity to signal ratio (AASR) for each pixel in the following operations: TIFF0007700388000023.tif10158

[0075] In step 500, an azimuth ambiguity mask 401 is generated from the ambiguity map, for example, by segmentation or binarization using an appropriate threshold. In this way, one or both of the map and the mask are generated corresponding to all or part of the original image data. For the mask, the threshold can be selected according to the method by which the image data was acquired or the imaging mode. The mask can be used to emphasize ambiguous pixels by overlaying it on the original image. The ambiguity mask also enables the calculation of the percentage of the image affected by ambiguity energy.

[0076] Note that in this example, the algorithm is applied to parts of the data. The complete image is split into tiles and the algorithm is executed independently for each tile. The generation of the ambiguity map can be used to automatically generate quality metrics from the perspective of the occurrence of ambiguity. Furthermore, the algorithm can be used to identify areas of the image where ambiguity suppression is required.

[0077] In this example where the data includes single look data, each phase derivative value is weighted by a coefficient according to the difference between range looks, and the 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 ambiguity energy but is not an exact measure of the signal-to-ambiguity ratio. Generally, a map of values can be generated using any of the methods described here where phase derivative values are calculated, enabling the identification of pixels affected by ambiguity.

[0079] The above PVA algorithm can be used to identify regions containing ambiguity in images formed from SAR SLC data. Further, this algorithm is used to determine whether further processing of the SAR SLC data is necessary to suppress ambiguity. Additionally, a PVA map generation algorithm can be used to automatically generate quality metrics related to the occurrence of ambiguity. For example, an ambiguity map generated with an appropriate threshold can be used to determine the proportion of the image affected by the energy of the ambiguity and may be used to evaluate the effectiveness of image suppression techniques, some examples of which are given below.

[0080] Examples of the PVA algorithm have been tested and verified using simulation data and real data. Below, the performance metrics calculated in simulation and the results obtained from real data are shown. A dedicated SAR SLC data simulator was used for the purpose of generating simulated ambiguity to verify the algorithm. The SAR SLC data simulator generates raw data of the target using the full antenna pattern radiation including sidelobes that generate unwanted received energy. The simulated data of the sidelobes is inserted into the actual scenario following the processing operation: - The SLC data is defocused in range and azimuth to generate raw data. - The simulated raw data of the ambiguity is added to the actual raw data according to the principle of overlap and sum. - This data is focused in range and azimuth to obtain the ambiguity simulated with real data.

[0081] The position and signal-to-clutter ratio are randomly defined using a uniform distribution. The SAR data simulator is a useful tool for reproducing realistic on-demand scenarios for generating specific targets required for testing and validating algorithms. Simulations of 50 first-order and 50 second-order ambiguities were used in the calculation of the performance metrics. In this example, only the strip map acquisition mode was used in the calculation of the metrics.

[0082] The PVA algorithm enables the detection of ambiguities and the generation of ambiguity maps. Its performance has been measured using simulation data. The detection of an ambiguity is considered successful when the minimum cluster of n ambiguity pixels is detected as an ambiguity and shows a differential phase higher than the threshold T used to quantify the AASR in operation 500. In this simulation, 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. The data is embedded with a simulated ship 560 along with two realistic ambiguities related to ships. The SAR SLC data was processed using phase fluctuation analysis according to the example described above and was successful in detecting both the right ambiguity 570 and the left ambiguity 580 as shown by the dark and bright points. Since ships are very small targets when imaging 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 TIFF0007700388000024.tif37153

[0085] Table 1 shows the ambiguity detection rates (%) for orders 1 and 2. TOT is the average value of the ambiguity order detection rate. The missing detection of the algorithm is related to the level of the simulated ambiguity energy. If the energy of the simulated target SCR (signal-to-clutter ratio) in the real background is too low, the ambiguity may become invisible and the algorithm may fail. Figure 6 also shows the PDV map of the image (generated in operation 500 of Figure 4) that identifies the locations where the PDV value is different from zero.

[0086] The PVA algorithm has also been tested with real images. Figures 6a and 6b show the results of ambiguity detection (AASR or PDV map) in stripmap and spotlight images respectively, where the dark regions represent the ambiguity masks indicating the detected ambiguities. In Figure 6a, the bright urban area 600 appears three times in the image (once at the corrected position of 600 and twice more at positions 610 and 620). Since ambiguity 610 is on the water surface, it is clearly incorrect. Ambiguity 620 is partially on the water surface and partially on land. The PVA algorithm detects the ambiguities and the ambiguity masks are created to emphasize them by darkening them. Also, colors can be used in the ambiguity masks to highlight the ambiguities detected in the SAR image.

[0087] This algorithm has obtained very good results with simulations and real data. The implemented algorithm solves the problem of ambiguity detection with a lightweight and simple technique. This algorithm also functions when the ambiguity signature cannot be easily separated from the main signal. Some of the advantages of the PVA algorithm over other ambiguity detection methods are the processing speed and the independence from specific models such as antenna patterns. Furthermore, since it can be used for parallel processing, the processing speed is further improved. The dedicated spectrum filtering reduces the sensitivity of the algorithm to the multipath in urban areas that causes many false detections and the difficulty of separating azimuth and range ambiguities when strong range ambiguities exist.

[0088] In the examples described so far, methods for detecting the ambiguity in SAR images have been improved. It is also desirable to have an improved method for detecting and suppressing the ambiguity in SAR images. As described in the background, existing methods for detecting and suppressing ambiguity are troubled by many limitations.

[0089] Next, an improved method for suppressing azimuth ambiguity that overcomes some of the problems in the known methods will be described. This suppression method can be used alone or in combination with the above-described detection method using the phase differential value. For example, it can be used in combination with the PVA detection method according to the present disclosure to determine the timing when an azimuth ambiguity detection / suppression method is required or to evaluate the effectiveness of the azimuth ambiguity detection / suppression method.

[0090] The suppression method may include, for each SAR image, applying an amplitude threshold to the Doppler spectrum to detect the ambiguity energy in the spectrum, and generating a modified Doppler spectrum with the ambiguity energy suppressed by replacing the amplitude value of the detected ambiguity energy. Then, for the affected pixels, image data with azimuth ambiguity suppressed may be generated using the modified Doppler spectrum. Hereinafter, an example of this suppression method will be described in the form of an algorithm.

[0091] A proposed algorithm for suppressing azimuth ambiguity in SAR SLC data is named selective Doppler frequency suppression (SDFS). This 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 ambiguity in SAR data, or can be used iteratively to detect and filter all ambiguity signatures in the Doppler spectrum. For example, after the suppression algorithm is applied to SAR SLC data, the data is used to generate image data, and then an ambiguity detection method such as the above-mentioned PVA method is applied. The ambiguity detection method is used to determine the effect of suppression, and if necessary, the suppression can be repeated until an acceptable level of ambiguity suppression is achieved (e.g., until a level that meets a predetermined criterion). For example, to improve the suppression, iterations of the suppression method may be performed on previously azimuth-ambiguity-suppressed image data.

[0092] Generally, the suppression method can be performed on SAR image data in the form of the received Doppler spectrum for each image, which is also referred to here as the "signature". The Doppler spectrum is composed of amplitude values corresponding to each frequency in the spectrum.

[0093] Specific examples of how to achieve this are described below. Let the Doppler spectrum of each pixel of the main signal and the ambiguity before RMC be as follows: TIFF0007700388000025.tif30158

[0094] Here, TIFF0007700388000026.tif10150 is the azimuth antenna pattern, f R is the Doppler rate, TIFF0007700388000027.tif9158 is the Doppler frequency corresponding to the side lobe of the antenna pattern that generated the ambiguity, and k ∈ Z. After RMC and azimuth compression, which are performed by multiplying the range-compressed data spectrum by TIFF0007700388000028.tif14158, the azimuth reference function, the data is as follows: TIFF0007700388000029.tif43158

[0095] TIFF0007700388000030.tif9158 represents the residual amplitude signal that depends on the range time and azimuth frequency after range migration compensation performed to compensate for the energy coming from the antenna pattern main beam, and R res is the residual range migration of the ambiguity. This term indicates that the ambiguity spectrum signature depends on range and azimuth, and 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. By this threshold, TIFF0007700388000031.tif15158, the term of the azimuth-dependent spectrum signature of the main signal represented by the term, and the range and azimuth dependence of the spectrum signature of the ambiguity that defines the energy skew in the range-Doppler region It can be separated from the item of TIFF0007700388000032.tif12158.

[0096] An example of the selective Doppler frequency suppression method is shown in FIG. 7. The process starts from the SAR SLC data of 700. In step 710, the spectrum of the SAR data is shifted to the Doppler centroid. As a result, data with a symmetric Doppler spectrum centered on the Doppler centroid can be obtained. TIFF0007700388000033.tif9158

[0097] As a result, the Doppler spectrum is as follows: TIFF0007700388000034.tif11158

[0098] In step 720, a normalization filter is applied to the image data. By this filtering, the Doppler energy of the azimuth-dependent spectral signature is normalized, and the power of the ambiguous signal with respect to the main signal increases. Due to this normalization, the power of the properly focused main signal of the target with high backscattering decreases, but the improperly focused ambiguity signal does not decrease. Therefore, the power of the ambiguity signal effectively increases, making detection easier. This operation is represented as follows: TIFF0007700388000035.tif12158

[0099] In step 730, an azimuth ambiguity map AASR(s,t) is generated. This can be generated using the PVA algorithm. Also, instead of the PVA algorithm, other detection algorithms can be used to generate other maps indicating where the ambiguity exists in the AASR map or the image data. The amount of ambiguity energy in the image is quantified by the condition AASR(s,t)>T. As an example, a threshold of T = 0.62 2 is used for the strip map image, and T = 0.7 for the spotlight image.2 The threshold value of is used. Therefore, the threshold value may depend on the method by which the image data is generated.

[0100] The generation of the ambiguity map is an optional step used when 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 the fast Fourier transform: TIFF0007700388000036.tif11158

[0102] The normalized Doppler spectrum has the energy of the normalized main target, and only the part of the ambiguity energy remains unchanged. This facilitates the detection of the ambiguity signature. The normalized Doppler spectrum is obtained by normalizing the data (amplitude only) in the image region and then calculating the Doppler spectrum. This operation can improve the detection of the ambiguity signal in a scene with strong targets. Then, suppression can be performed.

[0103] Next, in steps 750, 751, 752, 753, the absolute value of the normalized Doppler spectrum is analyzed, and an adaptive threshold value is used according to, for example, the spectral statistical parameters, and the formula TIFF0007700388000037.tif12158, an ambiguity signal (for example, an ambiguity signal depending on range time and azimuth time) can be detected. In the flow of FIG. 7, the amplitude is extracted in step 750, and the Doppler spectrum is averaged using an average convolution filter in step 751: TIFF0007700388000038.tif9158

[0104] Here, the absolute value of the normalized Doppler spectrum can be convolved with the averaging filter h. In step 752, statistical parameters, such as S(f d, the mean μσ and standard deviation of (t) are used to calculate the adaptation threshold: TIFF0007700388000039.tif9158 where k is an empirically calculated constant. This can be used to generate a mask for subsequent thresholding operations on the amplitude data. The statistical parameters are TIFF0007700388000040.tif15158 can be calculated in the Doppler spectrum of the range. BD is the Doppler spectrum used in this process. The azimuth ambiguity in the normalized Doppler spectrum can be detected using the following conditions: TIFF0007700388000041.tif9158

[0105] In step 753, a thresholding operation is performed, where values exceeding the threshold determined in operation 752 are excluded.

[0106] In step 755, for each azimuth column, the fitting of the values of |Z(:,t)| may be calculated using a polynomial fitting that excludes ambiguous amplitude values. In other words, the ambiguous amplitude values from the normalized Doppler spectrum can be replaced by the fitted function. By this operation, the energy of the ambiguity is suppressed, and the suppressed amplitude is generated, to which extracted in step 754 the phase of the SAR SLC data is multiplied to obtain a suppressed or filtered Doppler spectrum: TIFF0007700388000042.tif10158

[0107] In step 760, the suppressed Doppler spectrum is inverse fast Fourier transformed with respect to the azimuth time to obtain the suppressed or filtered SAR SLC data as follows: TIFF0007700388000043.tif10158

[0108] In step 765, an azimuth ambiguity map AASR(s,t) is generated based on the filtered SLC data. Similar to step 730, the AASR map can be generated using the PVA algorithm. Also, instead of the PVA algorithm, other detection algorithms can be used to generate an AASR map or another map indicating where ambiguity exists in the image data, and from which the ratio of the image containing ambiguity can be calculated.

[0109] In step 770, the filtered AASR map generated in step 765 is compared with the AASR reference map generated in step 730. If the comparison meets a predetermined criterion (e.g., the difference between the two), until the filtering no longer causes a decrease in the AASR calculated by the PVA detection algorithm, or until the maximum number of iterations N max is reached, by sending it back to step 720, the filtered TIFF0007700388000044.tif10158 can repeatedly execute the detection and suppression algorithm. At this point, the filtered SLC data is passed to step 780, and the azimuth suppression algorithm according to this embodiment is completed. The filtered SLC data can be formed into an (ambiguity-suppressed) image or used in other ways.

[0110] Similar to 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 effectiveness of the suppression method and does not necessarily form part of the suppression method. If the comparison is not desired, the filtered SLC generated in step 760 can be directly passed to step 780 at the end of the algorithm.

[0111] In summary, the criteria for determining whether to execute an iteration may be comparative ones such as the improvement of ambiguity suppression compared to the previous iteration, or absolute ones 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] Note that in the suppression method described with reference to FIG. 7, threshold processing or segmentation operations may be performed for each iteration of the suppression method, whereas in the stand-alone detection method described with reference to FIG. 4, it may be performed only once. In the specific example of FIG. 7, the PVA algorithm (and related threshold processing) is executed multiple times to generate an AASR reference map (step 765) and to generate an AASR filtered map (step 730).

[0113] To explain how the SDFS algorithm functions, FIG. 8 shows an image of a ship 810, with an ambiguity 820 visible on the right side of the image. FIG. 9a shows the Doppler spectrum of the image data of FIG. 8, having a main target represented by the central straight line 910 and the energy of the ambiguity represented by the right diagonal line 920. FIG. 9b shows the Doppler spectrum after normalization, which has the effect of reducing the power of the main target. Here, some of the energy of the ambiguity 920, although previously masked by the main target, is more visible and easier to detect.

[0114] The SDFS algorithm has been tested and verified using simulated data and actual data. Below, the performance metrics calculated in the simulation and the results obtained from the actual data are shown.

[0115] The SDFS algorithm provides a lightweight and efficient method for ambiguity suppression and has been demonstrated to function well even in cases where the ambiguity is weak. In the presence of strong targets such as in an urban environment, the ambiguity energy may be masked by the target energy, leading to potential failure. The PVA algorithm is used in the calculation of performance metrics. Performance is calculated for the simulation dataset of ambiguities detected by the PVA algorithm; 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 at a frequency corresponds to the signature energy of the suppressed ambiguity spectrum, the false detection suppression rate at a frequency refers to the non-ambiguity spectrum that was erroneously suppressed, and the suppression rate in an image is the amount of ambiguity suppressed in the image. Table 2 TIFF0007700388000045.tif59153

[0117] The difference in the results between primary and secondary ambiguities is mainly due to two factors. On the one hand, the primary ambiguity has a higher SCR than the secondary ambiguity because the energy of the secondary side lobe is low. On the other hand, the secondary ambiguity has a larger residual range migration, resulting in a higher sensitivity to detecting range-azimuth-dependent signatures. The proportion of the spectrum that is erroneously suppressed as an ambiguity is less than 1% in both cases.

[0118] Figure 10 is a graph showing the ratio of the suppression rate to the ambiguity coverage rate at a frequency. A linear regression between the suppression rate and the ambiguity coverage is shown. A low ambiguity coverage rate means that there are very small ambiguities and / or very few ambiguities in the image, and a high ambiguity coverage rate means that there are more or larger ambiguities in the image. As can be seen from Figure 10, the main contribution to the suppression rate is the ambiguity coverage rate within the image. If the ambiguity coverage rate is too low, it becomes 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 improves. When the ambiguity coverage rate exceeds 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, taken using the strip map imaging mode. An ambiguity 1110 can be clearly seen 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 ambiguity at 1120 has been suppressed. Repeatedly re-running the algorithm can help to further suppress the ambiguity until no further improvement can be achieved.

[0120] Similarly, Figure 12a shows a scene taken using the spotlight mode with a large and distinct ambiguity located at 1210. Figure 12b shows the result of the ambiguity suppression. As can be seen at 1220, the ambiguity has been very effectively suppressed by the SDFS algorithm.

[0121] The SDFS algorithm for the detection and suppression of azimuth ambiguity achieved very good results in simulations and real data. The implemented algorithm solves the problem of ambiguity suppression in a lightweight and simple way. Ambiguity suppression is performed by an algorithm that does not reduce the resolution, preserves the phase, and functions even when the ambiguity signature cannot be easily separated from the main signal. The advantages of the SDFS algorithm are the processing speed and independence from a specific model. Furthermore, this algorithm can suppress signals that are not properly separated from the main signal, and the phase is retained after suppression. Its limitations are the sensitivity to configuration parameters and the suppression of useful signals under some conditions.

[0122] The phase variation analysis (PVA) method for ambiguity detection and the selective Doppler frequency suppression (SDFS) method for detecting and suppressing azimuth ambiguity described in this disclosure can both be used independently. However, they can also be used together in a synergistic way. As described above, the effectiveness of SDFS suppression may be determined by detecting the ambiguity in the azimuth ambiguity suppression image data using the PVA method.

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

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

[0125] When this process is completed, the new image with suppressed ambiguity can be fed back to the PVA algorithm again in step 1302 to determine whether the criterion is met. This process is repeated until the image criterion is met, no further improvement is detected, or a certain maximum number of iterations is reached (the checks for the last two conditions are not shown in Figure 13).

[0126] In one embodiment, the method of Figure 13 can also be implemented by using the PVA algorithm in step 1302 and a different suppression algorithm in step 1305. Similarly, in another embodiment, the method can be implemented by using a different ambiguity detection method in step 1302 and the SDFS algorithm for detecting and suppressing ambiguity in step 1305.

[0127] The processing of SAR data to detect and / or suppress azimuth ambiguity can be performed either on-board the satellite or at a ground station, depending on the available computing power. Further, the operations described herein may be performed in a distributed computing system, which may or may not include a computing system mounted on the satellite. Accordingly, some embodiments of the invention described herein provide a computing system configured to operate SAR according to any of the methods described herein, an example of which is shown in FIG. 14.

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

[0129] A computing system that may be used in any implementation of the methods described herein is schematically shown in FIG. 14.

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

[0131] Computing system 1400 may include, for example, one or more controllers such as a central processing unit processor (CPU), a chip, or a controller 1405 that may be any suitable processor or computing or calculating device such as the FPGA described above, an operating system 1415, a memory 1420 that stores executable code 1425, a storage 1430 that 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 within one or more controllers, such as controller 1405, may be configured to execute any of the methods described herein. For example, one or more processors within controller 1405 may be connected to a memory 1420 that stores software or instructions that, when executed by the one or more processors, cause the one or more processors to execute a method according to some embodiments of the present invention. The controller 1405 or the central processing unit within the controller 1405 may be configured to execute some of the operations shown in FIGS. 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, and this processor controls subsequent operations in FIGS. 4, 7, and 8 according to one or more algorithms that may be stored as part of the executable code 1425.

[0134] The input device 1435 may be a mouse, keyboard, touch screen or pad, or any suitable input device, or may comprise them. As indicated by block 1435, it will be appreciated that any suitable number of input devices may be operably connected to the computing system 1400. The output device 1440 may comprise one or more displays, speakers, and / or any other suitable output device. As indicated by block 1440, it will be appreciated that any suitable number of output devices may be operably connected to the computing system 1400. The input and output devices may be used, for example, to enable 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 functions of any of the computing systems described herein may be distributed among multiple computing systems.

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

[0137] In this application, it is recognized that firmware and software are individually valuable commodities that can be traded. This is designed to include software that is computed or controlled on "dumb" or standard hardware to perform desired functions. It is also aimed at including software that "describes" or defines hardware configurations, such as HDL (Hardware Description Language) software for designing silicon chips or configuring general-purpose programmable chips to perform desired functions.

[0138] The above embodiments are almost automated. In some examples, the user or operator of the system can manually instruct some of the operations of the method to be performed.

[0139] In the described embodiments of the present invention, the terrestrial station may be composed of a computing and / or electronic system as described with reference to FIG. 14.

[0140] Here, the "computing system" is used to refer to any device having the processing ability to execute instructions. Those skilled in the art will understand that such processing ability can be incorporated into many different devices, and thus the term "computing system" includes personal computers, servers, smart mobile phones, personal digital assistants, and many other devices.

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

[0142] Any reference to an "item" or "piece" refers to one or more of these items, unless otherwise specified. As used herein, the term "comprising" means including the operations or actions or elements of a specified method, 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] Furthermore, to the extent that the term "comprising" is used within the detailed description or claims, since the term "comprising" is interpreted as a transitional term within the claims, this term is intended to have the same inclusiveness as the term "including".

[0144] The accompanying figures illustrate exemplary methods. The methods are shown and described as a series of operations to be performed in a particular order, but it should be understood and appreciated that the methods are not limited by the order. For example, some operations can occur in a different order than those described herein. Also, an action can occur simultaneously with another action. Furthermore, in some cases, not all operations may be required to implement the methods described herein.

[0145] The order of operations or actions of the methods described in this specification is illustrative, but the operations or actions can be executed in any suitable order or, where appropriate, simultaneously. Further, without departing from the scope of the subject matter described herein, operations or actions can be added or replaced, or individual operations or actions can be deleted in any manner. Aspects of any of the above embodiments can be combined with aspects of any of the other above embodiments to form further embodiments.

[0146] The description of the above preferred embodiments is shown by way of example only, and it should be understood that those skilled in the art can make various modifications. The above content includes an example of one or more embodiments. Of course, it is impossible to describe every possible modification and variation of the above devices or methods for the purpose of explaining the above aspects, but those skilled in the art will recognize that many further modifications and arrangements of various aspects are possible. Accordingly, the described aspects are intended to 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 clauses of the following numbers. 1. A computer-implemented method for detecting ambiguity in synthetic aperture radar (SAR) image data, wherein the SAR data includes amplitude and phase values for each pixel in the image, the method comprising: calculating at least one phase derivative value for each pixel represented by the SAR data in the spatial direction; determining a threshold value for the phase derivative value; and determining that a pixel having a phase derivative value exceeding the threshold value is an ambiguity. 2. The method according to clause 1, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to azimuth. 3. The method according to clause 1 or 2, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range. 4. The method according to clause 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 phase derivative values. 5. The method according to clause 4, wherein the threshold value is determined from the product of the phase derivative values. 6. The method according to any of the preceding clauses, wherein the calculation of the at least one phase derivative value is performed on a subset of the image data. 7. The method according to any of the preceding clauses, further comprising filtering the image data to reduce sidelobes before calculating the one or more phase derivative values. 8. The method according to clause 6, wherein generating a Doppler spectrum of the image data, and the filtering is performed on the Doppler spectrum. 9. The method according to any of the preceding clauses, wherein the data comprises single look data. 10. The method according to clause 8, further comprising weighting the one or more phase derivative values with a coefficient according to the difference between range looks, and the threshold value is applied to the weighted phase derivative values. 11. The method according to clause 9, wherein the difference between range looks is calculated using first and second sub-apertures. 12. The method according to clause 10, wherein the first and second sub-apertures are symmetric. 13. The method according to clause 12, wherein the first and second sub-apertures each select the first 50% and the last 50% of the SAR SLC data, respectively, and the first and second sub-apertures are symmetric. 14. The method according to any of the preceding clauses, further comprising shifting the data to the Doppler centroid before calculating the at least one phase derivative value. 15. The method according to any of the preceding clauses, further comprising generating an ambiguity map corresponding to the image based on the at least one phase derivative value. 16. The method according to any of the preceding clauses, comprising segmenting the phase derivative values to generate a mask corresponding to the image. 17. The method according to any of the preceding clauses, comprising normalizing data to attenuate a spectral signature that depends only on azimuth before calculating the at least one phase derivative value. 18. The method according to clause 16, wherein segmenting the phase derivative values to generate a mask comprises using a threshold. 19. The method according to any of the preceding clauses, which is performed on data compensated for range migration. 20. The method according to any of the preceding clauses, which is performed on data processed to form a SAR image. 21. The method according to any of the preceding clauses, further comprising suppressing ambiguity in the synthetic aperture radar (SAR) image data. 22. Suppressing ambiguity in the synthetic aperture radar (SAR) image data comprises: generating a Doppler spectrum of the image data; applying an amplitude threshold to the Doppler spectrum of the image data to exclude values below the threshold due to ambiguity energy in the spectrum; replacing the excluded amplitude values to generate a modified Doppler spectrum with suppressed ambiguity energy; using the modified Doppler spectrum to generate image data with suppressed azimuth ambiguity, the method according to clause 21. 23. A computing system comprising one or more processors configured to execute a method according to any of the preceding clauses. 24. A computer-readable medium comprising instructions that, when executed in a computing system, cause the computing system to execute a method according to any of clauses 1 to 22. 25. A computer-implemented method for suppressing ambiguity in the synthetic aperture radar (SAR) image data, wherein the data includes a Doppler spectrum obtained from the received SAR signal, 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 with suppressed ambiguity energy; and generating image data with suppressed azimuth ambiguity using the modified Doppler spectrum. A computer-implemented method comprising: 26. The method according to clause 25, wherein the amplitude threshold is an adaptive threshold based on statistical parameters of the Doppler spectrum. 27. The method according to clause 25 or 26, wherein the Doppler spectrum is obtained by normalizing only the amplitude of the SAR data in the image area and calculating the Doppler spectrum based on the normalized data. 28. The method according to clause 27, further comprising shifting the data to the Doppler centroid, wherein the normalization comprises normalizing the shifted SAR SLC data to attenuate a spectrum signature that depends only on azimuth. The method. 29. The method according to any of the preceding clauses, wherein the replacement is performed using a fitting function. 30. Detecting ambiguity in the image data with suppressed azimuth ambiguity, and if the amount of ambiguity does not meet a predetermined criterion, performing any of the procedures of the preceding clauses on the image data with suppressed azimuth ambiguity. The method according to any one of the preceding clauses, comprising: 31. The method according to clause 30, wherein the predetermined criterion comprises an ambiguity energy threshold. 32. The method according to clause 30 or 31, wherein the predetermined criterion comprises an improvement in ambiguity suppression compared to the SLC data for which the suppression was performed. 33. Detecting ambiguity comprises calculating at least one phase derivative value for each pixel represented by SAR data with respect to the spatial direction, and determining a threshold value of the phase derivative value, and determining that a pixel having a phase derivative value exceeding the threshold value is an ambiguity, the method according to clause 30, 31 or 32 comprising the above. 34. The method according to clause 33, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to azimuth. 35. The method according to clause 33 or 34, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range. 36. The method according to clause 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 according to clause 36, wherein the threshold value is determined from a product of the phase derivative values. 38. The method according to any one of clauses 33 to 37, wherein the calculation of the at least one phase derivative value is performed on a subset of the image data. 39. The method according to any one of clauses 33 to 37, comprising filtering the image data to reduce side lobes before calculating the at least one phase derivative value. 40. The method according to clause 38, comprising generating a Doppler spectrum of the image data, wherein the filtering is performed on the Doppler spectrum. 41. The method according to any one of clauses 33 to 40, comprising weighting the one or more phase derivative values with a coefficient according to the difference between range looks, and the threshold value is applied to the weighted phase derivative values. 42. The method according to clause 41, wherein the difference between range looks is calculated using first and second sub-apertures. 43. The method according to clause 42, wherein the first and second sub-apertures are symmetric. 44. The method according to clause 43, wherein the first and second sub-apertures each select the first 50% and the last 50% of the SAR SLC data, and the first and second sub-apertures are symmetric. 45. The method according to any one of clauses 33 to 44, further comprising shifting the data to the Doppler centroid before calculating the at least one phase differential value. 46. The method according to any one of clauses 33 to 44, further comprising generating an ambiguity map corresponding to the image based on the at least one phase differential value. 47. The method according to any one of clauses 33 to 44, further comprising segmenting the phase differential value to generate a mask corresponding to the image. 48. Generating azimuth ambiguity suppression image data using a modified Doppler spectrum comprises multiplying the phase of the input data by the modified Doppler spectrum and inverse-transforming the Doppler spectrum with respect to azimuth. The method according to any one of clauses 25 to 47. 49. A computing system comprising one or more processors configured to execute the method according to any one of clauses 25 to 48. 50. A computer-readable medium comprising instructions that, when executed in a computing system, cause the computing system to execute the method according to any one of clauses 25 to 48.

Claims

1. A computer-implemented method for suppressing ambiguity in synthetic aperture radar (SAR) image data, said data including a Doppler spectrum obtained from a received SAR signal, applying an amplitude threshold to the Doppler spectrum of the received SAR signal and excluding values exceeding the threshold due to ambiguity energy in the spectrum; replacing the excluded amplitude values using a fitting function to generate a modified Doppler spectrum with suppressed ambiguity energy; generating image data with suppressed azimuth ambiguity using the modified Doppler spectrum. A computer-implemented method comprising:

2. The method according to claim 1, wherein the amplitude threshold is an adaptive threshold based on statistical parameters of the Doppler spectrum.

3. The method according to claim 1, wherein the Doppler spectrum is obtained by normalizing only the amplitude of the SAR data in the image region and calculating the Doppler spectrum based on the normalized data.

4. The method according to claim 3, comprising shifting the data to the Doppler centroid, wherein the normalization comprises normalizing the shifted SAR SLC data to attenuate a spectrum signature that depends only on azimuth. The method.

5. Detecting ambiguity in the image data with suppressed azimuth ambiguity, and if the amount of ambiguity does not meet a predetermined criterion, performing the procedure according to claim 1 on the image data with suppressed azimuth ambiguity. The method according to claim 1, comprising:

6. The method according to claim 5, wherein the predetermined criterion comprises an ambiguity energy threshold.

7. The method according to claim 5, wherein the predetermined criterion comprises an improvement in ambiguity suppression compared to the SLC data for which the suppression was performed.

8. Detecting ambiguity comprises calculating at least one phase differential value for each pixel represented by SAR data in the spatial direction; determining a threshold for the phase differential value; determining that a pixel having a phase differential value exceeding the threshold is an ambiguity. The method according to claim 5, comprising:

9. The method according to claim 8, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to azimuth.

10. The method according to claim 8, wherein calculating at least one phase derivative value comprises calculating a phase derivative value with respect to range.

11. The method according to claim 8, 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.

12. The method according to claim 11, wherein the threshold value is determined from the product of the phase derivative values.

13. The method according to claim 8, wherein the calculating of the at least one phase derivative value is performed on a subset of the image data.

14. The method according to claim 8, further comprising filtering the image data to reduce sidelobes before calculating the at least one phase derivative value.

15. The method according to claim 8, comprising weighting the one or more phase derivative values with a coefficient according to the difference between range looks, and the threshold value is applied to the weighted phase derivative values.

16. The method according to claim 15, wherein the difference between range looks is calculated using first and second sub-apertures.

17. The method according to claim 16, wherein the first and second sub-apertures are symmetric.

18. The method according to claim 17, wherein the first and second sub-apertures each select the first 50% and the last 50% of the SAR SLC data, and the first and second sub-apertures are symmetric.

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

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

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