Method for reconstructing an image of a scene

Abstract

The present invention relates to a method for reconstructing an image of a scene using an antenna system and comprising, for each pixel of the image: a. receiving samples of wide-band time-domain signals backscattered by reflectors of the scene; b. for each direction among a plurality of directions, determining, based on the received samples, new samples of a new time-domain signal associated with said each direction, respectively, each new signal corresponding to a wide-band plane wave in said each direction, respectively; c. for each direction among the plurality of directions, selecting, from the new samples of the respective new time-domain signal, samples corresponding to a there-and-back path time of said new signal from an origin of the image to said each pixel; and d. determining a light intensity of said each pixel based on delayed samples.

Description

[0001] DESCRIPTION

[0002] Title of the invention: Method for reconstructing an image of a scene

[0003] Technical field

[0004] The present invention relates to the field of sonar or radar imaging, and the detection of objects from an antenna, sonar or radar system, in particular a synthetic aperture system.

[0005] Prior art

[0006] Knowledge of an aquatic environment represents a major challenge for a large number of applications. For example, the exploration of the underwater environment plays a very important role in many fields, such as the oil industry or the deployment of civil or military vessels. Accurate imaging of submerged objects and / or the seabed makes it possible to inspect structures and detect objects under the water's surface, such as shipwrecks or underwater mines, submarine cables or even moving objects.

[0007] Unlike electromagnetic waves, which propagate with difficulty in an aquatic environment, acoustic waves are well-suited to underwater detection and have quickly established themselves in this field. Sonar systems (for "SOund Navigation And Ranging") have thus become the preferred means for bathymetry and the detection of objects in aquatic environments. The angular resolution of a sonar system is linked to two main parameters: the frequency of the acoustic wave, and the length of the antenna, composed of one or more sensors. By increasing the frequency of the acoustic wave, the resolution is improved, but the range of the system decreases, so that the possibilities of applications over long distances are greatly reduced.

[0008] Inspired by work in radar (for RAdio Detection And Ranging), synthetic aperture sonar (SAS) systems began to emerge in the 1970s. The principle of a SAS system is to virtually increase the size of the antenna, by combining the signals from the backscattering of successive sound pulses (also called "pings"), and thus improve the resolution of the sonar system. An example of a SAS system is shown in Figure 1a, in the context of a towed linear antenna, mounted on an autonomous underwater vehicle (AUV) traveling along a straight path 101.In an active SAS system, incident waves in the form of sound pulses are emitted by the linear antenna at different positions 103a, 103b, 103c, 103d along the trajectory 101. When an incident wave interacts with an object 102, a fraction of this incident wave is returned in the direction from which it came (backscatter phenomenon). The backscattered signals can be combined to produce an image of the seabed, and in particular of the object 102 (fixed or mobile) located in the field of the antenna, for example on the seabed.More precisely, by performing a coherent integration of the backscattered signals taking into account the delays (or path differences) of the signals relative to each other due to the successive positions of the antenna, it is possible to simulate a so-called "synthetic" antenna of large dimension (LSA length much greater than the LR length of the real antenna), which would be impossible to produce for technical and cost reasons. The resolution of the SAS system is therefore greatly improved compared to a conventional sonar system.

[0009] It is conceptually very convenient to treat object 102 as a fictitious source radiating towards the vehicle with a fictitious speed of sound equal to the real speed divided by two (this model is known in seismic as the "exploding reflector model"). The factor two is introduced to compensate for the difference between the round trip path in the real case and the single path in the fictitious case. Imaging is then similar to the reconstruction of a field of such sources. When this field contains only a single point source, located for example at 102, the corresponding image is called the point spread function, or spatial impulse response, and is sufficient to completely characterize the imaging system, by the principle of superposition of linear systems.

[0010] Data processing in a SAS system requires precise knowledge of the path differences between the backscattered signals received at different antenna positions, and therefore in particular the movements of the autonomous underwater vehicle. However, such knowledge is difficult to obtain, as shown in Figure 1 b, which represents an example of a theoretical trajectory and an example of a real trajectory of an autonomous marine or underwater vehicle. In this example, the autonomous underwater vehicle 104 is assumed to follow a theoretical rectilinear trajectory 105 shown at the top of Figure 1 b. Due to parasitic movements (for example, yaw, pitch, swerve, etc.) linked to the aquatic environment, the real trajectory 106 actually followed by the vehicle 104 may be very different from the theoretical trajectory 105, as shown at the bottom of Figure 1 b.In addition to the curvature of the actual trajectory 106, it is noted that the vehicle 104 may be oriented along an axis making an angle α relative to the direction of the nominal trajectory, as shown in Figure 1 b. Such an angle may develop in particular in the presence of a current perpendicular to the trajectory. Several methods of the prior art make it possible to effectively measure trajectory errors, i.e. the differences between the actual trajectory 106 and the theoretical trajectory 105 followed by the vehicle 104, as well as the attitudes of the vehicle (for example the angle α shown at the bottom of Figure 1 b). These methods make it possible to determine the positions of the antenna and the successive path differences in a precise manner. However, knowledge of these elements is not sufficient; it is also necessary that the methods for forming images from the collected data can integrate them effectively.

[0011] Schematically, there are two types of methods used in the prior art for image formation in SAS systems: temporal methods (i.e., methods in which the data are processed only in the time domain), and frequency methods (i.e., methods in which the data are processed only in the frequency domain).

[0012] Temporal methods, such as the backprojection algorithm, also called delay and sum beamforming, advantageously integrate all the determined path differences, thus leading to a very accurate reconstruction of the seabed and the object. Overall, the backprojection algorithm is based on calculating the sum of the signals received by the different sensors of the antenna at different positions, to which respective delays have been applied to compensate for their round-trip propagation times from the sensor to the pixel of the image considered. In what follows, such application of a delay to a signal to compensate for its propagation time is called "backpropagation", "backprojection" or "migration" (terminology borrowed from the field of seismic science).In the migration algorithm, the received signals are modeled by cylindrical or spherical waves, which are migrated to the place where the source is supposed to be located and which are summed, to obtain a new signal whose energy can then be calculated in order to deduce the scattering power of the source (and therefore the intensity of the image pixel associated with this source). Such methods are very expensive in terms of calculation. Indeed, because of the curvature of the wave surfaces, it is not possible to migrate the waves to an entire group of pixels at once, for example an entire row or column of the image. The migration, and the associated interpolations, must be repeated for each pixel of the image, which requires a computer with a high weight and energy consumption. These constraints are not acceptable in the context of applications embedded in autonomous marine or underwater vehicles.

[0013] On the other hand, frequency-based methods, such as the Omega-k (or co-k) algorithm, are much faster because they require much less computation and lower power consumption. These methods are mainly based on the Fourier diffraction theorem, which uses monochromatic plane waves, i.e. narrowband plane waves (more precisely, this theorem provides the Fourier transform of the scattered or backscattered field associated with an object insonified by a monochromatic plane wave). However, the Fourier diffraction theorem presupposes an "ideal" antenna, i.e. an antenna following a uniform rectilinear motion. For this reason, frequency-based methods have difficulty taking into account antenna deformations (i.e., the trajectory and angle errors mentioned above) and even more difficultly their variation over time, i.e., dynamic deformations.In existing frequency methods, approximations are made to integrate the estimated trajectory errors and “motion compensation” algorithms are used, but the results obtained remain significantly less good than those of time-based methods.

[0014] There is therefore a need for an image formation method that is fast, accurate, and low energy consumption, to be implemented within a SAS system on board an autonomous vehicle with limited resources.

[0015] It is noted that, if the principles and embodiments described prove to be particularly advantageous in the field of synthetic antenna sonars, they are also applicable in the field of synthetic antenna radars (or synthetic aperture radars, or SAR, for "Synthetic Aperture Radar" in English) and have the same advantages in terms of energy consumption, calculation speed and precision. In addition, even if the invention is particularly advantageous in the context of synthetic aperture antenna systems, it is applicable to other types of antenna systems, in particular systems comprising a physical antenna emitting a set of pulses and receiving backscattered signals in response to these pulses. Such systems are notably used in ultrasound medical imaging.

[0016] Statement of the invention

[0017] To address at least one of the problems mentioned above, the invention proposes to decompose broadband signals received by a synthetic antenna sonar or radar system from a source into a plurality of broadband plane waves in the time domain, using a method for forming broadband and far-field time channels. Then, for each plane wave formed, a migration of this wave towards a pixel of the image where the source is supposed to be located is implemented, also in the time domain. As detailed below, these two main steps can be implemented with a reasonable computational cost. Furthermore, the use of broadband signals is well suited to sonar signals (as well as to certain radar systems), and therefore allows more accurate results than prior art methods based on narrowband signals. The proposed method is therefore both accurate and inexpensive in terms of computations.

[0018] There is thus proposed a method for reconstructing an image of a scene by an antenna system, said image comprising a plurality of pixels, the method being implemented by computer and comprising, for each pixel among the plurality of pixels: a. receiving samples of broadband temporal signals backscattered by reflectors of the scene for one or more sensors of the antenna system; b. for each direction among a plurality of directions, calculating, from the samples received by said one or more sensors, new samples of a new temporal signal respectively associated with said each direction, each new signal corresponding respectively to a broadband plane wave in said each direction; c.for each direction among the plurality of directions, selecting, from the new samples of the respective new time signal, samples corresponding to a round trip travel time of said new signal from an origin of the image to said each pixel; and d. determining a light intensity of said each pixel from the selected samples. By "antenna system", is meant a system comprising a physical antenna, or a synthetic aperture antenna system. By "scene", is meant a portion of the space of which one seeks to reconstruct an image. For example, in the case of a synthetic antenna sonar system, the scene may designate a limited portion of the seabed, of which one wishes to obtain an image.Alternatively, one may wish to obtain a continuous image of the seabed, in which case this seabed is first cut into limited portions from which images are obtained as described previously and then juxtaposed to make a continuous image.

[0019] The present invention advantageously uses broadband signals, and allows more accurate results to be obtained than methods which assume narrowband signals, this assumption often not being valid in many applications such as seabed imaging for example.

[0020] It is noted that step b typically corresponds to a path formation step, which is a well-known technique in the field of antenna processing for locating sources, during which the signals received by the different sensors are combined so as to form new signals associated with a set of given directions. Path formation consists of compensating for path differences between the sensors in the given directions. In synthetic antenna processing, which uses signals received from several successive transmissions, it is necessary to compensate for these path differences on the round-trip paths. It is possible to approximate the round-trip travel time to an object 102 by twice the “simple” travel time between a fictitious geometric point in space, called the phase center, and said object, as if the transmission and reception took place at the same location.The phase center corresponds to the midpoint between the position in space occupied by the transmitter at the instant of transmission and that occupied by the receiving sensor at the instant of reception of the echo from the object 102. This approximation makes it possible to simplify the description of the invention but it is by no means obligatory. It is also possible to calculate exactly the round-trip travel times by taking into account the spatial separation between transmission and reception. In the context of the present invention, the new signals formed correspond to plane waves, as if the object 102 were located at infinity. This is a method of forming channels known as far field. The use of such a method for a synthetic antenna is part of the originality of the invention because it is well known that synthetic imaging is carried out in the near field in the vast majority of cases.For many high-resolution sonar systems, the object 102 is a few hundred meters from the sonar while the far field of the synthetic antenna is several kilometers away. For this reason, all prior art time-domain methods use spherical or cylindrical waves, i.e., so-called near-field channel formation methods, which alone make it possible to obtain a correctly focused image in a single step. In the invention, the far-field channel formation is only a second step b, the focused image being produced only in the following step c. The decomposition into plane waves is not intended to focus an image but to reduce the computational load.

[0021] Step c corresponds to a migration of the plane waves thus formed towards the pixels of the image where the sources that gave rise to them are supposed to be located. Unlike the methods of the prior art, the migrated waves are the newly formed plane waves and not the received spherical or cylindrical waves, which proves to be much more efficient in terms of calculation time because the migration can be carried out simultaneously for all the pixels of a row or a column of the image by a simple dilation of the signal, without there being any need to restart the migration for each pixel.

[0022] The light intensity of a pixel can correspond to its gray level.

[0023] Such a method advantageously makes it possible to construct an image of a scene observed by a synthetic aperture system quickly, precisely and with low energy consumption.

[0024] In one or more embodiments, the antenna system may be a synthetic aperture radar or a synthetic aperture sonar.

[0025] In the case of synthetic aperture sonar, the scene may correspond to a limited portion of a seabed.

[0026] In one or more embodiments, the method may further comprise receiving data relating to a variation in motion of the system relative to a theoretical trajectory. New samples of the new time signals may then be further calculated from said data. Furthermore, since the processing is done in the time domain and not in the frequency domain, these motion variations may themselves vary rapidly over time without the computational load being affected.

[0027] Thus, the method advantageously integrates motion errors and their variation over time, and provides much more accurate results than frequency methods which have great difficulty in dealing with dynamic deformations of the synthetic antenna. In one or more embodiments, the new samples of the new time signals can be calculated using a method for forming wideband and far-field time channels.

[0028] In these embodiments, the path forming method is based on the assumption that the sources are located in the far field, i.e. far enough from the sensors so that the wavefront of the received signals can be considered as planar.

[0029] For example, the formation of the broadband and far-field time channels may be based on an iterative algorithm of the kind described in "A fast beamforming algorithm" by Kenneth M. Houston, IEEE Oceans Conference Record 1 (1994) 211-216 or algorithms of the same nature that are known to those skilled in the art.

[0030] As described below, this algorithm has a computational complexity of O(Nlog2N), while time-path formation methods generally have a computational complexity of O(N 2 ). Such an algorithm therefore makes it possible to implement step b quickly.

[0031] In one or more embodiments, step c may include implementing at least one Z-Chirp transform, which is a transform for efficiently expanding or compressing a signal.

[0032] The Z-Chirp transform also has a computational complexity of O(Nlog2N), thus allowing a rapid implementation of step c.

[0033] In one or more embodiments, the light intensity of said each pixel may be a function of a sum of values ​​of the selected samples.

[0034] Another aspect of the invention relates to a device for reconstructing an image of a scene from data from a synthetic aperture antenna system, said image comprising a plurality of pixels. This device may comprise: an input interface for: a. receiving samples of broadband temporal signals backscattered by reflectors of the scene for one or more sensors of the antenna system.

[0035] The device may further comprise a circuit for implementing, for each pixel among the plurality of pixels: b. for each direction among a plurality of directions, calculating, from the samples received by said one or more sensors, new samples of a new time signal respectively associated with said each direction, each new signal corresponding respectively to a broadband plane wave in said each direction; c. for each direction among the plurality of directions, selecting, from the new samples of the respective new time signal, samples corresponding to a round trip travel time of said new signal from an origin of the image to said each pixel; and d. determining a light intensity of said each pixel from the selected samples.

[0036] The image reconstruction device may be integrated into the synthetic aperture antenna system, or be a device separate from the synthetic aperture antenna system.

[0037] A computer program, implementing all or part of the process described above, installed on pre-existing equipment, is in itself advantageous, since it makes it possible to obtain an image of the scene precisely and with a relatively reduced calculation cost.

[0038] Thus, the present invention also relates to a computer program comprising instructions for implementing the method described above, when this program is executed by a processor.

[0039] This program may use any programming language (e.g., an object language or otherwise), and may be in the form of interpretable source code, partially compiled code, or fully compiled code.

[0040] Figure 5 described in detail below, may form the flowchart of the general algorithm of such a computer program, according to one or more embodiments.

[0041] Another aspect relates to a non-transitory recording medium of a computer-executable program, comprising a data set representing one or more programs, said one or more programs comprising instructions for, upon execution of said one or more programs by a computer comprising a processing unit operatively coupled to memory means and to an input / output interface module, to execute all or part of the method described above.

[0042] Brief Description of the Drawings Other features, details and advantages of the invention will become apparent from the detailed description below. This is purely illustrative and should be read in conjunction with the attached drawings, in which:

[0043] [Fig. 1 a] Figure 1a shows an example of a synthetic aperture sonar system;

[0044] [Fig. 1 b] Figure 1 b illustrates an example of a theoretical trajectory and an actual trajectory of an autonomous underwater vehicle on which an antenna is mounted as part of a synthetic aperture sonar system;

[0045] [Fig. 2] Figure 2 shows an exemplary coordinate system that can be used to describe the motion of the phase center C of the sonar in embodiments of the invention;

[0046] [Fig. 3] Figure 3 is an illustration of the Fourier diffraction theorem;

[0047] [Fig. 4] Figure 4 represents an example of migration of a plane wave towards a pixel of the image;

[0048] [Fig. 5] Figure 5 is a flowchart of a method of reconstructing the image of an object according to one or more embodiments;

[0049] [Fig. 6] Figure 6 represents the signal samples in the Fourier plane at different stages of the migration, according to one or more embodiments;

[0050] [Fig. 7a] and [Fig. 7b] Figures 7a and 7b respectively represent the point spread functions obtained by a method of the prior art on the one hand, and an image reconstruction method according to an embodiment of the invention on the other hand;

[0051] [Fig. 8] Figure 8 represents a schematic block diagram of an information processing device for implementing one or more embodiments of the invention.

[0052] Detailed description

[0053] In the following, it is initially assumed that the mobile device on which the antenna used to reconstruct an image is mounted, for example an autonomous marine or underwater vehicle, follows a theoretical uniform rectilinear motion. It is noted that the terms "antenna" and "sonar" are used interchangeably. In this context, the phase center of the sonar, denoted C and defined as the point located in the middle of the position occupied by the sonar at the time of transmission of the acoustic wave and the position occupied by the sonar at the time of reception of the wave backscattered by an object or by the seabed in a given direction, moves in theory at constant speed along an axis (Ox).The trajectory errors presented previously and illustrated in Figure 1 b are assumed to be known, for example using a prior art method, such as the method described in patent application FR 1457951 filed on August 25, 2014 in the name of ECA ROBOTICS.

[0054] Figure 2 represents an example of a coordinate system that can be used to describe the movement of the phase center C of the sonar in embodiments of the invention. In Figure 2, the point S represents the source of the signal received by one of the sensors of the antenna. By "source", we mean a point of the observed scene (i.e. of the space insonified by the synthetic antenna) of which we wish to obtain an image, each pixel of the image corresponding for example to the power of the field scattered by a point of this scene. For example, the source can correspond to a point of an object located at the bottom of the water. According to the example of Figure 2, the phase center C of the sonar is assumed, in theory, to move along the axis (Ox) at constant speed. The distance x between the origin O of the coordinate system and the point C along the axis (Ox) of movement of the sonar is commonly called "azimuth" in the SAR literature in English.The distance r corresponds to the orthogonal distance from S to the axis (Ox) and is commonly called "slant range" or simply "range" in SAR literature. The coordinate system represented is a cylindrical coordinate system in which the axis of the cylinder corresponds to the axis of the trajectory (Ox). Due to the symmetry of revolution around the axis (Ox), the study of the signals received from a source S towards the phase center C of the sonar can be carried out in the two-dimensional space Oxr. The angle 9' formed between the axis (Ox) of displacement of the sonar and the direction from the center C towards the source S is commonly called "bearing", and we denote 9 = TT-9' its supplementary angle. It is noted that O can correspond, for example, to the initial position of the sonar (i.e. the position at which the sound pulse is emitted), or to the initial position of the center of the sonar C, or to a point chosen arbitrarily on the axis of movement of the sonar.

[0055] As mentioned above, most imaging methods for SAS systems are derived from methods initially developed for radar signals, in the context of SAR systems. In the radar domain, the signals used are generally considered to be narrowband. It is recalled that a signal can be considered narrowband if the time taken by a plane wave to insonify the entire antenna (i.e. the difference between the time taken by the wave to insonify the antenna sensor furthest from the source and the time taken by the wave to insonify the antenna sensor closest to the source) is very small compared to the duration of the sound pulse (i.e. the duration of the ping). In this case, it is considered that all the antenna sensors are insonified approximately at the same time.For example, this approximation can be considered valid when the ratio of the time taken by a plane wave to insonify the entire antenna to the duration of the sound pulse is less than 0.1. The above condition is often verified in the radar domain (even if in some cases it is not applicable), so that methods used in SAR imaging based on narrowband signals generally provide good results. However, it is generally not applicable in the sonar domain.

[0056] Prior art frequency methods used in SAS systems, which are mainly based on the Fourier diffraction theorem, use narrowband signal modeling. The principle of the Fourier diffraction theorem is described, for example, in Chapter 6 of the book "Principles of Computerized Tomography Imaging" by Avinash C. Kak and Malcolm Slaney, series "Classics in Applied Mathematics, 33" or in Chapter 3 of Malcolm Slaney's thesis "Imaging with Diffraction Tomography" defended at Purdue University, and is shown in Figure 3.

[0057] In this Figure 3, an object 301 is shown insonified by a monochromatic plane wave 302. The scattered field 303 can then be measured. It is noted that in the context of sonar applications, we are interested in the backscattered field, but the principle remains the same as for a scattered field. The Fourier diffraction theorem establishes that the Fourier transform of the scattered field 303 along the axis 304 corresponds to the value of the two-dimensional (2D) Fourier transform of the object 301 along a circular arc 305 in the frequency domain. To obtain the 2D Fourier transform of the complete object 301, it is necessary to insonify this object 301 under different directions 304 and at different frequencies, in order to obtain a family of circular arcs 305. An image of the object 301 can then be obtained by applying an inverse Fourier transform to the family of circular arcs 305 obtained.It is noted that this theorem is based on monochromatic plane waves 302, and therefore applies to narrowband signals.

[0058] However, as mentioned above, for sonar signals, the condition for approximating the received signals by narrowband signals is generally not verified. Also, methods that use narrowband signals (such as the frequency methods of the prior art such as the ω-k algorithm) are in reality poorly suited to sonar imaging, and provide degraded results. In the context of the present invention, a new method of SAS imaging from broadband signals is thus proposed. This new method is based on a new writing of the problem from broadband signals, which is now detailed.

[0059] In the following, uppercase letters are used to represent functions and quantities associated with narrowband signals, while lowercase letters are used to represent functions and quantities associated with wideband signals.

[0060] It is assumed that the phase center C of the sonar moves at constant speed along the (Ox) axis, with x the azimuth and r the orthogonal distance to the (Ox) axis, as defined above with reference to Figure 2. Due to the rotational symmetry about the (Ox) axis, the problem can be studied in the two-dimensional space Oxr.

[0061] First, it is assumed that the variables studied are continuous and come from a narrowband signal, for example a monochromatic continuous wave of wavenumber k, with k = 2π / λ, λ being the wavelength.

[0062] The H signal k(x,r) received by the phase center of the sonar when it is located at a distance x from point O on the (Ox) axis from a source located at an orthogonal distance r on the (Or) axis (i.e. having an azimuth x = 0 and an orthogonal distance r, which corresponds to point S' in Figure 2) can be expressed, if we ignore the propagation losses: where 0 is the angle defined with reference to Figure 2, u = sin0 and B(u, k) is the sonar beam pattern of the wave of wave number k.

[0063] Time t and angular frequency co, as well as orthogonal distance r = ct / 2 and variable k = 2ω / c (C being the speed of sound), orthogonal distance r and variable k' = 2k, or variable u derived from bearing 0 (u = sin 0) and the scaled sensor array length x' = 2kx, are four examples of pairs of Fourier conjugate (or dual) variables commonly used in signal processing. According to these notations, the narrowband plane wave angular spectrum G(u, r, k) is defined as follows:

[0064] As detailed in Appendix A, it can be shown, using a stationary phase approximation, that: with v = cos 0.

[0065] This extends the cylindrical standing wave from S' to a family of outgoing plane waves moving towards the sonar: where F*, 1denotes the one-dimensional inverse Fourier transform associated with the dual variables u and x' = 2kx.

[0066] Let W(u, k) be the narrowband plane wave angular spectrum of the raw narrowband data D(x, k) defined by: where D(x, k) represent the raw data from the backscattering of the monochromatic plane wave of wave number k emitted at point O (i.e. when x = 0) and received when the phase center is located at a distance x from point O on the (Ox) axis, and where F xl denotes the one-dimensional fast Fourier transform associated with the dual variables u and x' = 2kx.

[0067] From the theory of matched filtering and the convolution theorem, we obtain the following expression for the narrowband SAS image Or denotes the conjugate of G(u, r, k) and I(x, r, k) corresponds to the intensity (or gray level) for the image pixel having coordinates (x, r) in the coordinate system of Figure 2.

[0068] It appears from this formula that the narrowband SAS image I(x, r, k) can be obtained by weighting the angular spectrum W(u, k) by B(u, k), then by performing a migration (or backpropagation) of the narrowband plane waves towards each point (or pixel) P of coordinates (x, r) of the image, by applying to W(u, k) a phase shift of 2k(xu + rv), which can be associated with the propagation delay 2(xu + rv) / c corresponding to the round trip travel time of the plane wave coming from point O and heading in direction 0 and pixel P.

[0069] The principle of plane wave migration is shown in Figure 4. In this figure, it is assumed that the plane wave originates from point O in a direction 401 forming an angle 0 with the axis (Or), the direction 401 being orthogonal to the wavefront 402. The path difference corresponds to the vector OP projected in the direction of propagation of the wave, which is also equal to the distance OP', since P and P' are on the same wave plane. As shown in Figure 4, this path difference is equal to xu + rv, with u = sin 0 and v = cos 0. Thus, for the round trip of the plane wave from its emission at O ​​and its reception at (x, r), the total distance is equal to 2(xu + rv). By "migration" or "backpropagation" we therefore mean an application of a phase shift to compensate for the round-trip travel time of the wave to go from its emission point O to point P.

[0070] The broadband SAS image i(x, r) can be obtained in an elementary way by linear superposition of the components I(x, r, k) of the narrowband SAS image, i.e. by backpropagating all the components W(u, k) of the broadband signal (i.e. all the narrowband plane waves resulting from the decomposition of the broadband signal) to which a weighting has been applied by a narrowband directivity diagram B(u, k).

[0071] In other words, the broadband SAS image i(x, r) can be obtained by decomposing the broadband signal into a plurality of monochromatic (i.e. narrowband) plane waves, then by performing a weighting of these narrowband waves followed by a migration towards each point P with coordinates (x, r) of the image. This migration can be carried out as detailed above, i.e. by applying a phase shift corresponding to the round trip time from O to P in the 0 direction, which is equal to 2(xu + rv) / c.

[0072] Let w(u, r) be the broadband plane wave angular spectrum, defined as follows: J where F / ” 1 represents the one-dimensional inverse Fourier transform associated with the dual variables r and k. Similarly, the broadband raw data d(x, r) are defined as follows:

[0073] We further introduce the following function b(u,r): where B(u, k) is the directivity diagram defined previously.

[0074] The convolution product of b(u, r) and w(u, r) can be written: which means that the weighting of narrowband plane waves by B(u, k) corresponds in broadband to a filtering of the angular spectrum by the function b(u, r).

[0075] We deduce that the wideband SAS image i(x, r) can be obtained directly by performing a backpropagation of the wideband plane waves, previously filtered by b(u,r), towards each point P with coordinates (x, r) of the image:

[0076] Thus, the processing of data from the synthetic aperture system (SAS or SAR) can be performed directly in the time domain via a formation of broadband channels in the far field (i.e., considering plane waves) followed by a migration (or backpropagation) of the plane waves in the Cartesian grid (i.e., towards the points / pixels of the image).

[0077] It is recalled here that channel formation (or beamforming) is a method well known to those skilled in the art for extracting from a signal the components propagating in a given direction 0. The most classic form of channel formation in the time domain, called spatial filtering by delay and sum (or "delay and sum beamforming" in English), consists of delaying the signals received by the different sensors of the antenna, and summing all of the delayed signals.

[0078] Path formation and migration in the time domain can be very simply implemented for a plane wave (or, equivalently, cylindrical waves considered in the far field) which propagates in the direction perpendicular to the trajectory Ox. Indeed, in this case, the wavefronts are parallel to the direction axis (Ox), and are therefore aligned with the pixel grid of the image. It is therefore sufficient to choose the sampling period in slant distance of the signal corresponding to the plane wave equal to the step between the lines of the image to perform the migration without any calculation.

[0079] In the general case of a plane wave propagating in a given direction there is a contraction of the path difference between two consecutive pixels of the same column of the SAS image which results from Thales' theorem. The distance between these two pixels, once projected in the direction of propagation of the wave is smaller by a factor v = cos 0. It will therefore be necessary, to migrate a plane wave on a column of the image, to expand the signal by this factor which depends on 0.

[0080] We deduce from this a new method of processing signals from a synthetic aperture system, one embodiment of which is shown in Figure 5.

[0081] First, wideband raw data is received at the various sensors of the antenna (step 501 of Figure 5). In one or more embodiments, this raw data is received in the form of an NxP matrix, where P is the number of sensors of the antenna, and N is the number of samples of the source signal received per sensor. This data is time-domain data.

[0082] For example, if the source emits a signal s(t) at a time t, the signal received on the sensor p can be written in the form: where tp is the propagation time taken by the wave between the source and the sensor p, and β p (t) models the ambient noise on sensor p at time t. This signal r p (t) can be segmented into blocks (called "snapshots" in English) of the same duration with Typically, the signal can be considered stationary during each snapshot k. The signal received during a snapshot k can be sampled at a frequency F e respecting Shannon's theorem, which allows us to obtain N = F e S t values ​​received on each sensor during a snapshot k. The N-tuple of values ​​for each sensor forms a vector r p (t k ) of dimension N*1. The raw data received at step 501 can then correspond to the concatenation of the vectors

[0083] Then, in step 503, new wideband time signals are determined from the received data, by applying a method for forming wideband and far-field time channels. In the far field, the wavefronts can be considered as planar, so that the new time signals correspond to plane waves.

[0084] We recall here that the formation of time channels consists of delaying the signals received by the different sensors (i.e. the data received at step 501). We then perform the sum of all the delayed signals in a given direction 0, to obtain a new signal. For example, for a direction 0, the new signal can be of the form:

[0085] In wideband, far-field pathforming, each new signal represents a wideband plane wave received in a given 0 direction.

[0086] In practice, it is possible to sample the new signal s k (u) to obtain for example M samples s k (u m ) with m=1,...,M. At the end of step 502, we therefore have a set of samples corresponding to different directions 0.

[0087] In a step 504, the samples obtained during the formation of broadband time channels are backpropagated to the points / pixels of the Cartesian grid of the image, using a migration (or backpropagation) method illustrated in Figure 4: a wave is emitted in a direction 0 from the point O. To determine the contribution of the received signal to the light intensity of the pixel P with coordinates (x,r), it is necessary to compensate for the travel time of the wave from O=(0,0) to P, which is also equal to the travel time between O and P', since P and P' are on the same wave plane. At the end of step 504, a set of delayed samples is therefore obtained, and each of these delayed samples corresponds to a contribution of a plane wave in a given direction to a pixel P(x,r) of the image.

[0088] The SAS image can then be reconstructed (step 505) from these backpropagated samples. In one or more embodiments, the intensity (i.e. the gray level) of the image of a given pixel corresponds to the sum of all the samples received for this pixel, after channel formation (502) and backpropagation (503).

[0089] In one or more embodiments, data relating to the actual movement of the antenna may be received at an optional step 502. As detailed previously, in the context of an on-board sonar system, the trajectory errors of the antenna relative to a theoretical trajectory may be significant and must be taken into account for the processing of the received data, in particular at the level of the channel formation step 503. It is noted that steps 501 and 502 may be carried out in this order, in the reverse order or in parallel.

[0090] There are methods in the prior art having a low computational cost for steps 503 and 504, thus allowing rapid data processing, reduced energy consumption and low weight of the computer.

[0091] In a particular embodiment, it is assumed that raw data (from step 501 of Figure 5) and possibly motion data (from step 502 of Figure 5) are available. The raw data are, for example, data in (x,r). For each pair of coordinates (x,r), and therefore for each pixel P of coordinates (x,r), a set of samples respectively associated with this pixel is therefore received. For the formation of broadband and far-field channels (step 502), it is possible to use the algorithm described in “A fast beamforming algorithm” by Kenneth M. Houston, IEEE Oceans Conference Record 1 (1994) 211-216.This algorithm proposes a fast channel formation method from wideband signals, which is significantly less computationally expensive than the conventional channel formation method (called sum-and-delay beamforming, or DSBF), in which the signals are delayed according to the calculated path differences and then summed. This algorithm is an iterative algorithm, in which a DSBF is first calculated for several subgroups of sensors and in a limited number of directions. Then, at each step, the channels from pairs of subgroups are combined and the number of directions considered is increased. This algorithm provides very satisfactory results, for a computational complexity of O(Nlog2N), while the conventional DSBF algorithm has a computational complexity of O(N. 2). Even though this algorithm was not developed for large antenna arrays and has not been used in this context until now, it proves to be particularly suitable for implementing step 503. By applying this algorithm, samples in (u,r) are obtained.

[0092] For plane wave backpropagation (step 504 in Figure 5), it is possible to use a Chirp-Z Transform (CZT), described for example in "Signal Processing Algorithms", Samuel Stearns and Ruth David, Prentice-Hall, Inc. The CZT is a transformation that allows a signal to be expanded or compressed by linear frequency modulation. It is known that this transformation can be expressed as a convolution product, and implemented by performing two consecutive Fast Fourier Transforms (FFTs). The computational complexity of this transformation is O(Nlog2N).

[0093] To implement the migration step 504, it is possible to successively apply to the data resulting from the formation of channels:

[0094] - a CZT on the orthogonal distance r: we then obtain data in (u,f);

[0095] - a CZT on the azimuth x: we then obtain data in (x,f); and

[0096] - an inverse Fourier transform on r: we recover data in (x,r).

[0097] The principle of CZT, and in particular the compression or expansion of signals, is shown in Figure 6.

[0098] Figure 6 represents the output signal of the channel formation step in the Fourier plane. Initially, the data 601 from the channel formation method 503 are represented by circles and are therefore located on a polar grid represented by solid lines. The circular arcs correspond to the different frequencies according to the Fourier diffraction theorem and the rays to the directions 0 of propagation of plane waves. To migrate these samples 601 to the pixels of a Cartesian grid (represented by dashes in the figure), it is necessary to perform:

[0099] - a dilation along the rays u until intersection with the Cartesian grid: we obtain the samples 602 represented by triangles; then

[0100] - a compression along a line of the Cartesian grid up to a point of the grid: we obtain the 603 samples represented by squares. The SAS image is then obtained by a two-dimensional Fourier transform. Unlike the prior art, the transition to a Cartesian grid is obtained only by 1D dilations, which are fast, and not complicated interpolations (like the Stolt interpolation) which are very expensive in terms of computation time.

[0101] Figures 7a and 7b respectively represent the point spread functions obtained by the Omega-k method on the one hand, and by an image reconstruction method according to an embodiment of the present invention on the other hand. It appears from these figures that the point spread function (or PSF) is much more spread out for the Omega-k algorithm than for the method according to the present invention, which means that the resolution of an imaging system according to the present invention is better than the resolution of an imaging system based on the Omega-k algorithm.This is due to the fact that the method according to the present invention uses broadband signals directly, while the Omega-k method uses a two-dimensional Fourier transform and not channel formation, and that an interpolation, so-called Stolt interpolation, is then necessary in the Fourier plane before the inverse Fourier transform, leading to a degradation of the PSF.

[0102] Indeed, an advantage of the method described in Figure 5 is that broadband plane waves can be calculated directly in the time domain for a deformed antenna array (which is the case for a towed sonar mounted on an autonomous underwater vehicle), if the deformations (i.e., trajectory errors) are known, for example, using a prior art motion estimation method. Thus, the method is more accurate than prior art methods that use narrowband signals.

[0103] Another advantage is that there are fast (in terms of computational cost) methods for performing steps 503 and 504 of Figure 5. For example, using an iterative algorithm like the one described in “A fast beamforming algorithm” by Kenneth M. Houston, IEEE Oceans Conference Record 1 (1994) 211-216 for step 503, and CZT transformations for step 504, the image reconstruction method shown in Figure 5 has a linearithmic computational complexity, i.e., in O(Nlog2N), i.e., of the same order of magnitude as the Omega-k algorithm. In comparison, the backprojection algorithm, which is a time-domain method incorporating exact path differences, has a quadratic complexity, i.e., in O(N 2 ). The invention thus provides a method that is both precise and rapid.

[0104] Figure 8 represents a schematic block diagram of an information processing device 800 for implementing one or more embodiments of the invention. The device 800 may comprise a memory 805 for storing instructions allowing the implementation of the method, the data from the received backscattered signal, and temporary data for carrying out the different steps of a method as described above.

[0105] The device may further comprise a circuit 804. This circuit may be, for example:

[0106] - a processor capable of interpreting instructions in the form of a computer program, or - an electronic card whose steps of the method of the invention are described in silicon, or

[0107] - a programmable electronic chip, such as an FPGA chip (for “Field-Programmable Gate Array” in English), a SOC (for “System On Chip” in English), a GPU (for “Graphics Processing Unit” in English), or an ASIC (for “Application Specific Integrated Circuit” in English).

[0108] SOCs, or systems on chips, are embedded systems that integrate all the components of an electronic system into a single chip. An ASIC is a specialized electronic circuit that combines custom features for a given application. ASICs are typically configured during manufacturing and can only be simulated by the user. Field-Programmable Gate Arrays (FPGAs) are electronic circuits that can be reconfigured by the user.

[0109] The device 800 may comprise an input interface 803 for receiving data from the backscattered signal, and an output interface 806 for providing the image of an object located on the seabed and / or location data for such an object. Finally, the computer may comprise, to allow easy interaction with a user, a screen 801 and a keyboard 802. Of course, the keyboard is optional, particularly in the context of a computer in the form of a touch pad, for example.

[0110] Depending on the embodiment, the device 800 may be a computer, a computer network, an electronic component, or other apparatus having a processor operably coupled to a memory, as well as, depending on the embodiment selected, a data storage unit, and other associated hardware such as a network interface and a media reader for reading and writing to a removable storage medium (not shown in the figure). The removable storage medium may be, for example, a compact disc (CD), a digital video / versatile disc (DVD), a flash drive, a USB flash drive, etc.

[0111] Depending on the embodiment, the memory, the data storage unit or the removable storage medium contains instructions which, when executed by the control circuit 804, cause this control circuit 804 to perform or control the input interface 803, output interface 806, data storage in the memory 805 and / or data processing parts according to one or more embodiments of the proposed method. Furthermore, the functional diagram presented in Figure 5 is a typical example of a program of which certain instructions can be carried out with the device 800. In this respect, Figure 5 can correspond to the flowchart of the general algorithm of a computer program within the meaning of the invention.

[0112] Of course, the present invention is not limited to the embodiments described above as examples; it extends to other variants. In particular, as mentioned above, the present invention is applicable in the context of conventional fixed antenna systems (sonar or radar), comprising a physical antenna comprising a transmitter and a plurality of sensors (receivers), in which a series of pulses are emitted and in which the return signals of these pulses are received by the different sensors. In this case, each phase center corresponds to the middle of the transmitter and each sensor. Thus, the present invention can be used in many other fields, such as ultrasonic medical imaging (ultrasound, Doppler, etc.).

[0113] Depending on the embodiment selected, certain acts, actions, events, or functions of each of the methods described herein may be performed or occur in a different order than they were described, or may be added, merged, or may not be performed or occur, as the case may be. In addition, in some embodiments, certain acts, actions, or events are performed or occur concurrently and not successively.

[0114] Although described through a number of detailed exemplary embodiments, the proposed method and the equipment for implementing the method include various variations, modifications and improvements which will be apparent to those skilled in the art, it being understood that these various variations, modifications and improvements are part of the scope of the invention, as defined by the claims which follow. In addition, different aspects and features described above may be implemented together, or separately, or substituted for each other, and all of the different combinations and sub-combinations of the aspects and features are part of the scope of the invention. Furthermore, some systems and equipment described above may not incorporate all of the modules and functions described for the preferred embodiments. Appendix A

[0115] We have:

[0116] By making the change of variable we can write:

[0117] The phase derivative

[0118] Using a stationary approximation of the phase, we obtain: where sgn{x) denotes the sign of the real number x.

[0119] We deduce from this:

[0120] Ignoring the slowly varying terms, we obtain the following approximation:

Claims

DEMANDS 1. A method for reconstructing an image of a scene by means of an antenna system, said image comprising a plurality of pixels, the method being implemented by computer and comprising, for each pixel among the plurality of pixels: a. receiving (501) samples of broadband time-domain signals backscattered by reflectors of the scene for one or more sensors of the antenna system; b. for each direction among a plurality of directions, calculating (503), from the samples received by said one or more sensors, new samples of a new time-domain signal respectively associated with said each direction, each new signal corresponding respectively to a broadband plane wave in said each direction; c.for each direction among the plurality of directions, select (504) from the new samples of the respective new time signal samples corresponding to a round-trip travel time of said new signal from an origin of the image to said each pixel; and d. determine (505) a light intensity of said each pixel from the selected samples.

2. Method according to claim 1, wherein the antenna system is a synthetic aperture radar or a synthetic aperture sonar.

3. Method according to claim 2, wherein the antenna system is an aperture synthesis sonar, and wherein the scene is a limited portion of a seabed.

4. A method according to any one of the preceding claims, further comprising a receiving (502) of data relating to a variation in motion of the system with respect to a theoretical trajectory, wherein the new samples of the new time signals are further calculated from said data.

5. A method according to any one of the preceding claims, wherein the new samples of the new time signals are calculated using a far-field, broadband time channel formation method.

6. Method according to claim 5, wherein the formation of the broadband and far-field time channels is based on an iterative algorithm.

7. A method according to any one of the preceding claims, wherein step c comprises an implementation of at least one Z-Chirp transform.

8. A method according to any one of the preceding claims, wherein the light intensity of said each pixel is a function of a sum of values ​​of the selected samples.

9. Device for reconstructing an image of a scene from data from an antenna system, said image comprising a plurality of pixels, the device comprising: an input interface for: a. receiving (501) samples of broadband time-domain signals backscattered by reflectors of the scene for one or more sensors of the antenna system; the device further comprising a circuit for implementing, for each pixel among the plurality of pixels: b. for each direction among a plurality of directions, calculating (503), from the samples received by said one or more sensors, new samples of a new time-domain signal respectively associated with said each direction, each new signal corresponding respectively to a broadband plane wave in said each direction; c.for each direction among the plurality of directions, select (504) from the new samples of the respective new time signal samples corresponding to a round-trip travel time of said new signal from an origin of the image to said each pixel; and d. determine (505) a light intensity of said each pixel from the selected samples.

10. Product computer program comprising instructions for implementing the process according to any one of claims 1 to 8, when this program is executed by a processor.

11. Non-transient computer-readable recording medium on which a program is recorded for the implementation of the method according to any one of claims 1 to 8 when this program is executed by a processor.

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