WO2023152434A1

WO2023152434A1 - Method for reconstructing an image of a scene

Info

Publication number: WO2023152434A1
Application number: PCT/FR2023/050108
Authority: WO
Inventors: Marc Pinto
Original assignee: Eca Robotics
Priority date: 2022-02-09
Filing date: 2023-01-27
Publication date: 2023-08-17
Also published as: FR3132584B1; FR3132584A1

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

DESCRIPTION

Title of the invention: Process for reconstructing an image of a scene

Technical area

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.

Prior technique

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 ships. Accurate imaging of submerged objects and/or the seabed makes it possible, in particular, to inspect structures and detect objects below the surface of the water, such as shipwrecks or underwater mines, underwater cables sailors or moving objects.

Unlike electromagnetic waves which are difficult to propagate 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 privileged 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, made up 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.

Inspired by work carried out in the field of radar (for "RAdio Detection And Ranging" in English), synthetic aperture sonar systems (or synthetic aperture sonar, or SAS, for "Synthetic Aperture Sonar" in English) began to emerge in the 1970s. The principle of an SAS system is to virtually increase the size of the antenna, by combining the signals resulting from the backscattering of successive sound pulses (also called "pings") , and thus improve the resolution of the sonar system. An example of an SAS system is shown in Figure 1a, as part of a towed linear antenna, mounted on an autonomous underwater vehicle (or AUV, for "autonomous underwater vehicle" in English) moving along a rectilinear trajectory 101 In an active SAS system, incident waves in the form of sound pulses are emitted from the linear antenna at different positions 103a, 103b, 103c, 103d along the path 101. When an incident wave interacts with an object 102, a fraction of this incident wave is returned in the direction from which it originated (backscatter phenomenon, or “backscatter” in English). 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 at the bottom of the sea. More precisely, by carrying out 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" large antenna (of LSA length much greater than the LR length of the actual antenna), which would be impossible to achieve for technical and cost reasons. The resolution of the SAS system is therefore greatly improved compared to a conventional sonar system.

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") , or “exploding reflector model” in English). 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 comprises only one point source, located for example at 102, the corresponding image is called the point spread function, or spatial impulse response, and is sufficient to fully characterize the imaging system, by the principle of superposition of linear systems.

Data processing in a SAS system requires precise knowledge of the path differences between the backscattered signals received at different positions of the antenna, and therefore in particular the movements of the autonomous underwater vehicle. However, such knowledge is difficult to obtain, as shown in FIG. 1b, which represents an example of a theoretical trajectory and an example of a real trajectory of an autonomous marine or submarine vehicle. In this example, the autonomous underwater vehicle 104 is assumed to follow a theoretical rectilinear trajectory 105 represented at the top of FIG. 1b. Due to parasitic movements (for example, yaw, pitch, yaw, etc.) related to the aquatic environment, the real trajectory 106 actually followed by the vehicle 104 can be very different from the theoretical trajectory 105, as represented at the bottom of the Figure 1b. In addition to the curvature of the actual trajectory 106, it is noted that the vehicle 104 can be oriented along an axis making an angle α with respect to the direction of the nominal trajectory, as shown in Figure 1b. Such an angle can 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 the trajectory errors, that is to say the differences between the real trajectory 106 and the theoretical trajectory 105 followed by the vehicle 104, as well as the attitudes of the vehicle (for example the angle a represented 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 of forming images from the collected data can integrate them effectively.

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

Temporal methods, such as the backprojection algorithm (or "backprojection" in English), also called spatial filtering by delay and summation (or "delay and sum beamforming" in English), advantageously integrate all the determined path differences, leading thus to a very precise reconstruction of the seabed and the object. Overall, the back-projection algorithm is based on the calculation of 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 to the considered image pixel. In what follows, such an application of a delay to a signal to compensate for its propagation time is called “backpropagation”, “backprojection” or even “migration” (terminology borrowed from the field of seismic). In the migration algorithm, the received signals are modeled by cylindrical or spherical waves, which are migrated towards the place where the source is supposed to be located and that we sum, to obtain a new signal whose energy we can then calculate in order to deduce the scattering power of the source (and therefore the intensity of the pixel of the image associated with this source). Such methods are very computationally expensive. Indeed, because of the curvature of the wave surfaces, it is not possible to migrate the waves towards an entire group of pixels at the same time, for example an entire row or an entire column of the image. It is necessary to restart the migration, and the associated interpolations, for each pixel of the image, which requires a computer having a weight and a high energy consumption. These constraints are not acceptable in the context of applications on board autonomous marine or submarine vehicles.

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

There is therefore a need for an image formation method which is both fast, precise, and low energy consumption, to be implemented within a SAS system embedded in an autonomous vehicle provided with limited resources. .

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 accuracy. Furthermore, even if the invention is particularly advantageous in the context of synthetic aperture antenna systems, it is applicable for 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 ultrasonic medical imaging.

Disclosure of Invention

To respond to 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 domain temporal, thanks to a broadband and far-field temporal channel formation method. 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 wideband signals is well suited to sonar signals (as well as to certain radar systems), and therefore allows more accurate results than the methods of the prior art based on narrowband signals. The proposed method is therefore both accurate and inexpensive in terms of calculations.

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 : has. receiving broadband temporal signal samples backscattered from reflectors in 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 wide plane wave tape in said each direction; vs. for each direction among the plurality of directions, selecting, among the new samples of the respective new temporal signal, samples corresponding to a round trip 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. “Antenna system” means a system comprising a physical antenna, or a synthetic aperture antenna system. By “scene”, it is understood a portion of the space of which one seeks to reconstruct an image. For example, in the case of a sonar system with synthetic antenna, the scene can designate a limited portion of the seabed, of which one wishes to obtain an image. Alternatively, it may be desired to obtain a continuous image of the seabed, in which case this bottom is cut beforehand into limited portions, the images of which are obtained as described previously and then juxtaposed to produce a continuous image.

The present invention advantageously uses broadband signals, and makes it possible to obtain more precise results than methods which presuppose narrowband signals, this assumption often not being valid in many applications such as seabed imaging. For example.

It is noted that step b typically corresponds to a channel formation step, which is a technique well known in the field of antenna processing for locating sources, during which the signals received by the various sensors are combined. so as to form new signals associated with a set of given directions. Lane formation consists of compensating for the 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 outward and return 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 in the same place. The phase center corresponds to the midpoint between the position in space occupied by the transmitter at the time of emission and that occupied by the receiving sensor at the time of reception of the echo of the object 102. This approximation makes it possible to simplify the disclosure of the invention but it is by no means mandatory. It is also possible to calculate exact 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 so-called far-field method of channel formation. 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 performed in the near field in the vast majority of cases. For many high-resolution sonar systems, object 102 is a few hundred meters from the sonar while the far field of the synthetic antenna is several kilometers away. It is for this reason that all the temporal methods of the prior art use spherical or cylindrical waves, that is to say so-called near-field channel formation methods, which alone make it possible to obtain in a single stage a properly focused image. In the invention, the formation of channels in the far field is only a second step b, the focused image being produced only in the next step c. The decomposition into plane waves does not aim to focus an image but to reduce the computational load.

Stage c corresponds to a migration of the plane waves thus formed towards the pixels of the image where the sources which 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 spherical or cylindrical waves received, which proves to be much more efficient in computation time because the migration can be carried out simultaneously for all the pixels of a line or a column of the image by a simple expansion of the signal, without there being any need to start the migration again for each pixel.

The luminous intensity of a pixel can correspond to its gray level.

Such a method advantageously makes it possible to construct an image of a scene observed by a synthetic aperture system in a rapid, precise manner and with low energy consumption.

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

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

In one or more embodiments, the method may further comprise receiving data relating to a variation in movement of the system relative to a theoretical trajectory. The new samples of the new time signals can then further be calculated from said data. Furthermore, since the processing is done in the time and non-frequency domain, these motion variations can themselves vary rapidly over time without the computational load being affected.

Thus, the method advantageously integrates the motion errors and their variation over time, and provides much more precise results than the frequency methods which have great difficulty in dealing with the dynamic deformations of the synthetic antenna. In one or more embodiments, the new samples of the new time signals may be computed using a broadband, far-field time channeling method.

In these embodiments, the channel formation method is based on the assumption that the sources are located in the far field, that is to say far enough from the sensors for the wave front of the signals received to be considered. as blueprint.

For example, the formation of broadband and far-field temporal channels can 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 similar algorithms that are known to those skilled in the art.

As described below, this algorithm has O(Nlog2N) computational complexity, while time channeling methods typically have O(N ² ) computational complexity. Such an algorithm therefore makes it possible to implement step b rapidly.

In one or more embodiments, step c can comprise an implementation of at least one Z-Chirp transform, which is a transform making it possible to expand or compress a signal in an effective manner.

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

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.

Another aspect of the invention relates to a device for reconstructing an image of a scene from data coming from a synthetic aperture antenna system, said image comprising a plurality of pixels. This device may include: an input interface for: a. receiving broadband time signal samples backscattered from reflectors in the scene for one or more sensors of the antenna system.

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 temporal signal respectively associated with said each direction, each new signal respectively corresponding to a broadband plane wave in said each direction; vs. for each direction among the plurality of directions, selecting, among the new samples of the respective new temporal signal, samples corresponding to a round trip 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.

The device for reconstructing an image can be integrated into the synthetic aperture antenna system, or be a device separate from the synthetic aperture antenna system.

A computer program, implementing all or part of the method described above, installed on pre-existing equipment, is in itself advantageous, since it makes it possible to obtain an image of the scene in a precise manner and with a relatively low computational cost.

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.

This program can use any programming language (for example, an object language or other), and be in the form of interpretable source code, partially compiled code or fully compiled code.

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

Another aspect relates to a non-transitory recording medium of a computer-executable program, comprising a set of data 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 operationally coupled to memory means and to an input/output interface module, to execute all or part of the method described above.

Brief description of the drawings Other characteristics, details and advantages of the invention will appear on reading the detailed description below. This is purely illustrative and should be read in conjunction with the attached drawings, on which:

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

[Fig. 1b] Figure 1b 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;

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

[Fig. 3] Figure 3 is an illustration of Fourier's diffraction theorem;

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

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

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

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

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

detailed description

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

Figure 2 shows an example of a coordinate system that can be used to describe the motion of the sonar phase center C in embodiments of the invention. In Figure 2, point S represents the source of the signal received by one of the sensors of the antenna. By "source", it is understood a point of the observed scene (i.e. space insonified by the synthetic antenna) from which one wishes to obtain an image, each pixel of the image corresponding for example to the power of the field diffused 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 supposed, 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 displacement 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 the SAR literature in English. The coordinate system shown is a cylindrical coordinate system in which the axis of the cylinder corresponds to the axis of the path (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 θ′ formed between the axis (Ox) of displacement of the sonar and the direction of the center C towards the source S is commonly called “bearing”, and we denote θ=TT-9′ its additional 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 an arbitrarily chosen point on the axis of sonar movement.

As mentioned above, most of the imaging methods for SAS systems are derived from methods originally developed for radar signals, within the framework 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 to be narrowband if the time taken by a plane wave to insonify the entire antenna (ie the difference between the time taken by the wave to insonify the sensor of the antenna furthest from the source and the time taken by the wave to insonify the sensor of the antenna closest to the source) is very small in front of the duration of the sound pulse (ie the duration of the ping). In this case, it is considered that all the sensors of the antenna are insonified approximately at the same time. For example, it can be considered that this approximation is valid when the ratio between the time taken by a plane wave to insonify the whole of the antenna and the duration of the sound pulse is less than 0.1. The above condition is often verified in the radar domain (although in some cases it is not applicable), so methods used in SAR imagery relying on narrowband signals generally provide good results. However, it is generally not applicable in the sonar field.

Prior art frequency methods used in SAS systems, which are mainly based on the Fourier diffraction theorem, use narrowband signal modeling. The principle of Fourier's diffraction theorem is described for example in chapter 6 of the book "Principles of Computerized Tomography Imaging" by Avinash C. Kak and Malcolm Slaney, collection "Classics in applied mathematics, 33" or in chapter 3 of the thesis from Malcolm Slaney "Imaging with diffraction tomography" defended at Purdue University, and is represented in Figure 3.

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, one is interested in the backscattered field, but the principle remains the same as for a diffused field. The Fourier diffraction theorem states 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 an arc of circle 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 relies on monochromatic plane waves 302, and therefore applies to narrowband signals.

However, as mentioned above, for sonar signals, the condition for approximating the signals received by narrow band signals is generally not verified. Also, methods that use narrowband signals (such as prior art frequency methods such as the ω-k algorithm) are actually poorly suitable for 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 relies on a new writing of the problem from broadband signals, which is now detailed.

In what follows, capital 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.

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

Initially, it is assumed that the variables studied are continuous and come from a narrow band signal, for example a monochromatic continuous wave of wavenumber k, with k = 2π/λ, λ being the length of wave.

The signal H _k (x,r) received by the sonar phase center when the latter is located at a distance x from the point O on the axis (Ox) from a source located at an orthogonal distance r on the axis (Or) (ie having an azimuth x = 0 and an orthogonal distance r, which corresponds to point S' in Figure 2) can be expressed, ignoring propagation losses:

where 0 is the angle defined with reference to Figure 2, u = sin0 and B(u, k) is the round-trip sonar directivity diagram (or "beam pattern") of the wave of number of k-wave.

The time t and the angular frequency co, as well as the orthogonal distance r = ct/2 and the variable k = 2ω/c (C being the speed of sound), the orthogonal distance r and the variable k' = 2k, or even the variable u derived from the bearing 0 (u = sin 0) and the length of the scaled sensor array x' = 2kx, are four examples of pairs of conjugate (or dual) Fourier variables commonly used in the field of signal processing. According to these notations, we define the angular spectrum in narrow-band plane waves G(u, r, k) as follows:

As detailed in Appendix A, it can be shown, using a stationary phase approximation, that:

with v = cos 0.

This makes it possible to extend the cylindrical stationary wave coming from S' to a family of outgoing plane waves moving towards the sonar:

where F*, ¹ denotes the one-dimensional inverse Fourier transform associated with the dual variables u and x' = 2kx.

Let W(u, k) be the narrowband plane wave angular spectrum of the raw narrowband data D(x, k) defined by:

where the D(x, k) represent the raw data resulting from the backscattering of the monochromatic plane wave of wave number k emitted at point O (ie when x = 0) and received when the phase center is located at a distance x from point O on the axis (Ox), and where F _xl designates the one-dimensional fast Fourier transform associated with the dual variables u and x' = 2kx.

From matched filtering theory and the convolution theorem, we get 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 pixel of the image having coordinates (x, r) in the system coordinates in Figure 2.

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

The principle of the migration of a plane wave is represented in Figure 4. In this figure, it is assumed that the plane wave comes from the 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 plane of wave. 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", it is therefore understood an application of a phase shift to compensate for the round trip travel time of the wave to go from its point O of emission to the point P.

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 back-propagation all the components W(u, k) of the wideband signal (i.e. all the narrowband plane waves resulting from the decomposition of the wideband signal) to which a weighting has been applied by a narrowband directivity diagram B(u , k).

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 performing a weighting of these narrow band waves followed by a migration towards each point P of coordinates (x, r) of the image. This migration can be performed as detailed above, i.e. by applying a phase shift corresponding to the round-trip travel time from O to P in the direction 0, which is equal to 2(xu + rv)/c .

Let w(u, r) be the angular broadband plane wave 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) is defined as follows:

We also introduce the following function b(u,r):

where B(u, k) is the directivity diagram defined previously.

The convolution product of b(u, r) and w(u, r) can be written:

which means that the weighting of the plane waves at narrow band by B(u, k) corresponds in wide band to a filtering of the angular spectrum by the function b(u,r).

We deduce that the broadband SAS image i(x, r) can be obtained directly by carrying out a back-propagation of the broadband plane waves, previously filtered by b(u,r), towards each point P of coordinates (x, r) picture:

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

It is recalled here that the formation of channels (or formation of beams, or "beamforming" in English) 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 form the The most classic way of forming channels in the time domain, called spatial filtering by delay and summation (or "delay and sum beamforming" in English), consists in delaying the signals received by the various sensors of the antenna, and summing the set of delayed signals.

Channel 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 wave fronts 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 oblique distance of the signal corresponding to the plane wave equal to the pitch between the lines of the image to carry out the migration without any calculation.

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 the theorem of Thales. 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 make a dilation of the signal of this factor which depends on 0.

We deduce a new method of processing signals from a synthetic aperture system, an embodiment of which is shown in Figure 5.

First of all, broadband raw data is received at the level of the various sensors of the antenna (step 501 of FIG. 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 the number of samples of the source signal received per sensor. These data are time data.

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 the 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, we can consider that the signal is stationary on during each snapshot k. The signal received during a snapshot k can be sampled at a frequency F _e respecting Shannon's theorem, which makes it possible 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

Then, at step 503, new wideband time signals are determined from the data received, by applying a method of forming broadband and far-field temporal channels. In the far field, the wavefronts can be considered plane, so that the new temporal signals correspond to plane waves.

It is recalled here that the formation of time channels consists in delaying the signals received by the various sensors (ie the data received at step 501 ). The sum of all the signals delayed in a given direction 0 is then performed to obtain a new signal. For example, for a 0 direction, the new signal can be of the form:

In broadband and far-field channel formation, each new signal represents a broadband plane wave received in a given 0-direction.

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, there is therefore a set of samples corresponding to different directions 0.

At a step 504, the samples obtained during the formation of broadband temporal channels are back-propagate towards the points/pixels of the Cartesian grid of the image, thanks to a migration method (or back-propagation) illustrated in FIG. 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 of coordinates (x,r), it is necessary to compensate the travel time of the wave by 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 picture.

The SAS image can then be reconstructed (step 505) from these back-propagated 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 formation of channels (502) and backpropagation ( 503).

In one or more embodiments, data relating to the actual movement of the antenna can be received at an optional step 502. As detailed previously, within the framework of an onboard sonar system, the trajectory errors of the antenna with respect to a theoretical trajectory can be significant and must be taken into account for the processing of the data received, in particular at the level of the step 503 of formation of channels. Note that steps 501 and 502 can be performed in this order, in reverse order, or in parallel.

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

In a particular embodiment, it is assumed that raw data (resulting from step 501 of FIG. 5) is available, and possibly movement data (resulting from step 502 of FIG. 5). 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 broadband and far-field beamforming (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 offers a fast method of forming beams from broadband signals, significantly less expensive in terms of calculations than the conventional beamforming method (called "sum-and-delay beamforming" in English, or DSBF), in which the signals are delayed according to the calculated and then summed rate differences. 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 pathways 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), whereas the conventional DSBF algorithm has a computational complexity of O(N ² ). Even if this algorithm has not been developed for large antenna arrays and has not been used in this context up to now, it proves to be particularly suitable for implementing step 503. By applying this algorithm, we obtain samples in (u,r).

For the backpropagation of the plane waves (step 504 of FIG. 5), it is possible to use a Z-Chirp transform, or CZT (for “Chirp-Z Transform”), described for example in “Signal Processing Algorithms », Samuel Stearns and Ruth David, Prentice-Hall, Inc. The CZT is a transformation allowing to expand or compress a signal 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 (or FFTs). The computational complexity of this transformation is in O(Nlog2N).

To implement the migration step 504, it is possible to successively apply to the data resulting from the channel formation:

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

- a CZT on the azimuth x: we then obtain data in (x,f); And

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

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

FIG. 6 represents the output signal of the channel formation step in the Fourier plane. Initially, the data 601 resulting 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 Fourier's diffraction theorem and the rays to the 0 directions of plane wave propagation. To perform the migration of these samples 601 towards the pixels of a Cartesian grid (represented by dashes in the figure), it is necessary to perform:

- an expansion along the rays u up to intersection with the Cartesian grid: the samples 602 represented by triangles are obtained; Then

- a compression along a line of the Cartesian grid up to a point of the grid: the samples 603 represented by squares are obtained. The SAS image is then obtained by a two-dimensional Fourier transform. Contrary to the prior art, the transition to a Cartesian grid is obtained only by 1D expansions, which are rapid, and not by complicated interpolations (such as the Stolt interpolation) which are very costly in computation time.

FIGS. 7a and 7b represent respectively the spread functions of the point 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, for "point spread function" in English) is much more spread 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 process according to the present invention uses broadband signals directly, while the Omega-k method uses a two-dimensional Fourier transform and not lane formation, and an interpolation, called Stolt interpolation, is then necessary in the Fourier plane before the inverse Fourier transform, leading to a degradation of the PSF.

Indeed, an advantage of the method described in Figure 5 is that the 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 underwater vehicle). autonomous sailor), if the deformations (i.e. the trajectory errors) are known, for example by using a motion estimation method of the prior art. Thus, the method is more accurate than prior art methods which use narrowband signals.

Another advantage is that there are fast methods (in terms of computational cost) to perform steps 503 and 504 of Figure 5. For example, using an iterative algorithm like the one described in "A fast beamforming algorithm" of 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 linear computational complexity, i.e. in O(Nlog2N), ie of the same order of magnitude as the Omega-k algorithm. In comparison, the back-projection algorithm, which is a temporal method integrating the exact path differences, has a quadratic complexity, ie in O(N ² ). The invention thus proposes a method that is both precise and rapid.

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

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

- 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 else

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").

SOCs or system on a chip are embedded systems that integrate all the components of an electronic system into a single chip. An ASIC is a specialized electronic circuit that groups functionalities tailored to a given application. ASICs are usually configured when manufactured and can only be simulated by the user. Programmable logic circuits of the FPGA (Field-Programmable Gate Array) type are electronic circuits reconfigurable by the user.

The device 800 may include an input interface 803 for receiving data from the backscattered signal, and an output interface 806 for supplying the image of an object located at the bottom of the sea and/or data from location of such an object. Finally, the computer can include, to allow easy interaction with a user, a screen 801 and a keyboard 802. Of course, the keyboard is optional, especially in the context of a computer in the form of a touch pad, For example.

Depending on the embodiment, the device 800 can be a computer, a computer network, an electronic component, or another device comprising a processor operatively coupled to a memory, as well as, according to the chosen embodiment, a data storage unit, and other associated hardware such as a network interface and a media drive for reading removable storage media and writing to such media (not shown in the figure). The removable storage medium can be, for example, a compact disc (CD), a digital video/versatile disc (DVD), a flash disc, a USB key, etc.

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

Of course, the present invention is not limited to the embodiments described above by way of examples; it extends to other variants. In particular, as mentioned above, the present invention is applicable in the context of conventional fixed antenna (sonar or radar) systems, 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 various sensors. In this case, each phase center corresponds to the middle of the emitter and of each sensor. Thus, the present invention can be used in many other fields, such as ultrasonic medical imaging (echography, Doppler, etc.).

Depending on the chosen embodiment, certain acts, actions, events or functions of each of the methods described in this document may be performed or occur in a different order from that in which they were described, or may be added, merged or else not be effected or not occur, as the case may be. Further, in some embodiments, certain acts, actions or events are performed or occur concurrently and not sequentially.

Although described through a certain number of detailed exemplary embodiments, the proposed method and the equipment for implementing the method include various variants, modifications and improvements which will appear obvious to those skilled in the art, it being understood that these various variants, modifications and improvements form part of the scope of the invention, as defined by the following claims. Additionally, various aspects and features described above may be implemented together, or separately, or substituted for each other, and all of the various combinations and sub-combinations of aspects and features are within the scope of the 'invention. Further, some systems and equipment described above may not incorporate all of the modules and functions described for the preferred embodiments. Annex A

We have :

By making the change of variable we can write:

The derivative of the phase

Using a stationary approximation of the phase, we get:

where sgn(x) denotes the sign of the real x.

We can deduce :

By ignoring the terms which vary slowly, we obtain the following approximation:

Claims

1. 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 (501) samples of wideband 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 (503), 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 wave planar broadband in said each direction; vs. for each of the plurality of directions, selecting (504), from among the new samples of the respective new time signal, samples corresponding to a round trip time of said new signal from an origin of the image to said each pixels; and D. determining (505) a light intensity of said each pixel from the selected samples.

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

3. Method according to claim 2, in which the antenna system is a synthetic aperture sonar, and in which the scene is a limited portion of a seabed.

4. Method according to one of the preceding claims, further comprising a reception (502) of data relating to a variation of movement of the system with respect to a theoretical trajectory, in which the new samples of the new temporal signals are further calculated at from said data.

5. Method according to one of the preceding claims, in which the new samples of the new temporal signals are calculated using a broadband and far-field temporal channel formation method.

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

7. Method according to one of the preceding claims, in which step c comprises an implementation of at least one Z-Chirp transform.

8. Method according to one of the preceding claims, in which 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 coming from an antenna system, said image comprising a plurality of pixels, the device comprising: an input interface for: a. receiving (501) samples of wideband temporal signals backscattered by reflectors of the scene for one or more sensors of the antenna system; the device further comprising circuitry for implementing, for each of 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 temporal signal respectively associated with said each direction, each new signal corresponding respectively to a wave planar broadband in said each direction; vs. for each of the plurality of directions, selecting (504), from among the new samples of the respective new time signal, samples corresponding to a round trip time of said new signal from an origin of the image to said each pixels; and D. determining (505) a light intensity of said each pixel from the selected samples.

10. Computer program product comprising instructions for implementing the method according to one of claims 1 to 8, when this program is executed by a processor.

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