FR3132584A1 - Process for reconstructing an image of a scene - Google Patents

Abstract

The present invention relates to a method for reconstructing an image of a scene by an antenna system and comprising, for each pixel of the image: a. receive broadband temporal signal samples backscattered from stage reflectors; b. for each of a plurality of directions, determining, from the received samples, new samples of a new time 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 delayed samples. [Fig. 5]

Description

Process for reconstructing an image of a scene

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.

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. Precise imaging of submerged objects and/or the seabed makes it possible to inspect structures and detect objects under the water surface, such as ship wrecks or underwater mines, underwater cables. sailors or moving objects.

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”, in English) have thus become favored 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 for 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 a SAS system is to virtually increase the size of the antenna, by combining signals from the backscattering of successive sound pulses (also called “pings” in English). , and thus improve the resolution of the sonar system.

An example of a SAS system is shown in the , 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. As part of 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, 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” antenna of large size (of length L _SA much greater than the length L _R of the real antenna), which it 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 the 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 seismics 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 in the real case and the one-way trip in the fictitious case. The imagery is then akin to the reconstruction of a field of such sources. When this field includes 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 completely 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 antenna positions, and therefore in particular the movements of the autonomous underwater vehicle. However, such knowledge is difficult to obtain, as shown in the , 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 supposed to follow a theoretical rectilinear trajectory 105 represented at the top of the . Due to parasitic movements (for example, yaw, pitch, yaw, etc.) linked to the aquatic environment, the real trajectory 106 actually followed by the vehicle 104 can be very different from the theoretical trajectory 105, as shown at the bottom of the . In addition to the curvature of the real 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 the . 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 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 α represented at the bottom of the ). These methods make it possible to determine the positions of the antenna and the successive path differences precisely. However, knowledge of these elements is not sufficient; the methods for forming images from the collected data must also be able to integrate them effectively.

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

Temporal methods, such as the backprojection algorithm, also called spatial filtering by delay and sum beamforming, advantageously integrate all the determined path differences, leading thus to a very precise reconstruction of the seabed and the object. Overall, the rear 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 at 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 even “migration” (terminology borrowed from the field of seismics). 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 which are summed, to obtain a new signal from which we can then calculate the energy in order to deduce the diffusion 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, we cannot 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 calculator with a high weight and energy consumption. These constraints are not acceptable in the context of on-board applications on autonomous marine or underwater vehicles.

On the other hand, frequency methods, such as the Omega-k (or ω-k) algorithm, are much faster because they require much less calculations 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 movement. For this reason, frequency methods have difficulty taking into account antenna deformations (i.e. the trajectory and angle errors mentioned above) and even more difficult their variation over time, i.e. 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 worse than those of temporal methods.

There is therefore a need for an image formation method that is both fast, precise, and low energy consumption, to be implemented within a SAS system onboard an autonomous vehicle 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 precision. 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 particularly used in ultrasound medical imaging.

To respond to at least one of the problems mentioned above, the invention proposes to decompose broadband signals received by a sonar or radar system with a synthetic antenna from a source into a plurality of broadband plane waves in the domain temporal, using a broadband and far-field temporal channel forming 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 temporal 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 some radar systems), and therefore allows more precise results than prior art methods relying on narrowband signals. The proposed method is therefore both precise and inexpensive in terms of calculations.

A method is thus proposed 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. receive samples of broadband temporal signals backscattered from reflectors in the scene to one or more sensors of the antenna system;

b. for each direction among a plurality of directions, calculate, 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 strip 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. determine 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”, we mean a portion of the space of which we seek to reconstruct an image. For example, in the case of a sonar system with a synthetic antenna, the scene can designate a limited portion of the seabed, of which we want to obtain an image. Alternatively, one may wish to obtain a continuous image of the seabed, in which case this bottom is cut beforehand into limited portions, images of which are obtained as described previously and then juxtaposed to make a continuous image.

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

It is noted that step b typically corresponds to a channel 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. Lane formation involves compensating for differences in path between sensors in given directions. In synthetic antenna processing, which uses signals received from several successive transmissions, it is necessary to compensate for these differences in operation 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 the said object, as if The transmission and reception took place at the same place. The phase center corresponds to the midpoint between the position in space occupied by the transmitter at the time of transmission and that occupied by the receiving sensor at the time of reception of the echo from the object 102. This approximation makes it possible to simplify the presentation of the invention but it is in no way obligatory. It is also possible to accurately calculate 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 carried out 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 methods of forming channels known as near field, which alone make it possible to obtain in a single stage a properly focused image. In the invention, the formation of far-field channels is only a second step b, the focused image being produced only in the next step c. The plane wave decomposition does not aim to focus an image but to reduce the computational load.

Step 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 turns out to be much more efficient in calculation time because the migration can be carried out simultaneously for all the pixels of a row or column of the image by a simple dilation of the signal, without the need to restart the migration for each pixel.

The light 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 an aperture synthesis system quickly, precisely and with low energy consumption.

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

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

In one or more embodiments, the method may further include 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 be further calculated from said data. Furthermore, as 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 movement errors and their variation over time, and provides much more precise results than 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 temporal signals may be calculated using a wide-band, far-field temporal channeling method.

In these embodiments, the channel formation method is based on the hypothesis that the sources are located in the far field, that is to say sufficiently far from the sensors so that the wave front of the signals received can be considered as a plan.

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 algorithms of the same nature which are known to those skilled in the art.

As described below, this algorithm has a computational complexity of O(Nlog ₂ N), while temporal pathway forming methods typically have a computational complexity of O(N ² ). Such an algorithm therefore makes it possible to implement step b quickly.

In one or more embodiments, step c may include an implementation of at least one Z-Chirp transform, which is a transform making it possible to expand or compress a signal efficiently.

The Z-Chirp transform also has a computational complexity of O(Nlog ₂ N), 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:

has. receive samples of broadband temporal signals backscattered from reflectors in the scene to 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, calculate, 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 strip 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. determine a light intensity of said each pixel from the selected samples.

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

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 low computational cost.

Thus, the present invention also targets a computer program comprising instructions for implementing the method described above, when this program is executed by a processor.

This program may 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.

There 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, during the 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.

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

There represents an example of a synthetic aperture sonar system;

There illustrates an example of a theoretical trajectory and a real trajectory of an autonomous underwater vehicle on which an antenna is mounted as part of a synthetic aperture sonar system;

There shows an example of a coordinate system that can be used to describe the movement of the sonar phase center C in embodiments of the invention;

There is an illustration of Fourier's diffraction theorem;

There represents an example of migration of a plane wave towards a pixel of the image;

There is a flowchart of a process for reconstructing the image of an object according to one or more embodiments;

There represents the samples of the signal in the Fourier plane at different stages of the migration, according to one or more embodiments;

And Figures 7a and 7b respectively represent the point spreading 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. go ;

There represents a schematic block diagram of an information processing device for implementing 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 underwater vehicle, follows a theoretical uniform rectilinear movement. 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, theoretically moves at constant speed along an axis (Ox). The trajectory errors presented previously and illustrated in are assumed to be known, for example thanks to 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.

There represents an example of a coordinate system that can be used to describe the movement of the sonar phase center C in embodiments of the invention. On the , the point S represents the source of the signal received by one of the antenna sensors. By “source” is meant a point of the observed scene (ie 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 diffused by a point in this scene. For example, the source may correspond to a point on an object located at the bottom of the water. According to the example of the , 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 sonar movement is commonly called "azimuth" in the English SAR literature. 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 trajectory (Ox). Due to the symmetry of revolution around the axis (Ox), the study of 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 movement of the sonar and the direction of the center C towards the source S is commonly called "bearing", and we note θ = π-θ' its additional angle. It is noted that O can correspond, for example, to the initial position of the sonar (ie 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.

As mentioned above, most imaging methods for SAS systems are derived from methods initially developed for radar signals, as part of SAR systems. In the radar field, the signals used are generally considered to be narrowband. We recall that a signal can be considered to be narrow band if the time it takes a plane wave to insonify the entire antenna (i.e. 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 sonify the sensor of the antenna 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, we consider that all the sensors of the antenna are insonified approximately at the same time. For example, we can consider that this approximation is valid when the ratio between the time it takes a plane wave to insonify the entire 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 the methods used in SAR imaging 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 primarily based on Fourier's diffraction theorem, use narrow-band signal modeling. The principle of Fourier's diffraction theorem is described for example in chapter 6 of the book "Principles of Computerized Tomographic Imaging" by Avinash C. Kak and Malcolm Slaney, collection "Classics in applied mathematics, 33" or in chapter 3 of the thesis of Malcolm Slaney “Imaging with diffraction tomography” supported at Purdue University, and is represented on the .

On this , 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 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 is based on monochromatic plane waves 302, and therefore applies to narrow band 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 narrow-band signals (such as prior art frequency methods 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 using broadband signals is thus proposed. This new method is based on a new writing of the problem using broadband signals, which is now detailed.

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.

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

Firstly, it is assumed that the variables studied are continuous and come from a narrow-band signal, for example a monochromatic continuous wave of wave number , with , being the wavelength.

The signal received by the phase center of the sonar when it is located at a distance from point O on the axis ( ) from a source located at an orthogonal distance on the axis (ie having an azimuth and an orthogonal distance , which corresponds to point S' of the ) can be expressed, if we ignore the propagation losses:

Or is the angle defined with reference to Figure 2 , And is the directivity diagram (or “beam pattern” in English) round-trip sonar of the wave number .

The weather and the angular frequency , as well as the orthogonal distance and the variable ( being the speed of sound), the orthogonal distance and the variable , or the variable derived from the deposit ( ) and the length of the scaled sensor array , 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 as following :

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

with .

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

Or denotes the one-dimensional inverse Fourier transform associated with dual variables And .

Either the narrow-band plane-wave angular spectrum of the narrow-band raw data defined by :

where the represent the raw data from the backscattering of the monochromatic plane wave of wave number emitted at point O (ie when ) and received when the phase center is located at a distance from point O on the axis ( ), and or denotes the one-dimensional fast Fourier transform associated with dual variables And .

From the theory of matched filtering and the convolution theorem, we obtain the following expression for the narrow-band SAS image :
Or denotes the conjugate of And corresponds to the intensity (or gray level) for the pixel of the image whose coordinates in the coordinate system of the .

It appears from this formula that the narrow-band SAS image can be obtained by weighting the angular spectrum by , then by performing a migration (or backpropagation) of the narrow-band plane waves towards each point (or pixel) P with coordinates of the image, by application to of a phase shift of , which can be associated with the propagation delay corresponding to the round trip travel time of the plane wave originating from point O and heading in the direction and the pixel P.

The principle of plane wave migration is shown 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 θ with the axis (Or), the direction 401 being orthogonal to the wave front 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 , with And . Thus, for the round trip of the plane wave from its emission at O and its reception at ( ), the total distance is equal to . 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 point P.

The broadband SAS image can be obtained in an elementary way by linear superposition of the components of the narrow-band SAS image, that is to say by backpropagating all the components of the broadband signal (ie all the narrow-band plane waves resulting from the decomposition of the broadband signal) to which weighting has been applied by a narrow-band directivity diagram .

In other words, the broadband SAS image can be obtained by decomposing the broadband signal into a plurality of monochromatic plane waves (ie narrow band), then by carrying out a weighting of these narrow band waves followed by a migration towards each point P of coordinates of the image. This migration can be carried out as detailed above, that is to say by application of a phase shift corresponding to the round trip travel time from O to P in the direction , which is worth .

Either the broadband plane wave angular spectrum, defined as follows:

Or represents the one-dimensional inverse Fourier transform associated with dual variables And .

Similarly, broadband raw data are defined as follows:

We further introduce the function next :

Or is the directivity diagram defined previously.

The convolution product of And can be written:

which means that the weighting of narrow-band plane waves by corresponds in broadband to a filtering of the angular spectrum by the function .

We deduce that the broadband SAS image can be obtained directly by carrying out a backpropagation of broadband plane waves, previously filtered by , towards each point P with coordinates of the image :

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

We recall 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. . The most classic form of channel formation in the time domain, called spatial filtering by delay and sum beamforming, consists of delaying the signals received by the various sensors of the antenna, and sum all the delayed signals.

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) that propagates in the direction perpendicular to the Ox trajectory. 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 Thales' theorem. The distance between these two pixels, once projected in the direction of propagation of the wave, is smaller by a factor . It will therefore be necessary, to migrate a plane wave on a column of the image, to dilate the signal by this factor which depends on .

We deduce from this a new method of processing signals from a synthetic aperture system, an embodiment of which is represented in the .

First of all, raw broadband data is received at the various sensors of the antenna (step 501 of the ). In one or more embodiments, this raw data is received in the form of an N×P matrix, where P is the number of antenna sensors, and N the number of source signal samples received per sensor. This data is temporal 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:

Or is the propagation time taken by the wave between the source and the sensor p, and models the ambient noise on the sensor p at time t. This signal can be segmented into blocks (called “snapshots” in English) of the same duration , with . Typically, we can consider that the signal is stationary during each snapshot k. The signal received during a snapshot k can be sampled at a frequency respecting Shannon's theorem, which allows us to obtain values received on each sensor during a snapshot k. The N-tuple of values for each sensor forms a vector of dimension N×1. The raw data received in step 501 can then correspond to the concatenation vectors for p=1,…,P.

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

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

In broadband, far-field channel forming, each new signal represents a broadband plane wave received in a given direction θ.

In practice, it is possible to sample the new signal to obtain for example M samples , with m=1,…,M. At the end of step 502, we therefore have a set of samples corresponding to different directions θ.

At a step 504, the samples obtained during the formation of broadband temporal channels are backpropagated towards the points/pixels of the Cartesian grid of the image, using a migration method (or backpropagation) illustrated on the : a wave is emitted in a direction θ from the point O. To determine the contribution of the signal received 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, we therefore obtain a set of delayed samples, 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, in the context of an on-board sonar system, the trajectory errors of the antenna by relation to a theoretical trajectory can be important and must be taken into account for the processing of the data received, in particular at the level of the path formation step 503. It is noted that steps 501 and 502 can be carried out in this order, in reverse order or in parallel.

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

In a particular embodiment, it is assumed that we have the raw data (from step 501 of the ), and possibly movement data (from step 502 of the ). The raw data are for example data in (x,r). For each pair of coordinates (x,r), and therefore for each pixel P with coordinates (x,r), we therefore receive a set of samples respectively associated with this pixel. 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 offers a fast method of channel formation from broadband signals, significantly less expensive in terms of calculations than the conventional channel formation method (called “sum-and-delay beamforming” in English, or DSBF), in in which the signals are delayed according to the calculated step differences 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 paths 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(Nlog ₂ N), while the conventional DSBF algorithm has a computational complexity of O(N²). Even if this algorithm has not been developed for large antenna networks and has not been used in this context until now, it turns out to be particularly suitable for implementing step 503. By applying this algorithm, we obtain samples in (u,r).

For the backpropagation of plane waves (step 504 of the ), it is possible to use a Z-Chirp transform, or CZT (for “Chirp-Z Transform” in English), described for example in “Signal Processing Algorithms”, Samuel Stearns and Ruth David, Prentice-Hall, Inc CZT is a transformation allowing a signal to be dilated 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 (or FFTs). The computational complexity of this transformation is O(Nlog ₂ N).

To implement migration step 504, it is possible to successively apply to the data resulting from the formation of channels:
- a CZT on the orthogonal distance r: we then obtain data in (u,f);
- a CZT on the azimuth x: we then obtain data at (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 represented on the .

There 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 in solid lines. The circular arcs correspond to the different frequencies according to Fourier's diffraction theorem and the rays to the directions θ of propagation of plane waves. To migrate these samples 601 to the pixels of a Cartesian grid (represented by dashes in the figure), you must perform:
- an expansion along the rays u until intersection with the Cartesian grid: we obtain the samples 602 represented by triangles; Then
- compression along a line of the Cartesian grid to a point on the grid: we obtain samples 603 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 (such as Stolt interpolation) which are very costly in calculation time.

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 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, 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 process described in is that broadband plane waves can be calculated directly in the time domain for a distorted antenna array (which is the case for a towed sonar mounted on an autonomous underwater vehicle), if the distortions (i.e. errors trajectory) are known, for example using a movement estimation method of the prior art. Thus, the method is more precise than prior art methods which use narrow band signals.

Another advantage is that there are fast methods (in terms of computational cost) for performing steps 503 and 504 of the . For example, using an iterative algorithm like that 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 process represented in has a linearithmic computational complexity, ie in O(Nlog ₂ N), that is to say of the same order of magnitude as the Omega-k algorithm. In comparison, the back-projection algorithm, which is a temporal method integrating exact path differences, has a quadratic complexity, ie in O(N²). The invention thus provides a process that is both precise and rapid.

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

The device may also include 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 process of the invention are described in silicon, or even

- 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).

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 brings together tailor-made functionalities for a given application. ASICs are generally configured during manufacture and can only be simulated by the user. FPGA (Field-Programmable Gate Array) type programmable logic circuits are electronic circuits that can be reconfigured 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 providing 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, in particular in the context of a computer having the form of a touch tablet, For example.

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

Depending on the embodiment, the memory, data storage unit, or removable storage medium contains instructions that, when executed by control circuit 804, cause 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 presented on the is a typical example of a program of which certain instructions can be carried out with the device 800. As such, the can 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 transmitter and each sensor. Thus, the present invention can be used in many other fields, such as ultrasound medical imaging (ultrasound, Doppler, etc.).

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

Although described through a certain number of detailed exemplary embodiments, the proposed method and the equipment for implementing the method include different variants, modifications and improvements which will be obvious to those skilled in the art, it being understood that these different variants, modifications and improvements form part of the scope of the invention, as defined by the claims which follow. Additionally, different aspects and features described above may be implemented together, or separately, or in substitution for each other, and all of the different combinations and sub-combinations of the aspects and features are within the scope of the application. 'invention. Additionally, 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 changing the variable we can write :

The derivative of the phase cancels out to the value:

Using a stationary approximation of the phase, we obtain:

Or designates the sign of reality .

We can deduce :

with .

Ignoring the slowly varying terms, we obtain the following approximation:

Claims (11)

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 (501) samples of wideband temporal signals backscattered from reflectors in the scene to one or more sensors of the antenna system;
b. for each direction among a plurality of directions, calculate (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 broadband plane in said each direction;
vs. for each direction among the plurality of directions, selecting (504), among the new samples of the new respective 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. determine (505) a light intensity of said each pixel from the selected samples. A method according to claim 1, wherein the antenna system is a synthetic aperture radar or a synthetic aperture sonar. A method according to claim 2, wherein the antenna system is a synthetic aperture sonar, and wherein the scene is a limited portion of a seabed. Method according to one of the preceding claims, further comprising reception (502) of data relating to a variation in movement of the system relative to a theoretical trajectory, in which the new samples of the new temporal signals are further calculated from said data. Method according to one of the preceding claims, in which the new samples of the new time signals are calculated using a wide-band and far-field time channel formation method. A method according to claim 5, wherein the formation of the broadband and far-field temporal channels is based on an iterative algorithm. Method according to one of the preceding claims, in which step c comprises an implementation of at least one Z-Chirp transform. 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. 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:
has. receiving (501) samples of wideband temporal signals backscattered from reflectors in the scene to 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, calculate (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 broadband plane in said each direction;
vs. for each direction among the plurality of directions, selecting (504), among the new samples of the new respective 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. determine (505) a light intensity of said each pixel from the selected samples. 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. 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.