CN108693529B - High-precision three-dimensional rapid imaging method and device based on MIMO-SAR - Google Patents

High-precision three-dimensional rapid imaging method and device based on MIMO-SAR Download PDF

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CN108693529B
CN108693529B CN201810572808.5A CN201810572808A CN108693529B CN 108693529 B CN108693529 B CN 108693529B CN 201810572808 A CN201810572808 A CN 201810572808A CN 108693529 B CN108693529 B CN 108693529B
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CN108693529A (en
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李超
高航
吴世有
张群英
刘小军
方广有
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Institute of Electronics of CAS
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Abstract

The invention discloses a high-precision three-dimensional rapid imaging method based on MIMO-SAR, which comprises the following steps: s1, sending a broadband signal to a target, and receiving an original echo signal obtained after the broadband signal is scattered by the target; s2, transforming the original echo signal to a space frequency domain corresponding to the MIMO array direction and the synthetic aperture direction to obtain an original space spectrum; s3, developing the phase offset factor to obtain a fixed distance phase offset factor, a fixed wave number phase offset factor and a Fourier transform factor; s4, combining the original space spectrum with a fixed distance phase shift factor and a Fourier transform factor to determine a fixed distance space spectrum; s5, combining the fixed distance spatial spectrum with the fixed wave number phase shift factor to obtain the spatial spectrum of each distance plane; and S6, determining an imaging function of the target according to the spatial spectrum of each distance plane. The invention also relates to a high-precision three-dimensional rapid imaging device based on the MIMO-SAR.

Description

High-precision three-dimensional rapid imaging method and device based on MIMO-SAR
Technical Field
The invention relates to the technical field of signal processing, in particular to a high-precision three-dimensional rapid imaging method and device based on MIMO-SAR.
Background
The radar three-dimensional real-time imaging device most commonly realizes the fast focusing in the azimuth direction through a two-dimensional array, and realizes the focusing in the range direction through a broadband signal. However, in an application scenario with a relatively high frequency band, such as a millimeter wave terahertz frequency band, due to the fact that the number of array elements of the two-dimensional array is large, under the existing conditions, a lot of costs are added to the system, and particularly, the cost of the existing millimeter wave terahertz device is relatively high. Although only a single array element is used for two-dimensional scanning, and a three-dimensional focusing image can also be obtained by combining a broadband signal, the data acquisition time is too long, and real-time imaging cannot be carried out.
A Multiple input Multiple Output Synthetic Aperture Radar (MIMO-SAR) combining the MIMO array and the Synthetic Aperture technology can reduce the number of array elements and system cost. However, the current imaging algorithm based on the device cannot simultaneously meet the requirements of high-precision imaging and quick imaging.
Disclosure of Invention
The invention aims to provide a high-precision three-dimensional rapid imaging method and device based on MIMO-SAR, so as to solve at least one technical problem.
In one aspect of the invention, a high-precision three-dimensional rapid imaging method based on MIMO-SAR is provided, which comprises the following steps:
s1, sending a broadband signal to a target, and receiving an original echo signal obtained after the broadband signal is scattered by the target;
s2, transforming the original echo signal to a space frequency domain corresponding to the MIMO array direction and the synthetic aperture direction to obtain an original space spectrum;
s3, developing the phase offset factor to obtain a fixed distance phase offset factor, a fixed wave number phase offset factor and a Fourier transform factor;
s4, combining the original space spectrum with a fixed distance phase shift factor and a Fourier transform factor to determine a fixed distance space spectrum;
s5, combining the fixed distance spatial spectrum with the fixed wave number phase shift factor to obtain the spatial spectrum of each distance plane; and the number of the first and second groups,
and S6, determining an imaging function of the target according to the space spectrum of each distance plane.
In some embodiments, in step S1, a three-dimensional coordinate system is constructed, where the x direction represents the MIMO array direction, the y direction represents the synthetic aperture direction, the z direction represents the distance direction, and the original echo signals are:
s(xt，xr，y，0，k)
wherein the transmitting antennas of the MIMO array are located at (x)tY, z), the receiving antenna is located at (x)rY, z), k is the wave number corresponding to different transmission frequencies of the broadband signal, and the distance of the plane where the MIMO-SAR is located at z equal to 0.
In some embodiments, in step S2, the original spatial spectrum obtained by performing three-dimensional fourier transform on the original echo signal to transform the original echo signal into the spatial frequency domain corresponding to the MIMO array direction and the synthetic aperture direction is formulated as:
Figure BDA0001685353700000021
wherein k isxt，kxr，kyRespectively represent xt，xrAnd y corresponds to the spatial frequency domain coordinate.
In some embodiments, in step S3, the phase shift factor is exp (jk)zz) developing the phase shift factor using the following equation to obtain a fixed distance phase shift factor and a fourier transform factor:
Figure BDA0001685353700000022
wherein: h0＝exp(j·2kbz)，
Figure BDA0001685353700000031
Figure BDA0001685353700000032
kcFor transmitting wave number, k, corresponding to the central frequency of the broadband signalb＝k-kc，z＝zM，zMTaking values for several real numbers at equal intervals in the distance direction z, z0Is the zMIs a middle point in the value range of (A), H1For a fixed distance phase shift factor, H2For a fixed wave number phase shift factor, H0The fourier transform factor corresponding to the broadband signal.
In some embodiments, step S4 includes:
s41, multiplying the original space spectrum by a fixed distance phase shift factor to obtain an initial fixed distance space spectrum;
and S42, combining the initial fixed distance spatial spectrum with the Fourier transform factor to perform inverse Fourier transform on the wave number dimension to obtain a fixed distance spatial spectrum.
In some embodiments of the present invention, the,
in step S41, the formula of the initial fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，kb)＝s(kxt，kxr，ky，0，kb)·H1(kxt，kxr，ky，z0，kb)；
in step S42, the formula of the fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，z)＝∫s(kxt，kxr，ky，z0，kb)·exp(j·2kbz)dkb。
in some embodiments, step S5 includes:
s51, multiplying the fixed distance space spectrum by the fixed wave number phase shift factor to obtain the space spectrum of each distance plane; and
and S52, rearranging the spatial spectrum of each distance plane by using the coordinate relation of the spatial frequency domain to obtain the rearranged spatial spectrum of each distance plane.
In some embodiments of the present invention, the,
in step S51, the spatial spectrum formula of each distance plane is:
s(kxt，kxr，ky，z)＝s(kxt，kxr，ky，z0，z)·H2(kxt，kxr，ky，z0，z)；
in step S52, the coordinate relationship of the spatial frequency domain includes:
kx＝kxt+kxr，ky＝kyt+kyr；
the formula of the spatial spectrum of each range plane after rearrangement is:
s(kx，ky，z)＝s(kxt，kxr，ky，z)rearrange。
in some embodiments, in step S6, the imaging function of the target is obtained by performing two-dimensional inverse fourier transform on the spatial spectrum of each distance plane, and the imaging function of the target is:
s(x，y，z)＝∫s(kx，ky，z)·exp(jkxx)·exp(jkyy)dxdy。
in another aspect of the present invention, there is also provided a high-precision three-dimensional fast imaging apparatus based on MIMO-SAR, comprising:
a memory to store instructions; and
and the processor is used for executing the high-precision three-dimensional rapid imaging method based on the MIMO-SAR according to the instruction.
Compared with the prior art, the high-precision three-dimensional rapid imaging method and device based on the MIMO-SAR at least have one or part of the following beneficial effects:
1. compared with the classic Back Propagation (BP) algorithm which can be used for any array form, the imaging speed is improved.
2. Compared with a Fast Fourier Transform (FFT) algorithm which is higher in imaging speed and approximate to a certain condition, the imaging quality is improved.
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FIG. 1 is a flowchart illustrating steps of a high-precision three-dimensional fast imaging method based on MIMO-SAR according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a high-precision three-dimensional fast imaging device based on MIMO-SAR in an embodiment of the present invention;
FIG. 3 is a schematic diagram of an example MIMO linear array;
FIG. 4 is a flowchart illustrating the detailed step of step S4 according to an embodiment of the present invention;
FIG. 5 is a flowchart illustrating the detailed step of step S5 according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of the results of three-dimensional imaging of a target according to an embodiment of the present invention;
FIG. 7 is a graphical representation of the results of two-dimensional imaging of a target at a distance R for an embodiment of the present invention;
fig. 8 is a schematic structural diagram of a high-precision three-dimensional fast imaging device based on MIMO-SAR according to an embodiment of the present invention.
Detailed Description
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
In one aspect of the present invention, a high-precision three-dimensional fast imaging method based on MIMO-SAR is provided, fig. 1 is a flowchart of steps of the high-precision three-dimensional fast imaging method based on MIMO-SAR according to an embodiment of the present invention, as shown in fig. 1, the method includes the following steps:
s1, sending a broadband signal to the target, and receiving an original echo signal obtained after the broadband signal is scattered by the target;
s2, converting the original echo signal to the space frequency domain corresponding to the MIMO array direction and the synthetic aperture direction to obtain an original space spectrum;
s3, developing the phase offset factor to obtain a fixed distance phase offset factor, a fixed wave number phase offset factor and a Fourier transform factor;
s4, combining the original space spectrum with a fixed distance phase shift factor and a Fourier transform factor to determine a fixed distance space spectrum;
s5, combining the fixed distance spatial spectrum with the fixed wave number phase shift factor to obtain the spatial spectrum of each distance plane;
and S6, determining an imaging function of the target according to the space spectrum of each distance plane.
In step S1, the wideband signal is transmitted by a transmitting element of the MIMO array, and a receiving element of the MIMO array receives the original echo signal.
In some embodiments, the MIMO array selects a linear array that transmits across the receive array, it being understood that other forms of MIMO array may be selected in other embodiments. Fig. 2 is a schematic diagram of a scene of a synthetic aperture simulation of a MIMO linear array according to an embodiment of the present invention, and fig. 3 is a schematic diagram of an example of a MIMO linear array according to an embodiment of the present invention, as shown in fig. 2 and fig. 3, in the MIMO linear array, a receiving array element has a spacing dRArranged with transmitting elements at a spacing d at both ends of the first and last receiving elementsTAnd (4) arranging. The receive array length is LR and the total receive and transmit array length is LT. The linear targets composed of two groups of target points are arranged in a cross mode, and the distance from the targets to the MIMO-SAR plane is R.
In some embodiments, referring to fig. 2, a three-dimensional coordinate system is constructed, where the x direction represents the MIMO array direction, the y direction represents the synthetic aperture direction, the z direction represents the distance direction, and the original echo signals are:
s(xt，xr，y，0，k)
wherein the transmitting antennas of the MIMO array are located at (x)tY, z), the receiving antenna is located at (x)rY, z), k is the wave number corresponding to different transmission frequencies of the broadband signal, and the distance of the plane where the MIMO-SAR is located at z equal to 0.
According to some embodiments, in step S2, the original echo signals are transformed into the spatial frequency domain corresponding to the MIMO array direction and the synthetic aperture direction by performing three-dimensional fourier transform on the original echo signals to obtain an original spatial spectrum, where the formula of the original spatial spectrum is:
Figure BDA0001685353700000061
wherein k isxt，kxr，kyRespectively represent xt，xrAnd y corresponds to the spatial frequency domain coordinate.
According to some embodiments, in step S3, the phase shift factor may be exp (jk)zz) using the following formulaAnd (3) expanding the phase shift factor to obtain a fixed distance phase shift factor, a fixed wave number phase shift factor and a Fourier transform factor:
Figure BDA0001685353700000062
wherein: h0＝exp(j·2kbz)，
Figure BDA0001685353700000063
Figure BDA0001685353700000064
kcFor transmitting wave number, k, corresponding to the central frequency of the broadband signalb＝k-kc，z＝zM，zMTaking values for several real numbers at equal intervals in the distance direction z, z0Is the zMIs a middle point in the value range of (A), H1For a fixed distance phase shift factor, H2For a fixed wave number phase shift factor, H0The fourier transform factor corresponding to the broadband signal.
Fig. 4 is a flowchart of the detailed steps of step S4 according to the embodiment of the present invention, and as shown in fig. 4, the step S4 may include the following sub-steps:
and S41, multiplying the original space spectrum by the fixed distance phase shift factor to obtain an initial fixed distance space spectrum.
For example, the formula for the initial fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，kb)＝s(kxt，kxr，ky，0，kb)·H1(kxt，kxr，ky，z0，kb)。
and S42, combining the initial fixed distance spatial spectrum with the Fourier transform factor to perform inverse Fourier transform on the wave number dimension to obtain a fixed distance spatial spectrum.
For example, the formula for the fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，z)＝∫s(kxt，kxr，ky，z0，kb)·exp(j·2kbz)dkb。
fig. 5 is a flowchart illustrating specific steps of step S5 according to an embodiment of the present invention, and as shown in fig. 5, the step S5 may include the following sub-steps:
and S51, multiplying the fixed distance space spectrum by the fixed wave number phase shift factor to obtain the space spectrum of each distance plane.
For example, the spatial spectrum formula for each distance plane is:
s(kxt，kxr，ky，z)＝s(kxt，kxr，ky，z0，z)·H2(kxt，kxr，ky，z0，z)，
and S52, rearranging the spatial spectrum of each distance plane by using the coordinate relation of the spatial frequency domain to obtain the rearranged spatial spectrum of each distance plane.
For example, the coordinate relationship of the spatial frequency domain includes:
kx＝kxt+kxr，ky＝kyt+kyr；
the spatial spectrum formula of each rearranged distance plane is as follows:
s(kx，ky，z)＝s(kxt，kxr，ky，z)rearrange
according to some embodiments, in step S6, the spatial spectrum of each range plane is subjected to a two-dimensional inverse fourier transform to determine an imaging function of the object, the imaging function of the object being obtained as:
s(x，y，z)＝∫s(kx，ky，z)·exp(jkxx)·exp(jkyy)dxdy。
an embodiment of the present invention will be described with reference to the accompanying drawings. Referring to fig. 2, an image of a target region is shown in fig. 2, and the following steps are performed to realize high-precision three-dimensional fast imaging based on MIMO-SAR.
And S1, sending a broadband signal to the target, and receiving an original echo signal obtained after the broadband signal is scattered by the target.
Constructing a three-dimensional coordinate system, wherein the X direction represents the MIMO array direction, the Y direction represents the synthetic aperture direction, and the Z direction represents the distance direction, and as shown in FIG. 2, the transmitting antennas of the MIMO array are positioned at (x)tY, z), the receiving antenna is located at (x)rY, z), the distance of the plane where the MIMO-SAR is located at z being 0, and k represents the wave number corresponding to different transmission frequencies of the broadband signal,
the original echo signal can be expressed as: s (x)t，xr，y，0，k)。
And S2, transforming the original echo signals to the space frequency domain corresponding to the MIMO array direction and the synthetic aperture direction to obtain an original space spectrum.
It is understood that, in the present embodiment, the transformation of the original scattered echo signal into the spatial frequency domain can be implemented by performing three-dimensional fourier transform on a simplified formula, and then the formula of the original spatial spectrum is:
Figure BDA0001685353700000081
wherein k isxt，kxr，kyRespectively represent xt，xrAnd y corresponds to the spatial frequency domain coordinate.
And S3, developing the phase shift factor to obtain a fixed distance phase shift factor, a fixed wave number phase shift factor and a Fourier transform factor.
In the present embodiment, the phase shift factor is exp (jk)zz) developing the phase shift factor using the following equation to obtain a fixed distance phase shift factor and a fourier transform factor:
Figure BDA0001685353700000082
wherein: h0＝exp(j·2kbz)，
Figure BDA0001685353700000091
Figure BDA0001685353700000092
kcFor transmitting wave number, k, corresponding to the central frequency of the broadband signalb＝k-kc，z＝zM，zMTaking values for several real numbers at equal intervals in the distance direction z, z0Is the zMIs a middle point in the value range of (A), H1For a fixed distance phase shift factor, H2For a fixed wave number phase shift factor, H0The fourier transform factor corresponding to the broadband signal.
And S4, combining the original space spectrum with the fixed distance phase shift factor and the Fourier transform factor to determine the fixed distance space spectrum.
In this embodiment, step S4 includes the following sub-steps:
s41, multiplying the original space spectrum by the fixed distance phase shift factor to obtain an initial fixed distance space spectrum, wherein the formula of the initial fixed distance space spectrum is as follows:
s(kxt，kxr，ky，z0，kb)＝s(kxt，kxr，ky，0，kb)·H1(kxt，kxr，ky，z0，kb)；
s42, performing inverse Fourier transform on the wave number dimension by combining the initial fixed distance spatial spectrum with the Fourier transform factor to obtain a fixed distance spatial spectrum, wherein the formula of the fixed distance spatial spectrum is as follows:
s(kxt，kxr，ky，z0，z)＝∫s(kxt，kxr，ky，z0，kb)·exp(j·2kbz)dkb。
and S5, combining the fixed distance space spectrum with the fixed wave number phase shift factor to obtain the space spectrum of each distance plane.
In this embodiment, step S5 includes the following sub-steps:
s51, multiplying the fixed distance space spectrum by the fixed wave number phase shift factor to obtain the space spectrum of each distance plane, wherein the space spectrum formula of each distance plane is as follows:
s(kxt，kxr，ky，z)＝s(kxt，kxr，ky，z0，z)·H2(kxt，kxr，ky，z0，z)；
s52, rearranging the spatial spectrum of each distance plane according to the coordinate relationship of the spatial frequency domain to obtain a rearranged spatial spectrum of each distance plane, where the coordinate relationship of the spatial frequency domain includes:
kx＝kxt+kxr，ky＝kyt+kyr；
the spatial spectrum formula of each rearranged distance plane is as follows:
s(kx，ky，z)＝s(kxt，kxr，ky，z)rearrange。
s6, performing two-dimensional inverse Fourier transform on the space spectrum of each distance plane to obtain a three-dimensional imaging function of the target as follows:
s(x，y，z)＝∫s(kx，ky，z)·exp(jkxx)·exp(jkyy)dxdy。
the imaging effect obtained according to the above method can be referred to fig. 6 and 7. Fig. 6 is a schematic diagram of a three-dimensional imaging result of the target obtained in this embodiment, and fig. 7 is a schematic diagram of a two-dimensional imaging result of the target at a distance R in this embodiment.
Therefore, the high-precision three-dimensional rapid imaging method based on the MIMO-SAR shortens the imaging time and improves the imaging quality.
In another aspect of the present invention, a high-precision three-dimensional fast imaging apparatus based on MIMO-SAR is further provided, and fig. 8 is a schematic structural diagram of the high-precision three-dimensional fast imaging apparatus based on MIMO-SAR according to an embodiment of the present invention, as shown in fig. 8, the apparatus includes:
a memory 81 for storing instructions; and
and a processor 82 for executing the MIMO-SAR based high-precision three-dimensional fast imaging method as described above according to the instructions in the memory 81.
In summary, according to the high-precision three-dimensional fast imaging method and device based on the MIMO-SAR of the present invention, compared with the classical BP algorithm that can be used in any array form, the imaging speed is significantly increased, and compared with the FFT fast algorithm that has a faster imaging speed and is approximated by a certain condition, the imaging quality is greatly improved.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A high-precision three-dimensional rapid imaging method based on MIMO-SAR comprises the following steps:
s1, sending a broadband signal to a target, and receiving an original echo signal obtained after the broadband signal is scattered by the target;
s2, transforming the original echo signal to a space frequency domain corresponding to the MIMO array direction and the synthetic aperture direction to obtain an original space spectrum;
s3, developing the phase offset factor to obtain a fixed distance phase offset factor, a fixed wave number phase offset factor and a Fourier transform factor;
s4, combining the original space spectrum with a fixed distance phase shift factor and a Fourier transform factor to determine a fixed distance space spectrum;
s5, combining the fixed distance spatial spectrum with the fixed wave number phase shift factor to obtain the spatial spectrum of each distance plane; and the number of the first and second groups,
and S6, determining an imaging function of the target according to the space spectrum of each distance plane.
2. The method according to claim 1, wherein in step S1, a three-dimensional coordinate system is constructed, wherein the x direction represents MIMO array direction, the y direction represents synthetic aperture direction, and the z direction represents distance direction, and the original echo signals are:
s(xt，xr，y，0，k)
wherein the transmitting antennas of the MIMO array are located at (x)tY, z), the receiving antenna is located at (x)rY, z), k is the wave number corresponding to different transmission frequencies of the broadband signal, and the distance of the plane where the MIMO-SAR is located at z equal to 0.
3. The method according to claim 2, wherein in step S2, the original spatial spectrum obtained by performing three-dimensional fourier transform on the original echo signal to transform the original echo signal to the spatial frequency domain corresponding to the MIMO array direction and the synthetic aperture direction has the following formula:
Figure FDA0002493165670000021
wherein k isxt，kxr，kyRespectively represent xt，xrAnd y corresponds to the spatial frequency domain coordinate.
4. The method of claim 3, wherein in step S3, the phase shift factor is exp (jk)zz) developing the phase shift factor using the following equation to obtain a fixed distance phase shift factor and a fourier transform factor:
Figure FDA0002493165670000022
wherein: h0＝exp(j·2kbz)，
Figure FDA0002493165670000023
Figure FDA0002493165670000024
kcFor transmitting wave number, k, corresponding to the central frequency of the broadband signalb＝k-kc，z＝zM，zMTaking values for several real numbers at equal intervals in the distance direction z, z0Is the zMIs a middle point in the value range of (A), H1For a fixed distance phase shift factor, H2For a fixed wave number phase shift factor, H0The fourier transform factor corresponding to the broadband signal.
5. The method of claim 4, wherein step S4 includes:
s41, multiplying the original space spectrum by a fixed distance phase shift factor to obtain an initial fixed distance space spectrum; and
and S42, combining the initial fixed distance spatial spectrum with the Fourier transform factor to perform inverse Fourier transform on the wave number dimension to obtain a fixed distance spatial spectrum.
6. The method of claim 5, wherein,
in step S41, the formula of the initial fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，kb)＝s(kxt，kxr，ky，0，kb)·H1(kxt，kxr，ky，z0，kb)；
in step S42, the formula of the fixed distance spatial spectrum is:
s(kxt，kxr，ky，z0，z)＝∫s(kxt，kxr，ky，z0，kb)·exp(j·2kbz)dkb。
7. the method of claim 6, wherein step S5 includes:
s51, multiplying the fixed distance space spectrum by the fixed wave number phase shift factor to obtain the space spectrum of each distance plane;
and S52, rearranging the spatial spectrum of each distance plane by using the coordinate relation of the spatial frequency domain to obtain the rearranged spatial spectrum of each distance plane.
8. The method of claim 7, wherein,
in step S51, the spatial spectrum formula of each distance plane is:
s(kxt，kxt，ky，z)＝s(kxt，kxr，ky，z0，z)·H2(kxt，kxr，ky，z0，z)；
in step S52, the coordinate relationship of the spatial frequency domain includes:
kx＝kxt+kxr，ky＝kyt+kyr；
the formula of the rearranged spatial spectrum of each distance plane is as follows:
s(kx，ky，z)＝s(kxt，kxr，ky，z)rearrangeand, coarse indicates rearrangement.
9. The method according to claim 8, wherein in step S6, the imaging function of the target is obtained by performing two-dimensional inverse fourier transform on the spatial spectrum of each distance plane, the imaging function of the target being:
s(x，y，z)＝∫s(kx，ky，z)·exp(jkxx)·exp(jkyy)dxdy。
10. a high-precision three-dimensional rapid imaging device based on MIMO-SAR comprises:
a memory to store instructions; and
a processor for executing the MIMO-SAR-based high-precision three-dimensional fast imaging method according to any one of claims 1 to 9, according to the instructions.
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