A fast backprojection imaging method based on range-varying spectrum correction

Abstract

The invention discloses a fast back-projection imaging method based on range space-variant spectrum correction, comprising: performing range-dimensional pulse compression on original echo sampling data to obtain range compression signals; performing range-dimensional Fourier transform and interpolation processing on the range compression signals to obtain echo signals; performing BP integral processing on the echo signals to obtain multiple sub-aperture images; performing correction, shifting and azimuth Fourier inverse transform on the sub-aperture images to obtain sub-aperture image wavenumber spectra, merging the sub-aperture image wavenumber spectra into long vectors to obtain full-aperture wavenumber spectrum images, performing Fourier transform on the full-aperture wavenumber spectrum images to obtain full-aperture focused SAR images; and performing geometric correction on the full-aperture focused SAR images to obtain full-aperture high-resolution SAR images. The projection imaging algorithm of the invention can correct the tilt of the spectrum after sub-aperture BP imaging, and is used to solve the problem of large bandwidth and easy spectrum folding caused by spectrum tilt in the existing time domain imaging algorithm.

Description

Technical Field

[0001] The invention belongs to the technical field of digital signal processing, and in particular relates to a fast back-projection imaging method based on distance space-variant spectrum correction. Background Art

[0002] Synthetic Aperture Radar (SAR) is the main body of radar imaging and has the widest application range. Synthetic aperture radar imaging technology processes the radar echo signal matrix in two dimensions, namely, distance and azimuth, to obtain high-resolution SAR images in two dimensions, clearly presenting the shape and fine structural features of the target, greatly improving the detection and identification capabilities of the target.

[0003] With the development of SAR imaging technology, the front-side and small-squint SAR technologies have been continuously matured and improved, and have been more and more widely used. At the same time, SAR is developing in the direction of multi-mode, multi-channel and multi-function. Modern SAR systems are no longer limited to high-resolution ground observation. Functions such as target detection, recognition and tracking based on SAR images are constantly developing. Front-side SAR has attracted attention in recent years due to its application needs in airborne fire control radars and missile-borne precision guidance radars. Aircraft and weapon systems equipped with front-side SAR systems are considered to be the magic weapon for winning on the battlefield in the future. Generally speaking, existing imaging algorithms can be divided into two categories: frequency domain imaging algorithms and time domain imaging algorithms. However, most frequency domain imaging algorithms approximate the target transfer function. The approximate conditions in these imaging algorithms are sensitive to SAR parameters, which bring more serious space-varying errors in large scene imaging, resulting in poor SAR image quality. The basis of the time domain imaging algorithm is the BP algorithm, namely the back projection algorithm. The BP algorithm constructs SAR images by calculating pixel by pixel, so the SAR image quality is high, but the amount of calculation is huge. In order to reduce the computational complexity of the BP imaging algorithm, the FBP algorithm and the FFBP algorithm were proposed successively. On this basis, some domestic scholars have proposed the AFBP algorithm based on spectrum fusion. This algorithm completes sub-image fusion through spectral splicing of sub-aperture images. The algorithm complexity and computational complexity are greatly reduced, and the algorithm's computational efficiency is further improved.

[0004] However, due to the certain inclination of the sub-aperture image spectrum and the large bandwidth, sub-aperture spectrum aliasing may occur in the case of high-resolution imaging of large-range and large-slant-angle scenes or when the azimuth sampling rate is low, resulting in poor imaging effect. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a fast back-projection imaging method based on distance space-variant spectrum correction. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0006] A fast back-projection imaging method based on range-variant spectrum correction, the fast back-projection imaging method comprising:

[0007] Step 1: Perform range-dimensional pulse compression on the original echo sampling data s of the missile-borne SAR image to obtain the range-compressed signal s after range pulse compression. M ;

[0008] Step 2: compress the distance signal s M Perform distance-dimensional Fourier transform and interpolation processing to obtain the echo signal after distance-dimensional interpolation processing

[0009] Step 3: Perform BP integration processing to obtain multiple sub-aperture images I u (r,α);

[0010] Step 4: sequentially process the sub-aperture images I u (r, α) is corrected, shifted and inversely Fourier transformed in azimuth to obtain a sub-aperture image wavenumber spectrum, the sub-aperture image wavenumber spectrum is merged into a long vector to obtain a full-aperture wavenumber spectrum image, so as to obtain a full-aperture focused SAR image of an oblique plane by Fourier transforming the full-aperture wavenumber spectrum image;

[0011] Step 5: Perform geometric correction on the full-aperture focused SAR image to obtain a full-aperture high-resolution SAR image.

[0012] In one embodiment of the present invention, the echo signal matrix s M The model is expressed as:

[0013]

[0014] The sinc function is represented by sinc(u)=sin(πu) / πu, where u represents the reference quantity, B represents the signal bandwidth, and K c =4π / λ c represents the distance from the wave number center, λ c =c / f c Indicates the wavelength corresponding to the carrier frequency, f c τ represents the carrier frequency, D represents the position of the radar antenna, L represents the length of the synthetic aperture, and Δt represents the fast time. p =2R / c, R represents the instantaneous distance from the radar antenna to any point target, and c represents the speed of light.

[0015] In one embodiment of the present invention, step 2 comprises:

[0016] Step 2.1: the echo signal matrix sM Perform distance Fourier transform to obtain distance frequency domain signal;

[0017] Step 2.2, using an eight-fold interpolation method to perform zero-filling processing on the range frequency domain signal to obtain a frequency domain zero-filled echo signal;

[0018] Step 2.3: Perform a range-direction inverse Fourier transform on the frequency domain zero-filled echo signal to obtain the echo signal sI M .

[0019] In one embodiment of the present invention, step 3 comprises:

[0020] Step 3.1: Divide the full aperture data into equal lengths l = L / N sub N sub sub-apertures, where L represents the synthetic aperture length, N sub represents the number of subapertures;

[0021] Step 3.2: In each of the sub-apertures, the echo signal Perform range dimension compression and two-dimensional coherent integration processing in the azimuth and time domains to obtain N sub Sub-aperture image I u (r,α).

[0022] In one embodiment of the present invention, the u-th sub-aperture image is expressed as:

[0023]

[0024] Among them, I u (r, α) represents the u-th sub-aperture image, (r, α) represents a point in the u-th sub-aperture image, R(x+x u ; r,α) represents the instantaneous distance from the radar to any point (r,α) in polar coordinates, x u represents the center of the u-th sub-aperture, and x represents the position of the radar antenna.

[0025] In one embodiment of the present invention, step 4 comprises:

[0026] Step 4.1: Correction function F along the distance direction r With the sub-aperture image I u (r, α) is multiplied to obtain the corrected sub-aperture image

[0027] Step 4.2: Set the shift function F a With sub-aperture images Multiply them to get the shifted sub-aperture image

[0028] Step 4.3: for the first sub-aperture image Perform inverse azimuthal Fourier transform to obtain the sub-aperture image wavenumber spectrum;

[0029] Step 4.4: Shift the wave number spectrum of the sub-aperture image wave number spectrum in azimuth so that the spectrum center of the sub-aperture image wave number spectrum moves from zero to the true center K αu , and merge the shifted sub-aperture image wave number spectra into a long vector to obtain a full-aperture wave number spectrum image;

[0030] Step 4.5: Perform Fourier transform on the full-aperture wavenumber spectrum image in the azimuth dimension, and perform modulus processing on the Fourier transformed image to obtain a full-aperture focused SAR image on an inclined plane.

[0031] In one embodiment of the present invention, the correction function F r It is expressed as:

[0032] F r =exp(j·K r α i )

[0033] Among them, α i Represents the grid angle dimension coordinate, K r =4π / λ r represents the frequency-domain spatially varying wave number center, λ r =c / (f c +f r ), f c Indicates the carrier frequency, f r ∈[-F s / 2,F s / 2],F s Indicates the radar range sampling frequency.

[0034] In one embodiment of the present invention, the corrected sub-aperture image It is expressed as:

[0035]

[0036] Among them, K α represents the angular domain wavenumber spectrum variable, K αu Indicates the center of the wavenumber spectrum, Δα=α-α p ,α p Indicates the angular coordinates of the target point.

[0037] In one embodiment of the present invention, step 5 comprises:

[0038] Based on the projection function, two-dimensional interpolation of the full-aperture focused SAR image in the distance dimension and the angle dimension is performed according to the coordinates (x, y) of the ground pixel points to obtain a full-aperture high-resolution SAR image.

[0039] In one embodiment of the present invention, the projection function is expressed as:

[0040]

[0041] Among them, (r, α) represents the coordinates of the point target in the inclined plane, (x, y) represents the coordinates of the ground pixel point corresponding to (r, α), γ represents the dive angle, and H represents the radar height.

[0042] Beneficial effects of the present invention:

[0043] The fast back-projection imaging algorithm based on distance-variant spectrum correction proposed in the present invention can correct the tilt of the spectrum after sub-aperture BP imaging, and is used to solve the problem of large bandwidth and easy spectrum folding caused by spectrum tilt in existing time-domain imaging algorithms.

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flowchart of a fast back-projection imaging method based on distance space-variant spectrum correction provided by an embodiment of the present invention;

[0046] Figure 2 A schematic flow chart of another fast back-projection imaging method based on distance-variant spectrum correction provided by an embodiment of the present invention;

[0047] Figure 3 1 is a schematic diagram of zero-filling in the frequency domain provided by an embodiment of the present invention;

[0048] Figure 4 It is a schematic diagram of the geometric relationship of front-side looking SAR imaging provided by an embodiment of the present invention;

[0049] Figure 5a-5g A SAR image obtained by processing simulation data provided by an embodiment of the present invention;

[0050] Figure 6a-6f This is a SAR image obtained by processing measured data provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0052] Embodiment 1

[0053] See also Figure 1 and Figure 2 , Figure 1 is a flow chart of a fast back-projection imaging method based on distance-variant spectrum correction provided by an embodiment of the present invention, Figure 2 A flowchart of another fast back-projection imaging method based on distance space-variant spectrum correction provided by an embodiment of the present invention is provided. An embodiment of the present invention provides a fast back-projection imaging method based on distance space-variant spectrum correction, and the fast back-projection imaging method includes steps 1 to 5, wherein:

[0054] Step 1: Perform range-dimensional pulse compression on the original echo sampling data s of the missile-borne SAR image to obtain the range-compressed signal s after range pulse compression. M .

[0055] In this embodiment, the model of the original echo sampling data s is:

[0056]

[0057] in, D represents the position of the radar antenna, L represents the length of the synthetic aperture, s T (τ) represents bandwidth B and carrier frequency f c The emission waveform, τ represents the fast time, Δt p =2R / c, corresponding to the time delay, R represents the instantaneous distance from the radar antenna to any point target, and c represents the speed of light.

[0058] Specifically, the original echo sampling data s is matched filtered along the range direction to obtain the range compression signal s M , the distance compresses the signal s M The model is expressed as:

[0059]

[0060] The sinc function is represented by sinc(u)=sin(πu) / πu, where u represents the reference quantity, B represents the signal bandwidth, and K c =4π / λ c represents the distance from the wave number center, λ c =c / f c Indicates the wavelength corresponding to the carrier frequency, f c Indicates the carrier frequency.

[0061] Step 2: Compress the distance signal s M Perform distance-dimensional Fourier transform and interpolation processing to obtain the echo signal after distance-dimensional interpolation processing

[0062] Step 2.1: For the echo signal matrix s MPerform distance Fourier transform to obtain the distance frequency domain signal.

[0063] Step 2.2, please refer to Figure 3 , using the eight-fold interpolation method to perform zero-filling processing on the range frequency domain signal to obtain a frequency domain zero-filled echo signal;

[0064] Step 2.3: Perform inverse Fourier transform on the frequency domain zero-filled echo signal to obtain the echo signal after distance dimension interpolation processing.

[0065] Step 3: Echo signal Perform BP integration processing to obtain multiple sub-aperture images I u (r,α).

[0066] Step 3.1: Divide the full aperture data into equal lengths l = L / N sub N sub sub-apertures, where L represents the synthetic aperture length, N sub Indicates the number of subapertures.

[0067] Step 3.2: In each sub-aperture, the echo signal The distance dimension compression and the coherent integration processing in the azimuth and time domains are performed to achieve precise focusing, thereby obtaining N sub Sub-aperture image I u (r,α).

[0068] Among them, the u-th sub-aperture image I u The impulse response function (IRF) of (r, α) can be calculated from the neighborhood pixels of a certain point (r, α) in the sub-aperture image, and the u-th sub-aperture image is expressed as:

[0069]

[0070] Among them, I u (r, α) represents the u-th sub-aperture image, (r, α) represents a point in the u-th sub-aperture image, R(x+x u ; r,α) represents the instantaneous distance from the radar to any point (r,α) in polar coordinates, x u represents the center of the u-th sub-aperture, and x represents the position of the radar antenna.

[0071] See also Figure 3 ,according to Figure 3 Schematic diagram of the dive SAR imaging geometric model. A polar coordinate system (r, θ) is established in the imaging oblique plane. The origin of the polar coordinate system is located at the center of the synthetic aperture. m At the moment, the radar reaches any target point P(rp ,θ p ) is given by:

[0072]

[0073] Among them, D(t m ) represents the position trajectory of the radar antenna phase center, α p = sinθ p , L represents the synthetic aperture length. Therefore, R(x+x u ; r, α) can be calculated according to the above formula.

[0074] Step 4: sequentially process the sub-aperture images I u (r, α) is corrected, shifted and inversely Fourier transformed in azimuth to obtain a sub-aperture image wavenumber spectrum, and the sub-aperture image wavenumber spectrum is merged into a long vector to obtain a full-aperture wavenumber spectrum image, so as to obtain a full-aperture focused SAR image of an inclined plane by Fourier transforming the full-aperture wavenumber spectrum image.

[0075] Step 4.1: Correct the function F along the distance direction r With sub-aperture image I u (r, α) is multiplied to obtain the corrected sub-aperture image

[0076] First, construct the distance-variant spectrum correction function F r , the correction function F r It is expressed as:

[0077] F r =exp(j·K r α i )

[0078] Among them, α i Represents the grid angle dimension coordinate, K r =4π / λ r represents the frequency-domain spatially varying wave number center, λ r =c / (f c +f r ), f c Indicates the carrier frequency, f r ∈[-F s / 2,F s / 2],F s Indicates the radar range sampling frequency.

[0079] Then, the correction function F is applied along the distance direction. r With sub-aperture image I u (r, α) is multiplied to correct the distance-varying component of the sub-aperture image spectrum. The correction process is specifically expressed as n=1,2,3,...,NRN, NRN represents the number of grid points in the distance dimension of the BP image, and the corrected sub-aperture image is obtained

[0080] Corrected sub-aperture image It is expressed as:

[0081]

[0082] Where X = x + x u , ΔR(X; r, α) represents R(X; r p ,α p ) and R(X; r p ,α). Expand ΔR(X; r,α) with a second-order Taylor series and ignore its high-order terms σ(X 3 )get:

[0083]

[0084] In the formula, the quadratic phase error In SAR applications, it can be easily controlled below π / 8 and can also be ignored.

[0085] Furthermore, the angular domain wave number variable is defined as:

[0086]

[0087] Among them, K α represents the angular domain wavenumber spectrum variable, K αu represents the center of the wavenumber spectrum, ΔK α Represents the wavenumber spectrum width.

[0088] Therefore, the simplified subaperture image becomes:

[0089]

[0090] Where Δα=α-α p ,α p Indicates the angular coordinates of the target point.

[0091] Step 4.2: Set the shift function F a With sub-aperture images Multiply them to get the shifted sub-aperture image

[0092] Specifically, the shift function F is constructed according to the center of the wavenumber spectrum. a , shift function F a It is expressed as:

[0093] F a =exp(j·Kαu α i )

[0094] Among them, α i Represents the grid angle dimension coordinate.

[0095] The shift function F a With sub-aperture images Multiply, and the shift process is expressed as Get the shifted sub-aperture image

[0096] Step 4.3: Sub-aperture image Perform inverse Fourier transform (IFFT) to obtain the sub-aperture image wave number spectrum. The expression of the sub-aperture image wave number spectrum is:

[0097]

[0098]

[0099] Where ΔA u Indicates the angular width, A cu Denotes the predefined angular coordinate center of the u-th sub-aperture image, redefines Δα as the angular sampling interval, and notices that the Nyquist sampling criterion is met only when the angular sampling rate of the sub-aperture image satisfies Δα≤λ / 2l.

[0100] Step 4.4: Shift the wavenumber spectrum of each sub-aperture image wavenumber spectrum in azimuth so that the spectral center of the sub-aperture image wavenumber spectrum moves from zero to the true center K αu , and merge the shifted sub-aperture image wavenumber spectra into a long vector to obtain the full aperture wavenumber spectrum image I RA (α).

[0101] Step 4.5: Perform Fourier transform (FFT) on the full-aperture wavenumber spectrum image in the azimuth dimension to transform the complete wavenumber spectrum back to the image domain, and perform modulus processing on the Fourier transformed image to obtain a full-aperture focused SAR image in the inclined plane.

[0102] Step 5: Perform geometric correction on the full-aperture focused SAR image to obtain a full-aperture high-resolution SAR image.

[0103] Specifically, based on the projection function, two-dimensional interpolation of the full-aperture focused SAR image in the distance dimension and the angle dimension is performed according to the coordinates (x, y) of the ground pixel points to obtain a full-aperture high-resolution SAR image.

[0104] In this embodiment, the projection function is expressed as:

[0105]

[0106] Among them, (r, α) represents the coordinates of the point target in the inclined plane, (x, y) represents the coordinates of the ground pixel point corresponding to (r, α), γ represents the dive angle, and H represents the radar height. According to the above projection function, the coordinates of the point target in the inclined plane (r, α) are converted into the projection grid point coordinates (x, y) of the ground plane.

[0107] The invention discloses a fast back-projection imaging algorithm based on range-variant spectrum correction. The algorithm divides full-aperture original echo data into uniform sub-apertures, and performs BP imaging respectively to obtain a plurality of low-resolution sub-aperture images. A range-variant spectrum correction function is constructed to correct the spectrum tilt of the sub-aperture images, and the wavenumber spectrum of the sub-aperture images is shifted and spliced ​​to obtain a full-aperture wavenumber spectrum. The full-aperture wavenumber spectrum is subjected to azimuth FFT to obtain a full-aperture SAR image. Finally, the full-aperture focused SAR image is geometrically corrected to obtain a full-aperture high-resolution SAR image.

[0108] The invention is specifically a fast back-projection imaging algorithm based on range-variant spectrum correction, which can be used for fast imaging processing of active radar seekers with imaging homing.

[0109] The fast back-projection imaging algorithm based on distance-variant spectrum correction proposed in the present invention can correct the tilt of the spectrum after sub-aperture BP imaging, and is used to solve the problem of large bandwidth and easy spectrum folding caused by spectrum tilt in existing time-domain imaging algorithms.

[0110] The following is a comparative experiment of simulation and measured data processing to illustrate the technical effects of the present invention.

[0111] Experimental conditions and contents:

[0112] The radar system parameters used in the simulation data imaging experimental data acquisition are shown in Table 1:

[0113] Table 1 Radar system parameters of simulation data

[0114] Band Ku-Band Front oblique angle 26° Sampling rate 360MHz bandwidth 300MHz high 5000m Beam width 6° Pulse Width 10us speed 200m / s

[0115] The imaging experiment was conducted using MATLAB software on a PC, where the PC was powered by an Intel Core I7-4790 processor with a CPU main frequency of 3.6 GHz.

[0116] Experimental results analysis:

[0117] The imaging results obtained are as follows Figure 5a-5g As shown, Figure 5a This is the two-dimensional spectrum diagram before the first sub-aperture spectrum correction. It can be seen that there is obvious spectrum folding; Figure 5b This is the two-dimensional spectrum diagram after the center of the first sub-aperture spectrum of the AFBP algorithm is shifted. Figure 5cThis is a two-dimensional spectrum diagram after the first sub-aperture spectrum correction shift of the present invention. It can be seen that under the same sampling rate, the correction of the spectrum by the present invention effectively avoids the spectrum folding; Figure 5d is the oblique plane image of the AFBP algorithm, Figure 5e This is the oblique plane image of the present invention. It can be clearly seen that the edge point position marked by the red circle is obviously defocused by the AFBP algorithm, and the present invention has a good focusing effect. The point target at the position marked by the red circle is analyzed. Figure 5f It is the contour map of point target of AFBP algorithm. Figure 5g This is the contour map of the point target of the present invention. It can be seen that the point target azimuth of the image obtained by the AFBP algorithm is obviously defocused, and the focusing effect of the present invention is good. Table 2 shows the PSLR, ISLR and resolution comparison of the point target at the circled position, which verifies the superiority of the present invention.

[0118] Table 2 Imaging quality evaluation

[0119]

[0120]

[0121] Experimental conditions and contents:

[0122] The radar system parameters used in the measured data imaging experiment data acquisition are shown in Table 3:

[0123] Table 3 Radar system parameters of measured data

[0124] Band Ka-band Front oblique angle 28° bandwidth 100MHz speed 50m / s high 3000m Beam width 6°

[0125] The imaging experiment was conducted using MATLAB software on a PC, where the PC CPU was an Intel Core I7-4790 processor with a main frequency of 3.6 GHz.

[0126] Experimental results analysis:

[0127] The imaging results obtained are as follows Figure 6a-6f As shown, Figure 6a This is the imaging result of the original AFBP algorithm processing the measured data. Figure 6b The imaging results of the measured data processed by the present invention show that the imaging effect of the center of the image of the two methods is good, and the outline of the overpass is clear, but the focusing effect of the edge points of the image is different. From the part marked by the red line in the figure, it can be clearly seen that the focusing effect of the strong scattering points at the edge of the image of the present invention is good; in order to more accurately distinguish the difference between the imaging results of the two processing methods, Figure 6c The interpolated image of the red line part of the image generated by the AFBP algorithm is given. Figure 6d The interpolation image of the red line part of the image formed by the present invention is given, Figure 6eThe energy contour map of the red line center point of the image generated by the AFBP algorithm is given. Figure 6f The energy contour map of the red line center point of the image formed by the present invention is given. By comparison, it can be clearly seen that the strong scattering points at the edge of the image formed by the AFBP algorithm are obviously defocused in azimuth. At the same time, Table 4 gives the image entropy comparison, and Table 5 gives the PSLR, ISLR and resolution comparison of the red frame center position. It can be found that the overall image quality and the focusing of the edge scattering points of the present invention are better than those of the original AFBP algorithm, which verifies the superiority of the present invention.

[0128] Table 4 Image entropy of images imaged by two processing methods

[0129] Treatment AFBP algorithm The present invention Image Entropy 7.15 7.41

[0130] Table 5 Imaging quality evaluation

[0131]

[0132] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification.

[0133] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art may understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude multiple situations. A single processor or other unit may implement several functions listed in a claim. Certain measures are recorded in different dependent claims, but this does not mean that these measures cannot be combined to produce good results.

[0134] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A fast back-projection imaging method based on range-variant spectrum correction, characterized in that: The fast back-projection imaging method comprises: Step 1: Perform range-dimensional pulse compression on the original echo sampling data s of the missile-borne SAR image to obtain the range-compressed signal s after range pulse compression. M ; Step 2: compress the distance signal s M Perform distance-dimensional Fourier transform and interpolation processing to obtain the echo signal after distance-dimensional interpolation processing Step 3: Perform BP integration processing to obtain multiple sub-aperture images I u (r,α); Step 4.1: Correction function F along the distance direction r With the sub-aperture image I u (r, α) is multiplied to obtain the corrected sub-aperture image The correction function F r Expressed as: F r =exp(j·K r α i ), where α i Represents the grid angle dimension coordinate, K r =4π / λ r represents the frequency-domain spatially varying wave number center, λ r =c / (f c +f r ), f c Indicates the carrier frequency, f r ∈[-F s / 2,F s / 2],F s represents the radar range sampling frequency; the corrected sub-aperture image It is expressed as: Among them, K α represents the angular domain wavenumber spectrum variable, K αu Indicates the center of the wavenumber spectrum, Δα=α-α p , α p represents the angular coordinates of the target point, and K α , K αu The expression is Step 4.2: Set the shift function F a With sub-aperture images Multiply them to get the shifted sub-aperture image Step 4.3: for the sub-aperture image Perform inverse azimuthal Fourier transform to obtain the sub-aperture image wavenumber spectrum; Step 4.4: Shift the wave number spectrum of the sub-aperture image wave number spectrum in azimuth so that the spectrum center of the sub-aperture image wave number spectrum moves from zero to the true center K αu , and merge the shifted sub-aperture image wave number spectra into a long vector to obtain a full-aperture wave number spectrum image; Step 4.5, performing Fourier transform on the full-aperture wavenumber spectrum image in the azimuth dimension, and performing modulus processing on the Fourier transformed image to obtain a full-aperture focused SAR image on an inclined plane; Step 5: Perform geometric correction on the full-aperture focused SAR image to obtain a full-aperture high-resolution SAR image.

2. The fast back projection imaging method according to claim 1, characterized in that: The echo signal matrix s M The model is expressed as: The sinc function is represented by sinc(u)=sin(πu) / πu, where u represents the reference quantity, B represents the signal bandwidth, and K c =4π / λ c represents the distance from the wave number center, λ c =c / f c Indicates the wavelength corresponding to the carrier frequency, f c represents the carrier frequency, D represents the position of the radar antenna, L represents the synthetic aperture length, τ represents the fast time, Δt p =2R / c, R represents the instantaneous distance from the radar antenna to any point target, and c represents the speed of light.

3. The fast back projection imaging method according to claim 1, characterized in that: The step 2 comprises: Step 2.1: the echo signal matrix s M Perform distance Fourier transform to obtain distance frequency domain signal; Step 2.2, using an eight-fold interpolation method to perform zero-filling processing on the range frequency domain signal to obtain a frequency domain zero-filled echo signal; Step 2.3: Perform a range-direction inverse Fourier transform on the frequency domain zero-filled echo signal to obtain the echo signal 4. The fast back projection imaging method according to claim 2, characterized in that: The step 3 comprises: Step 3.1: Divide the full aperture data into equal lengths l = L / N sub N sub sub-apertures, where L represents the synthetic aperture length, N sub represents the number of subapertures; Step 3.2: In each of the sub-apertures, the echo signal Perform range dimension compression and two-dimensional coherent integration processing in the azimuth and time domains to obtain N sub Sub-aperture image I u (r,α).

5. The fast back projection imaging method according to claim 1, characterized in that: The u-th sub-aperture image is expressed as: Among them, I u (r, α) represents the u-th sub-aperture image, (r, α) represents a point in the u-th sub-aperture image, R(x+x u ; r,α) represents the instantaneous distance from the radar to any point (r,α) in polar coordinates, x u represents the center of the u-th sub-aperture, and x represents the position of the radar antenna.

6. The fast back projection imaging method according to claim 1, characterized in that: The step 5 comprises: Based on the projection function, two-dimensional interpolation of the full-aperture focused SAR image in the distance dimension and the angle dimension is performed according to the coordinates (x, y) of the ground pixel points to obtain a full-aperture high-resolution SAR image.

7. The fast back projection imaging method according to claim 6, characterized in that: The projection function is expressed as: Among them, (r, α) represents the coordinates of the point target in the inclined plane, (x, y) represents the coordinates of the ground pixel point corresponding to (r, α), γ represents the dive angle, and H represents the radar height.

Images