Improved Omega-K imaging method based on FiNUFFT

Abstract

The invention discloses an improved Omega-K imaging method based on FiNUFFT, and the method comprises the steps: firstly assuming that an instantaneous slope distance between a vehicle-mounted FMCW SAR located at a point A (vtm, 0) on an x axis and a target P (Rssin theta s + x, Rscos theta s + y) at any point in a scene is R (tm; the method comprises the following steps of: performing Dechirp processing on an intermediate frequency echo signal (x, y), expressing the intermediate frequency echo signal after Dechirp processing and residual video phase compensation by a formula (1), performing azimuth fast Fourier transform (FFT) on the formula (1), performing matched filtering, and performing range resampling operation, azimuth residual phase compensation and azimuth IFFT on the formula by adopting FiNUFFT to obtain a final imaging result. According to the method, FiNUFFT is adopted to replace Stolt interpolation and subsequent distance direction IFFT processing, distance direction up-sampling operation does not need to be carried out on data, meanwhile, the time-consuming Stolt interpolation and the negative influence of errors possibly brought by the time-consuming Stolt interpolation on the imaging quality are avoided, and therefore the processing speed of an algorithm is remarkably improved on the premise that the imaging quality is guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of three-dimensional imaging, and in particular to an improved Omega-K imaging method based on FiNUFFT. Background Art

[0002] When the vehicle is driving, the vehicle-mounted millimeter-wave frequency modulated continuous wave synthetic aperture radar (FMCW SAR) usually focuses on warning the events ahead. Therefore, the SAR beam line of sight points obliquely forward and performs forward oblique mode vehicle-mounted millimeter-wave FMCW SAR imaging, which has extremely important research value. In view of the short range of vehicle-mounted millimeter-wave FMCW SAR and the large beamwidth in azimuth, the Omega-K imaging algorithm based on Stolt interpolation is usually adopted. However, the Stolt interpolation process will introduce approximation errors and put forward high requirements on the sample sampling rate, especially at the carrier frequency of the high working frequency band, the error is often more significant. In addition, the interpolation accuracy depends largely on the two-dimensional spectrum of the signal. When the sampling rate of the echo data is insufficient, the imaging quality of the interpolation method will be further affected. The computational complexity of Stolt interpolation is huge, which increases the time consumption of the imaging algorithm and reduces the processing efficiency, which is not conducive to the real-time processing of the signal.

[0003] Imaging accuracy and processing efficiency are key indicators for evaluating the performance of imaging algorithms. The design and implementation of imaging algorithms aim to balance the relationship between the two. In practical applications, the implementation of imaging algorithms is considered an engineering challenge. Imaging accuracy only needs to meet the requirements of vehicle-mounted FMCW SAR imaging, and there is no need to excessively pursue the high-precision performance of the algorithm. The balance between imaging accuracy and computational efficiency should be fully considered, and reasonable trade-offs should be made according to actual needs. At present, Stolt interpolation is usually implemented using the following three methods: one is the cubic spline interpolation method; the second is the sinc interpolation method; and the third is to use non-uniform Fourier transform (NUFFT) instead of Stolt interpolation and the subsequent range-directed inverse fast Fourier transform (IFFT). Under the condition that the vehicle-mounted platform is limited by cost and space, how to further improve the processing efficiency of the imaging algorithm while ensuring imaging quality is of great research significance.

[0004] Related references include:

[0005] [1] Kan Yingzhi. Millimeter-wave near-field three-dimensional imaging technology for hidden targets[D]. Changsha: National University of Defense Technology, April 2017.

[0006] KAN Yingzhi. Millimeter Wave Near-field Three-dimensional RadarImaging Technology for Concealed Target[D]. Changsha: National University ofDefense Technology, 2017.

[0007] [2] Xing Tao, Li Jun, Wang Guanyong, Hu Qingrong. SAR azimuth motion compensation algorithm based on non-uniform fast Fourier transform [J]. Journal of Electronics & Information Technology, 2014, 36(5): 1023-1029.

[0008] XING Tao, LI Jun, WANG Guanyong, HU Qingrong. An along-track motioncompensation algorithm based on non-uniform fast Fourier transform (NUFFT) for SAR. Journal of Electronics & Information Technology, 2014, 36(5): 1023-1029.

[0009] [3] Ian G. Cumming, Frank H. Wong. Synthetic Aperture Radar Imaging: Algorithms and Implementations [M]. Beijing: Electronic Industry Press, 2012.6

[0010] Ian G.Cumming, Frank H.Wong.Digital Processing of Synthetic ApertureRadar Data Algorithms and Implementations[M].Artech House Publishers(January31, 2005)

[0011] [4] Zeng Letian. Research on airborne high-resolution spotlight SAR imaging and motion compensation algorithm[D]. Xi'an: Xidian University, April 2016.

[0012] ZENG Letian.Study on Airborne Spotlight SAR Imaging and MotionCompensation with High-Resolution[D].Xi'an: Xidian University, 2016

[0013] [5]Cararra, WG, Goodman, RS, Majewski, RM (1995) Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Artech House, Boston.

[0014] In the case of squint, if the cubic spline interpolation method is used, it is first necessary to select a rectangular area in the oblique two-dimensional spectrum of the signal, which will lead to a reduction in the utilization rate of the signal's two-dimensional spectrum. As the squint angle increases, the utilization rate of the signal's two-dimensional spectrum will be further reduced, and may even cause the failure of spline interpolation. Although the NUFFT method avoids Stolt interpolation and the interpolation error it brings, and obtains good processing results, its operation speed is slow and the processing efficiency is low. Although sinc interpolation has high processing accuracy, can avoid the loss of signal two-dimensional spectrum utilization, and is suitable for signal interpolation processing under large squint conditions, its processing speed still needs to be further improved. Summary of the invention

[0015] The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and provide an improved Omega-K imaging method based on FiNUFFT, which is suitable for vehicle-mounted frequency modulated continuous wave synthetic aperture radar (FMCW SAR) and can solve the following technical problems:

[0016] 1) FiNUFFT is used to replace the time-consuming Stolt interpolation process and the distance IFFT operation, which not only ensures the imaging quality, but also significantly improves the processing efficiency of the algorithm, effectively solving the problem that the Stolt interpolation speed is slow and the imaging results are easily affected by the interpolation error;

[0017] 2) Before performing the improved Stolt interpolation, there is no need to upsample the data in the range direction, which can reduce the amount of data processed by the algorithm and further improve the processing efficiency of the imaging algorithm;

[0018] 3) The proposed algorithm can significantly improve computational efficiency by running only on the CPU, without relying on higher-configuration hardware such as GPU.

[0019] To solve the above technical problems, the present invention is implemented through the following technical solutions: an improved 0mega-K imaging method based on FiNUFFT.

[0020] The present invention has the following beneficial effects:

[0021] 1) Avoid the adverse effects of time-consuming Stolt interpolation and its errors on imaging effects, and significantly improve the processing efficiency of the algorithm while ensuring imaging quality.

[0022] 2) There is no need to upsample the data in the distance direction before interpolation, which reduces the amount of data to be processed and further improves the processing efficiency of the algorithm.

[0023] 3) The proposed algorithm can achieve significant improvement in computational efficiency by running only on the CPU, without relying on higher-configuration hardware such as GPU. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 FIG. 4 is a flowchart of the imaging algorithm of the present invention. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] The present invention can correctly implement FiNUFFT to replace Stolt interpolation and distance IFFT operation.

[0027] See also Figure 1 The method of the present invention uses FiNUFFT to replace Stolt interpolation and subsequent distance IFFT processing, without the need to perform distance upsampling on the data, while avoiding the negative impact of time-consuming Stolt interpolation and the errors it may bring on the imaging quality, thereby significantly improving the processing speed of the algorithm while ensuring the imaging quality. The specific implementation is as follows:

[0028] Assume that at t m time, located on the X-axis A(vt m , 0) point vehicle-mounted FMCW SAR and any point target P(R s sinθ s +x,R s cosθ s +y) is R(t m ; x, y), the intermediate frequency echo signal after Dechirp processing and residual video phase compensation can be expressed as

[0029]

[0030]

[0031]

[0032] Among them, τ is the distance fast time, c is the propagation speed of electromagnetic waves, T p is the FMCW pulse width, R ref is the reference slant distance, γ is the range modulation frequency, f c Indicates the carrier center frequency, represents the wavelength corresponding to the center frequency, v is the speed of the radar platform, K r is the distance wave number.

[0033] Performing azimuth fast Fourier transform (FFT) on equation (1), we have

[0034]

[0035] Perform matched filtering on equation (4), that is, multiply by

[0036]

[0037] Available

[0038]

[0039] FiNUFFT is used to perform range resampling on (6) (there is no need to perform range upsampling on (6) in advance; in the squint mode, the spline interpolation method and the sinc interpolation method may need to perform range upsampling on (6) first). The specific implementation process is as follows:

[0040] 1) Confirm The value range of K y The maximum and minimum values ​​of y max and K y min ;

[0041] 2) Considering that the frequency range of discrete-time signals is [-π, π), the K y Perform linear normalization, that is, K y The value range of is limited to the interval [-π, π), denoted by K ynorm ;

[0042] 3) Set the relative precision eps (1e-6 is sufficient, the smaller the value, the longer the processing time) and the symbol flag iflag (v1 is used);

[0043] 4) Let x be ss′ IF (K r , K x ; x, y), c is K ynorm, N is the number of rows in x, and x, c, iflag, eps, N are passed as parameters to the function "f = finufft1d1 (x, c, iflag, eps, N)". At this time, equation (6) becomes

[0044]

[0045] in, represents the central wave number, and B′ is a constant related to the range signal bandwidth.

[0046] The residual phase compensation in azimuth is performed on equation (7), that is, multiplying by

[0047]

[0048] And perform azimuth IFFT to obtain the final imaging result.

[0049] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. An improved 0mega-K imaging method based on FiNUFFT, including a near-field three-dimensional imaging model, characterized in that The following steps are involved: S1) Assume that at t m time, located on the x-axis A(vt m , 0) point vehicle-mounted FMCW SAR and any point target P(R s sinθ s +x,R s cosθ s +y) is R(t m ; x, y), the intermediate frequency echo signal after Dechirp processing and residual video phase compensation can be expressed as Among them, τ is the distance fast time, c is the propagation speed of electromagnetic waves, T p is the FMCW pulse width, R ref is the reference slant distance, γ is the range modulation frequency, f c Indicates the carrier center frequency, represents the wavelength corresponding to the center frequency, v is the speed of the radar platform, K r is the distance wave number; s2) Perform azimuth fast Fourier transform (FFT) on equation (1), and we have Perform matched filtering on equation (4), that is, multiply by Available S3) Use FiNUFFT to perform range resampling operation on equation (6); S4) Confirmation The value range of K y The maximum and minimum values ​​of ymax and K ymin ; Considering that the frequency range of discrete-time signals is [-π, π), in the interval [-π, π) for K y Perform linear normalization, that is, K y The value range of is limited to the interval [-π, π), denoted by K ynorm ; S5) Set the relative precision eps and the sign flag iflag; the relative precision eps takes the value 1e-6, and the sign flag iflag takes the value -1; let x be ss' IF (K r , K x ; x, y), c is K ynorm , N is the number of rows in x, and x, c, iflag, eps, N are passed as parameters to the function "f = finufftld1 (x, c, iflag, eps, N)". At this time, equation (6) becomes in, represents the central wave number, B′ is a constant related to the bandwidth of the range signal; S6) Perform azimuth residual phase compensation on equation (7), that is, multiply by S7) performs azimuth IFFT to obtain the final imaging result.

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