Data-driven fractional wavelet transform domain ISAR imaging method, device, storage medium and product

Abstract

The data-driven fractional wavelet transform domain ISAR imaging method, device, storage medium and product belong to the technical field of radar imaging, and solve the problems that the existing ISAR imaging technology cannot obtain high time-frequency resolution and the imaging quality is low due to the influence of cross terms. The method comprises the following steps: finding a fractional Fourier transform domain with energy aggregation of a to-be-processed signal, designing a fractional wavelet base function, filtering and decomposing the to-be-processed signal through a semi-discrete fractional convolution, then representing the decomposed signal through a Wigner distribution, and finally obtaining a time-frequency representation in which cross terms are eliminated. Compared with the traditional method, the present application ensures high resolution of ISAR imaging, and avoids the influence of cross terms. Therefore, the present application can realize high-quality ISAR imaging. The present application is suitable for inverse synthetic aperture radar (ISAR) imaging.

Description

Technical Field

[0001] The present application relates to the field of radar imaging technology, and in particular to ISAR imaging. Background Art

[0002] Synthetic Aperture Radar (SAR), developed from both airborne and satellite-based systems, not only provides target velocity and position information but also produces high-resolution spatial radar images. When the radar is fixed but the target is moving, the imaging radar, in this case an Inverse Synthetic Aperture Radar (ISAR), can search for targets in all directions and in all weather conditions, making it of great value in battlefield reconnaissance and civilian applications.

[0003] The classical ISAR imaging method is to use the echo signal after range tracking and Doppler tracking. (where m represents the distance unit) The signal r of m at different distances m (t) Performing Fourier transform (FT) can obtain a two-dimensional image: For any 1≤m≤M, R m (ω)=FT(r m (t)), where FT represents Fourier transform and ω represents the Doppler shift. The classic ISAR imaging method based on FT is primarily targeted at stationary moving targets. When the target's motion is complex and nonstationary, such as rotation or acceleration, the echo signal becomes nonstationary, and motion compensation often fails to produce a clear image.

[0004] At this time, it is necessary to use the time-frequency representation (TFR) analysis method instead of Fourier transform for focusing processing, specifically for the signal r at the distance m unit. m (t) and obtain a three-dimensional range-time-Doppler cube map: (For any 1≤m≤M, for signal r m (t) Perform TFR and get a set of q about time-frequency m (t,ω)). Common TFR methods include short-time Fourier transform (STFT) and Wigner-Ville distribution (WVD). However, STFT cannot achieve high time-frequency resolution, while WVD can achieve high resolution. However, WVD is affected by cross terms and cannot be used in practice. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems that existing ISAR imaging technology cannot achieve high time-frequency resolution and is affected by cross terms, resulting in low imaging quality. It provides a data-driven fractional wavelet transform domain ISAR imaging method, equipment, storage medium and product.

[0006] The application is realized by the following technical schemes, and the application provides a data-driven fractional wavelet transform domain ISAR imaging method, which comprises the following steps:

[0007] Step 1, acquiring the ISAR echo signal subjected to motion compensation wherein M represents the number of distance units, t represents time, and the loop variable s is initialized as 0;

[0008] Step 2, updating the loop variable s = s + 1, and decomposing the signal r s (t) under one s, specifically comprising the following steps:

[0009] Step 2.1, expressing r s (t) as a signal f(t), and calculating the angle α corresponding to the fractional Fourier transform domain with the best energy concentration of the signal f(t) op t ;

[0010] Step 2.2, calculating the support interval U of f(t) to be decomposed in the fractional Fourier transform domain with the best energy concentration of the angle α opt k = [u k-1 ,u k ], wherein 1≤k≤K, and K represents the number of intervals;

[0011] Step 2.3, according to the type of the support interval, calculating the support interval center c k of the support interval, constructing the fractional domain form of the fractional wavelet base function used for signal decomposition, and the type of the support interval comprises a finite support interval, a leftmost infinite support interval and a rightmost infinite support interval;

[0012] Step 2.4, performing inverse transformation of the Fourier transform on the fractional domain form of the fractional wavelet base function used for signal decomposition, wherein the transformation element is scaled by cscα op t to obtain the time domain form of the data-driven fractional wavelet base function used for signal decomposition;

[0013] Step 2.5, using the constructed fractional wavelet base function ψ k (t) to realize the decomposition of the signal f(t) through fractional convolution operation, and obtaining the decomposition signal

[0014] Step 2.6, for , performing the Wigner distribution related to it on , and obtaining wherein ω represents Doppler frequency; and performing the Wigner distribution related to it on ​By synthesizing, we can get the time-frequency representation result q under the distance unit s s (t,ω), specifically:

[0015] right

[0016] Step 3: Determine whether s is greater than or equal to M. If s is greater than or equal to M, it indicates that the time-frequency representation under each distance unit has been completed, and execute step 4; otherwise, return to step 2.

[0017] Step 4: Output the range-time-Doppler cubemap right Take a moment at time t and obtain a two-dimensional ISAR image of the target at that moment.

[0018] Furthermore, in step 2.1, the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is opt The method to obtain is:

[0019]

[0020] Among them, F α (u) is the fractional Fourier transform of f(t) at angle α.

[0021] Furthermore, in step 2.3, if the signal to be decomposed f(t) is at the α where its energy is best concentrated opt The support interval in the angle fractional Fourier transform domain belongs to the finite support interval, that is, Its interval length is defined as |U k |=u k+1 -u k , and then there is interval U k The center of the interval is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is

[0022] Furthermore, in step 2.3, if there is an infinite support interval on the left, then for the infinite support interval on the left, U1 = (-∞, u1], where |U1| = u2-u1, and the interval center of interval U1 is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is

[0023] Furthermore, in step 2.3, if there is an infinite support interval on the right, for the infinite support interval on the rightmost end U K =[u K-1 ,+∞), where |U K-2 |=uK-1 -u K-2 , and the interval U K The center of the interval is In the interval U K The fractional domain form of the fractional-order wavelet basis function designed above is

[0024]

[0025] Furthermore, in step 2.4, the time domain form of the fractional-order wavelet basis function used for signal decomposition is ψ k The specific method for obtaining (t) is: Where j represents the imaginary unit.

[0026] Furthermore, in step 2.5, the decomposed signal The specific method of obtaining is: 1≤k≤K, where *α opt Indicates angle α opt Fractional convolution under , Represents ψ k The conjugate of (t).

[0027] In a first aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the steps of the data-driven fractional wavelet transform domain ISAR imaging method as described above are executed.

[0028] In a second aspect, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a plurality of computer instructions, and the plurality of computer instructions are used to enable a computer to execute a data-driven fractional wavelet transform domain ISAR imaging method as described above.

[0029] In a third aspect, the present invention provides a computer program product, which, when executed by a processor, implements the data-driven fractional wavelet transform domain ISAR imaging method as described above.

[0030] Beneficial effects of the present invention:

[0031] The present invention improves the quality of ISAR imaging by eliminating the cross terms in WVD and using fractional wavelet basis functions. (K is the number of fractional wavelet basis functions) for any signal r under 1≤m≤M m (t) Perform semi-discrete fractional-order convolution filtering and then perform WVD to eliminate the cross terms.

[0032] The present invention aims to achieve high-resolution radar imaging. By utilizing fractional wavelet transform tools, a data-driven fractional wavelet basis function is designed to effectively remove cross terms in WVD. Designing a data-driven fractional wavelet basis function involves selecting the fractional domain at corresponding angles based on the characteristics of the signal to be processed in the fractional domain to divide the support interval of the fractional domain into the design of the fractional wavelet basis function.

[0033] In the fractional Fourier transform domain, where signal energy is optimally concentrated, a data-driven fractional wavelet basis function is constructed. After decomposing the signal, WVD is then performed to effectively remove cross-terms. Compared to existing methods, this radar imaging method achieves high resolution while minimizing the impact of cross-terms, resulting in high-quality images.

[0034] The present invention is applicable to inverse synthetic aperture radar ISAR imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0036] Figure 1 This is a block diagram of the ISAR imaging principle based on fractional wavelet of the present invention;

[0037] Figure 2 This is a block diagram of the signal decomposition principle of S2 based on the data-driven fractional wavelet transform domain in the eighth embodiment of the present invention;

[0038] Figure 3 Comparison diagram of ISAR imaging: (a) ISAR imaging image processed by traditional FT (b) ISAR imaging image processed by STFT (c) ISAR imaging image processed by WVD (d) imaging image processed by the present invention. DETAILED DESCRIPTION

[0039] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, but are not to be construed as limiting the present invention.

[0040] Specific embodiment 1: A data-driven fractional wavelet transform domain ISAR imaging method, the method comprising:

[0041] Step 1: Obtain motion-compensated ISAR echo signals Where M represents the number of distance units, t represents time, and the loop variable s is initialized to 0;

[0042] Step 2: Update the loop variable s=s+1, and for a signal r under s s (t) decomposition, including:

[0043] Step 2.1, r s (t) is expressed as signal f(t), and the angle α corresponding to the fractional Fourier transform domain where the energy of signal f(t) is optimally concentrated is calculated. opt ;

[0044] Step 2.2, calculate the α where the energy of f(t) to be decomposed is best concentrated opt The support interval U in the angle fractional Fourier transform domain k =[u k-1 ,u k ], where 1≤k≤K, K represents the number of intervals;

[0045] Step 2.3: Calculate the support interval center c of the support interval according to the type of support interval k , constructing a fractional domain form of a fractional-order wavelet basis function for signal decomposition, wherein the types of the support interval include a finite support interval, a leftmost infinite support interval, and a rightmost infinite support interval;

[0046] Step 2.4: Perform inverse Fourier transform on the fractional domain form of the fractional order wavelet basis function used for signal decomposition, wherein the transform element is scaled cscα opt Scale to obtain the time domain form of the fractional wavelet basis function for signal decomposition based on data driven k (t);

[0047] It should be noted that, among them, the scale of the transformation element is cscα opt The purpose of scaling here is to make the designed fractional-order wavelet basis function keep consistent with the corresponding filtering interval and the support interval of the divided fractional domain when performing fractional-order convolution with the signal.

[0048] Step 2.5: Use the constructed fractional wavelet basis function ψ k (t), the signal f(t) is decomposed by fractional convolution operation, and the decomposed signal is obtained

[0049] Step 2.6, for right Doing the Wigner distribution (WVD) on it, we get Where ω represents the Doppler frequency; By synthesizing, we can get the time-frequency representation result q under the distance unit s s (t,ω), specifically:

[0050] right

[0051] Step 3: Determine whether s is greater than or equal to M. If s is greater than or equal to M, it indicates that the time-frequency representation under each distance unit has been completed, and execute step 4; otherwise, return to step 2.

[0052] Step 4: Output the range-time-Doppler cubemap right Take a moment at time t and obtain a two-dimensional ISAR image of the target at that moment.

[0053] In this embodiment, the quality of ISAR imaging is improved by eliminating the cross terms in WVD and using fractional wavelet basis functions. (K is the number of fractional wavelet basis functions) for any signal r under 1≤m≤M m (t) Perform semi-discrete fractional-order convolution filtering and then perform WVD to eliminate the cross terms.

[0054] The goal of this embodiment is to achieve high-resolution radar imaging. By utilizing fractional wavelet transform tools, a data-driven fractional wavelet basis function is designed to effectively remove cross terms in the WVD. Designing a data-driven fractional wavelet basis function involves selecting the fractional domain at corresponding angles based on the characteristics of the signal to be processed in the fractional domain to design the fractional wavelet basis function.

[0055] In the fractional Fourier transform domain, where signal energy is optimally concentrated, a data-driven fractional wavelet basis function is constructed. After decomposing the signal, WVD is then performed to effectively remove cross-terms. This embodiment of radar imaging achieves high resolution while minimizing the impact of cross-terms, resulting in high-quality imaging.

[0056] Specific embodiment 2, this embodiment is a further limitation of the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment 1. In this embodiment, in step 2.1, the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is opt , further defined, including:

[0057] In step 2.1, the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is opt The method to obtain is:

[0058]

[0059] Among them, F α (u) is the fractional Fourier transform of f(t) at angle α.

[0060] In this embodiment, the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is given. opt The acquisition method can effectively construct the data-driven fractional wavelet basis function.

[0061] Specific embodiment three, this embodiment further limits the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment one. In this embodiment, step 2.3 is further limited, specifically including:

[0062] In step 2.3, if the signal to be decomposed f(t) is at the α where its energy is best concentrated opt The support interval in the angle fractional Fourier transform domain belongs to the finite support interval, that is, Its interval length is defined as |U k |=u k+1 -u k , and then there is interval U k The center of the interval is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is

[0063] In this embodiment, a fractional domain form of a data-driven fractional-order wavelet basis function is designed to construct a fractional-order wavelet basis function, which can effectively remove cross terms in WVD.

[0064] Specific embodiment 4: This embodiment further limits the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment 3. In this embodiment, step 2.3 is further limited, specifically including:

[0065] In step 2.3, if there is an infinite support interval on the left, then for the infinite support interval on the left, U1 = (-∞,u1], where |U1| = u2-u1, and the center of interval U1 is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is

[0066] In this embodiment, a fractional domain form of a data-driven fractional-order wavelet basis function is designed to construct a fractional-order wavelet basis function, which can effectively remove cross terms in WVD.

[0067] Specific embodiment 5. This embodiment further limits the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment 4. In this embodiment, step 2.3 is further limited, specifically including:

[0068] In step 2.3, if there is an infinite support interval on the right, for the infinite support interval U on the rightmost end K =[u K-1 ,+∞), where |U K-2 |=u K-1 -u K-2 , and the interval U K The center of the interval is In the interval U K The fractional domain form of the fractional-order wavelet basis function designed above is

[0069]

[0070] In this embodiment, for different support interval types, corresponding data-driven fractional-order wavelet basis functions in the fractional domain are designed to construct more effective fractional-order wavelet basis functions, thereby more effectively removing cross terms in WVD.

[0071] Specific embodiment six, this embodiment is a further limitation of the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment one. In this embodiment, in step 2.4, the fractional wavelet basis function ψ k (t) is further limited to include:

[0072] In step 2.4, the time domain form of the fractional wavelet basis function used for signal decomposition is ψ k The specific method for obtaining (t) is: Where j represents the imaginary unit.

[0073] In this embodiment, the fractional wavelet basis function ψ is given k (t) is obtained by using the data-driven fractional wavelet basis function (K is the number of fractional wavelet basis functions) for any signal r under 1≤m≤M m (t) Perform fractional-order convolution filtering and then perform WVD to eliminate the cross terms.

[0074] Specific embodiment six, this embodiment is a further limitation of the data-driven fractional wavelet transform domain ISAR imaging method described in embodiment one. In this embodiment, in step 2.5, the decomposed signal Further restrictions have been made, including:

[0075] In step 2.5, the decomposed signal The specific method of obtaining is: where *α opt Indicates angle α opt Fractional convolution under , Represents ψ k The conjugate of (t).

[0076] In this embodiment, a method for obtaining a decomposed signal based on a fractional-order wavelet basis function is provided, thereby ensuring that the radar imaging has high resolution while reducing the influence of cross terms, thereby forming high-quality imaging.

[0077] Specific embodiment eight, this embodiment is based on an embodiment of a data-driven fractional wavelet transform domain ISAR imaging method as described above, such as Figure 1 As shown, specifically including:

[0078] S1. Obtaining ISAR echo signals after motion compensation Initialize loop variable s=0.

[0079] S2, update the loop variable s=s+1, for a signal r under s s (t) is decomposed, and its principle block diagram is as follows Figure 2 As shown, the specific implementation process is as follows:

[0080] S2.1 will r s (t) is represented by the signal to be decomposed f(t), and the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is calculated. opt ,Right now

[0081]

[0082] S2.2. Calculate the α where the energy of f(t) to be decomposed is optimally concentrated. opt The support interval U in the angle fractional Fourier transform domain k =[u k-1 ,u k ], where 1≤k≤K. At the same time, calculate the support interval center c k .

[0083] S2.3. Based on the specific type of the calculated support interval, calculate the center of the support interval and construct the fractional domain form of the fractional-order wavelet basis function for signal decomposition. The following three cases are discussed:

[0084] (1) If the signal to be decomposed f(t) is at the α where its energy is best concentrated opt The support interval in the angle fractional Fourier transform domain belongs to the finite support interval, that is, Then the interval center And the fractional domain form of the fractional-order wavelet basis function

[0085]

[0086] (2) If there is an infinite support interval on the left, then for the infinite support interval on the left, U1 = (-∞, u1], then the center of the interval is And the fractional domain form of the fractional-order wavelet basis function,

[0087]

[0088] (3) If there is an infinite support interval on the right, for the infinite support interval on the rightmost end U K =[u K-1 ,+∞), then the center of the interval And the fractional domain form of the fractional-order wavelet basis function,

[0089]

[0090] S2.4, for Ψ k (ucscα) performs the inverse Fourier transform (the transform element is scaled cscα opt , and obtain the time domain form of the fractional wavelet basis function for signal decomposition based on data-driven k (t), i.e.

[0091]

[0092] S2.5, using the time domain form of the constructed fractional wavelet basis function ψ k (t), the signal f(t) is decomposed by fractional convolution operation, and the decomposed signal is

[0093]

[0094] S2.6. For According to formula (1) Doing the Wigner distribution (WVD) on it, we get Further the results By synthesizing, we can get the time-frequency representation result q under the distance unit s s (t,ω), where

[0095] S3. Determine whether s is greater than or equal to M. If s is greater than or equal to M, it means that the time-frequency representation of each distance unit has been completed. At this time, proceed to the next step. Otherwise, return to S2.

[0096] S4. Output range-time-Doppler cube map right Taking a moment at time t can obtain a two-dimensional ISAR image of the target at that moment.

[0097] The following simulation further illustrates this:

[0098] The data is the radar signal of the MIG-25 after range tracking and Doppler tracking. Here M=64.

[0099] By processing real aircraft data through various technologies, we can obtain Figure 3 The imaging diagram, Figure 3 (a) is the image after FT processing, where the outline of the aircraft cannot be clearly distinguished. Figure 3 (b) is the image after STFT processing, which shows the outline of MIG-25 more clearly, but has a lower time-frequency resolution. Figure 3 (c) shows the image obtained by WVD processing. It is found that it is greatly affected by the cross term and the outline of MIG-25 cannot be distinguished. Figure 3 (d) shows the effect after processing by the present invention. The image not only can clearly observe the outline of the aircraft, but also has good time-frequency resolution.

[0100] The Rayleigh entropy of the imaging results is usually chosen to measure the imaging effect, that is,

[0101]

[0102] Where TFR(t,ω) represents an arbitrary time-frequency representation, t and ω represent time and frequency, respectively. The parameter γ = 3 is generally chosen to calculate the Rayleigh entropy. A larger Rayleigh entropy indicates a blurrier image, while a smaller one indicates a clearer image. Figure 3 The Rayleigh entropy values ​​of FT, STFT, WVD and the present invention are 11.9135, 11.4041, 11.5065 and 10.3086 respectively. The present invention also has an advantage in terms of numerical value, which fully demonstrates that the present invention has a good imaging effect.

[0103] The concepts of fractional Fourier transform and fractional wavelet basis function are introduced below to analyze the method of this application:

[0104] For energy-finite time series Its WVD can be expressed as follows,

[0105]

[0106] Where the superscript symbol * represents the conjugate operation, ω represents the frequency, τ has the same effect as τ in convolution, and x = x(t). The fractional Fourier transform of

[0107]

[0108] Where, F α represents the fractional Fourier transform operator, and the kernel function Kα(u,t) is expressed as

[0109]

[0110] Where k∈Z, α represents the angle of the fractional Fourier transform, j represents the imaginary unit, the variable u is usually called the fractional frequency, and δ(·) represents the impulse function. The coordinate axis on which it is located is usually called the fractional Fourier transform domain (abbreviated as fractional domain). Correspondingly, the formula for the inverse transform of the fractional Fourier transform is

[0111]

[0112] In particular, when α=π / 2, the fractional Fourier transform degenerates into the traditional Fourier transform.

[0113] In addition, to simplify the analysis, we need to introduce the concept of convolution under semi-discrete fractional Fourier transform. and The fractional convolution is defined as

[0114]

[0115] Under the fractional Fourier transform, the fractional convolution satisfies

[0116]

[0117] Where G(ucscα) represents the Fourier transform of the signal g(t) (the transform element is scaled by cscα).

[0118] Furthermore, the definition of fractional wavelet transform is introduced. For any energy-limited signal f(t)∈L 2 The fractional wavelet transform of (R) is defined as

[0119]

[0120] Where, the kernel function ψ α,a,t The expression of (τ) is

[0121]

[0122] Where, the scale parameter a and the time shift parameter t satisfy: a∈R + , t∈R. According to the definition of fractional convolution, the definition of fractional wavelet transform can be rewritten as

[0123]

[0124] Therefore, combined with formula (4), it can also be rewritten as

[0125]

[0126] Where Ψ(ucscα) represents the Fourier transform of the mother wavelet function ψ(t) (the transform element is scaled by cscα). This shows that the fractional wavelet transform is essentially a set of multiplicative multiscale filters in the fractional Fourier transform domain. According to fractional Fourier transform theory, multiplicative filters in the fractional Fourier transform domain are linear time-varying filters, suitable for nonstationary signal processing.

[0127] Based on the above analysis, a data-driven signal decomposition method in the fractional wavelet transform domain of the present application is described below.

[0128] The fractional Fourier transform spectrum of is divided into K continuous intervals, each of which corresponds to a modal component with a compactly supported fractional Fourier transform spectrum centered at a certain fractional frequency. The endpoint set of the interval represents the support interval of the fractional Fourier transform spectrum, which can be defined as

[0129]

[0130] Record Order Represents the support interval set of the fractional Fourier transform spectrum. There are infinite support intervals on the left and right ends of the fractional Fourier transform spectrum. The support interval on the left is represented by U1=(-∞,u1], and the support interval on the right is represented by U K =[u K-1 ,+∞). For each support interval, its interval length is defined as |U k |=u k+1 -u k .

[0131] For the considered fractional Fourier transform spectrum support interval U n The center of is defined as

[0132]

[0133] Based on the description of the support interval of the fractional Fourier transform spectrum above, the construction of the data-driven fractional wavelet is given below. In order to fully reveal the time-frequency characteristics of the signal, the Gabor function is selected as the mother wavelet because the Gabor function has the best time-frequency energy aggregation and can provide the best time-frequency distribution rate. Therefore, the expression of the mother wavelet function can be obtained as follows:

[0134]

[0135] According to the definition of fractional wavelet transform, the fractional Fourier transform domain form of the mother wavelet function can be obtained by scaling the Fourier transform, that is,

[0136]

[0137] Where Ψ(ucscα) is the Fourier transform of the mother wavelet function ψ(t) (the transform element is scaled by cscα). Further, the parameter ν = 0 is selected. Then there is

[0138]

[0139] Under this parameter, 99.999% of the energy of the mother wavelet function is concentrated in the fractional Fourier transform domain interval [-sinα / 2, sinα / 2], and Ψ(0) = 1. Based on this, in the fractional Fourier transform domain finite support interval U k =[u k-1 ,u k ], that is, when 2≤k≤K-1, the fractional order wavelet basis function ψ used for signal decomposition k The fractional domain form of (t) is defined as

[0140]

[0141] Where, k (ucscα) is ψ k Fourier transform of (t) (the transformation element is scaled by cscα).

[0142] Similarly, on the infinite support interval U1 = (-∞, u1] at the left end, the fractional domain form of the fractional wavelet basis function used for signal decomposition is defined as

[0143]

[0144] Similarly, at the right end, there is an infinite support interval U K =[u K-1 ,+∞), the fractional domain form of the fractional-order wavelet basis function used for signal decomposition is defined as

[0145]

[0146] Based on the above results, the expression of data-driven fractional wavelet transform is

[0147]

Claims

1. A data-driven fractional wavelet transform domain ISAR imaging method, characterized in that: The method comprises: Step 1: Obtain motion-compensated ISAR echo signals Where M represents the number of distance units, t represents time, and the loop variable s is initialized to 0; Step 2: Update the loop variable s=s+1, and for a signal r under s s (t) decomposition, including: Step 2.1, r s (t) is expressed as signal f(t), and the angle α corresponding to the fractional Fourier transform domain where the energy of signal f(t) is optimally concentrated is calculated. opt ; Step 2.2, calculate the α where the energy of f(t) to be decomposed is best concentrated opt The support interval U in the angle fractional Fourier transform domain k =[u k-1 ,u k ], where 1≤k≤K, K represents the number of intervals; Step 2.3: Calculate the support interval center c of the support interval according to the type of support interval k , constructing a fractional domain form of a fractional-order wavelet basis function for signal decomposition, wherein the types of the support interval include a finite support interval, a leftmost infinite support interval, and a rightmost infinite support interval; Step 2.4: Perform inverse Fourier transform on the fractional domain form of the fractional order wavelet basis function used for signal decomposition, wherein the transform element is scaled cscα opt Scaling, obtaining the time domain form of the fractional wavelet basis function for signal decomposition based on data-driven; Step 2.5: Use the constructed fractional wavelet basis function ψ k (t), the signal f(t) is decomposed by fractional convolution operation, and the decomposed signal is obtained Step 2.6, for right Doing the Wigner distribution on it, we get Where ω represents the Doppler frequency; By synthesizing, we can get the time-frequency representation result q under the distance unit s s (t,ω), specifically: right Step 3: Determine whether s is greater than or equal to M. If s is greater than or equal to M, it indicates that the time-frequency representation under each distance unit has been completed, and execute step 4; otherwise, return to step 2. Step 4: Output the range-time-Doppler cubemap right Take a moment at time t and obtain a two-dimensional ISAR image of the target at that moment.

2. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 1, characterized in that: In step 2.1, the angle α corresponding to the fractional Fourier transform domain where the energy of the signal f(t) is optimally concentrated is opt The method to obtain is: Among them, F α (u) is the fractional Fourier transform of f(t) at angle α.

3. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 1, characterized in that: In step 2.3, if the signal to be decomposed f(t) is at the α where its energy is best concentrated opt The support interval in the angle fractional Fourier transform domain belongs to the finite support interval, that is, Its interval length is defined as |U k |=u k+1 -u k , and then there is interval U k The center of the interval is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is 4. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 3, characterized in that: In step 2.3, if there is an infinite support interval on the left, then for the infinite support interval on the left, U1 = (-∞,u1], where |U1| = u2-u1, and the center of interval U1 is In the interval U k The fractional domain form of the fractional-order wavelet basis function designed above is 5. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 4, characterized in that: In step 2.3, if there is an infinite support interval on the right, for the infinite support interval U on the rightmost end K =[u K-1 ,+∞), where |U K-2 |=u K-1 -u K-2 , and the interval U K The center of the interval is In the interval U K The fractional domain form of the fractional-order wavelet basis function designed above is 6. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 1, characterized in that: In step 2.4, the time domain form of the fractional wavelet basis function used for signal decomposition is ψ k The specific method for obtaining (t) is: Where j represents the imaginary unit.

7. The data-driven fractional wavelet transform domain ISAR imaging method according to claim 1, characterized in that: In step 2.5, the decomposed signal The specific method of obtaining is: in Indicates angle α opt Fractional convolution under , Represents ψ k The conjugate of (t).

8. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor runs the computer program stored in the memory, the steps of the method according to any one of claims 1 to 7 are performed.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a plurality of computer instructions, and the plurality of computer instructions are used to enable a computer to execute the method according to any one of claims 1 to 7.

10. A computer program product, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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