CN111881414B - Synthetic aperture radar image quality assessment method based on decomposition theory - Google Patents
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
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- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10032—Satellite or aerial image; Remote sensing
- G06T2207/10044—Radar image
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30168—Image quality inspection
Abstract
The invention discloses a synthetic aperture radar image quality evaluation method based on a decomposition theory, which comprises the following steps: step S1: SVD is used for rapidly obtaining accurate AF for the complex expression of the ambiguity function AF; the SVD is a singular value decomposition method and is used for solving the coupling problem of the distance direction and the azimuth direction in AF; step S2: the prior information is obtained, and a first zero point, a first side lobe peak value point and a 3dB point are obtained through a numerical method; step S3: according to the first zero point, the first side lobe peak point and the 3dB point obtained in the step S2, three quality parameters are obtained: ISLR, PSLR,3dB resolution. The invention has the advantages of simple principle, capability of reducing the complexity of calculation, improvement of the calculation precision and the like.
Description
Technical Field
The invention mainly relates to the technical field of radar imaging, in particular to a synthetic aperture radar image quality assessment method based on a decomposition theory.
Background
Synthetic aperture radar imaging quality is an important point in the design of synthetic aperture radar systems, where resolution, peak-to-side lobe ratio (PSLR), and Integrated Side Lobe Ratio (ISLR) are three important quality parameters that measure image quality. And the Ambiguity Function (AF) is a powerful mathematical tool to evaluate these three parameters. Therefore, it is important to find an accurate and rapid AF analysis method. The motion trajectory of the radar flying platform may be nonlinear due to factors such as the atmosphere, which may cause severe coupling of distance and azimuth directions, thereby complicating the fuzzy function analysis.
The existing fuzzy function analysis method comprises a numerical analysis method and an analytical method.
For the numerical analysis method, although the accuracy of the numerical analysis is high, if the number of sampling points in the distance direction and the azimuth direction is too large, the calculation complexity is greatly improved, and the calculation cost is increased.
For the analytic method, the nonlinear track of the radar flying platform can cause serious coupling of the distance and the azimuth, and the analytic method cannot fully consider the coupling of the distance and the azimuth, so that larger errors can be brought.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the technical problems existing in the prior art, the invention provides the synthetic aperture radar image quality evaluation method based on the decomposition theory, which has the advantages of simple principle, capability of reducing the calculation complexity and improving the calculation accuracy.
In order to solve the technical problems, the invention adopts the following technical scheme:
a synthetic aperture radar image quality evaluation method based on a decomposition theory comprises the following steps:
step S1: SVD is used for rapidly obtaining accurate AF for the complex expression of the ambiguity function AF; the SVD is a singular value decomposition method and is used for solving the coupling problem of the distance direction and the azimuth direction in AF;
step S2: the prior information is obtained, and a first zero point, a first side lobe peak value point and a 3dB point are obtained through a numerical method;
step S3: according to the first zero point, the first side lobe peak point and the 3dB point obtained in the step S2, three quality parameters are obtained: ISLR, PSLR,3dB resolution.
As a further improvement of the process of the invention: the step S1 includes:
step S101: introducing a small number of sampling points, performing singular value decomposition on the sampling points, and decoupling the distance and the azimuth;
step S102: mathematical deduction is carried out, AF is fitted into a high-order polynomial of distance and azimuth variables, double integral in AF is converted into product of two single integral, and finally the obtained AF expression is in the form of product of two single integral.
As a further improvement of the process of the invention: in the step S2, the method includes:
step S201: obtaining an approximate range of the parameter; calculating an approximate range of the three quality points using a sliding window method;
step S202: in obtaining the approximate range of three points, the three points are calculated by a numerical method.
As a further improvement of the process of the invention: the length of the sliding window is set to one tenth of 3dB resolution.
As a further improvement of the process of the invention: after obtaining the length of the sliding window, determining the range of the sliding window, wherein the specific method comprises the following steps:
for a given window w s ＝[a 1 ，b 1 ]If at a 1 Where the slope of AF is greater than zero, and at b 1 The slope at which is less than zero, the window range is the range of the first side lobe peak;
if the AF slope at the beginning of the window is less than zero and the AF slope at the end of the window is greater than zero, the window range is the range of the first zero;
after the first zero point is calculated, the 3dB point is positioned between the main lobe peak point and the first zero point;
if the windows are incorrect, the window range w needs to be updated s ＝[a 1 ，b 1 ]+Δl, where Δl is the length of the sliding window; and continuing the operation after updating the window range.
As a further improvement of the process of the invention: the step S202 includes:
calculating 3dB resolution to obtain the length of the sliding window;
determining the range of three quality points through a sliding window;
the slope according to AF is equal to zero at the peak value of the first side lobe, namely the first derivative of AF; the characteristic of jumping at the first zero point, calculating the peak point of the first side lobe and the first zero point by using a dichotomy;
is equal to at 3dB according to AFThe 3dB point is calculated using a dichotomy.
As a further improvement of the process of the invention: the step S3 specifically includes:
the 3dB resolution is defined as the 3dB width of AF, expressed and calculated by the following equation:
wherein the method comprises the steps ofAF amplitude representing 3dB point, +.>The AF amplitude of the main lobe peak point is represented.
PSLR is defined as the ratio of the first side lobe peak to the main lobe peak in dB calculated as:
wherein the method comprises the steps ofAF amplitude representing peak point of main lobe, +.>The AF magnitude of the first side lobe peak point is represented.
ISLR is defined as the energy ratio of the side lobe to the main lobe in dB, calculated as expressed in the following equation:
wherein the method comprises the steps ofRepresenting total energy->Representing the total energy of the main lobe, whereRepresenting the total energy of the side lobes.
Compared with the prior art, the invention has the advantages that:
1. the invention discloses a synthetic aperture radar image quality evaluation method based on a decomposition theory, which is used for solving the problem that a numerical analysis method and an analysis method are difficult to overcome.
2. The invention provides a synthetic aperture radar image quality evaluation method based on a decomposition theory, wherein the decomposition theory is an effective means for solving the coupling problem, and the invention provides a new AF analysis method by taking Singular Value Decomposition (SVD) as an example, and compared with a numerical analysis method, the invention greatly reduces the calculation complexity. Compared with an analysis algorithm, the method provided by the invention has higher calculation precision.
3. The analysis method is simple and convenient to calculate, but neglects the coupling of the AF distance direction and the azimuth direction, and has large calculation error. When the AF is analyzed by using a numerical method, if the accuracy requirement is high, the number of sampling points in the distance direction and the azimuth direction correspondingly increases, which leads to an increase in computational complexity. In the synthetic aperture radar image quality evaluation method based on the decomposition theory, the AF is calculated by using SVD, decoupling is performed by using a small number of sampling points, then an analytical expression of the AF is obtained, the calculation complexity is greatly reduced, and the calculation accuracy is not greatly different from that of a numerical method. The invention uses SVD to calculate and analyze AF, which not only can achieve higher calculation precision, but also can reduce the complexity of calculation.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of AF obtained based on SVD calculation in a specific application example of the present invention; wherein (a) is AF calculated based on an AF and numerical method calculated by SVD; (b) an error in AF obtained by SVD.
FIG. 3 is a schematic illustration of the invention in a specific application example for calculating the first derivative of AF; wherein (a) is a method for calculating the first derivative of AF based on SVD and the numerical method, and (b) is an error for obtaining the first derivative of AF using SVD.
Fig. 4 is an AF analysis chart in a specific application example of the present invention.
Fig. 5 is a schematic view of the satellite orbit in a specific application example of the present invention.
FIG. 6 is a diagram showing comparison of the accuracy of AF in a specific application example of the present invention; wherein (a) is a schematic diagram of calculating two-dimensional AFs using the algorithm proposed by the present invention; (b) is a schematic diagram of calculating two-dimensional AFs using a numerical algorithm. (c) To calculate the error, the color bar represents a percentage (i.e., 2 represents 2%), and x and y represent the longitude and latitude directions, respectively.
Detailed Description
The invention will be described in further detail with reference to the drawings and the specific examples.
As shown in fig. 1, the method for evaluating image quality of synthetic aperture radar based on decomposition theory of the present invention comprises the following steps:
step S1: and the accurate AF is obtained rapidly by using SVD for the existing complex expression of the ambiguity function AF.
SVD is singular value decomposition, which is an important matrix decomposition in linear algebra, and singular value decomposition is the popularization of feature decomposition on any matrix, and is mainly used for solving the coupling problem of distance direction and azimuth direction in AF.
Step S2: and obtaining prior information, and then solving a first zero point, a first side lobe peak point and a 3dB point by a numerical method.
Before calculating the three parameters (ISLR, PSLR,3dB resolution), three points (first zero, first side lobe peak point, 3dB point) need to be calculated. From fig. 3, it can be seen that the first derivative of AF is equal to zero at the peak of the first side lobe. Furthermore, since absolute value operation is used in solving AF, AF is discontinuous (jumps) at the first zero point, which can be clearly seen in fig. three. According to these two features, the peak value and the first zero point of the first side lobe can be calculated by using a numerical algorithm according to the first derivative of AF. Whereas at 3dB, the AF value is
Step S3: three quality parameters (ISLR, PSLR,3dB resolution) were found.
In a specific application example, the detailed flow of step S1 of the present invention includes:
step S101: introducing a small number of sampling points, performing singular value decomposition on the sampling points, and decoupling the distance and the azimuth;
step S102: mathematical deduction is carried out, AF is fitted into a high-order polynomial of distance and azimuth variables, double integral in AF is converted into product of two single integral, and finally the obtained AF expression is in the form of product of two single integral.
In a specific application example, the AF accuracy obtained by SVD is shown in fig. 1.
In a specific application example, the step S2 of the present invention includes:
step S201: obtaining an approximate range of the parameter;
the three quality points are calculated by a numerical algorithm, first of all, their approximate ranges need to be known. Otherwise, the numerical algorithm may not converge. In a specific application example, the present invention uses a sliding window method to calculate the approximate range of three quality points.
It should be noted that: the length of the sliding window determines its robustness. If the sliding window length is not appropriate, the calculated range may contain several zero and peak points.
The invention herein uses the algorithm in [1] to calculate the 3dB resolution to determine the range of the sliding window, in order to guarantee the robustness of the algorithm, in the preferred embodiment the invention sets the length of the sliding window to one tenth of the 3dB resolution.
Further, the present invention further provides a method for determining the range of the sliding window after obtaining the length of the sliding window, comprising:
for a given window w s ＝[a 1 ，b 1 ]If at a 1 Where the slope of AF is greater than zero, and at b 1 Where the slope is less than zero, the window range is the range of the first side lobe peak.
If the AF slope at the beginning of the window is less than zero and the AF slope at the end of the window is greater than zero, the window range is the range of the first zero point.
After the first zero point is calculated, the 3dB point is positioned between the main lobe peak point and the first zero point.
If the windows are incorrect, the window range w needs to be updated s ＝[a 1 ，b 1 ]+Δl, where Δl is the length of the sliding window. And continuing the operation after updating the window range. It should be noted that: a, a 1 Is a relatively small positive number.
Step S202: from the above analysis, the present invention has obtained an approximate range of three points, which can then be easily calculated by numerical methods (e.g., dichotomy), and overall, the solution process is as follows:
1. the 3dB resolution is calculated by the method in [1] to obtain the length of the sliding window.
2. The range of the three mass points is determined by a sliding window.
3. According to the characteristic that the slope of AF (namely the first derivative of AF) is equal to zero at the peak value of the first side lobe and jumps at the first zero point, the peak value point and the first zero point of the first side lobe are calculated by a dichotomy.
4. Is equal to at 3dB according to AFThe 3dB point can be calculated using a dichotomy.
The dichotomy is a method of gradually approaching the two end points of the interval to the zero point by continuously dividing the interval where the zero point of the function f (x) is located into two parts for the function y=f (x) with f (a) f (b) being less than 0 continuously on the intervals [ a, b ], and further obtaining the zero point approximation value. The invention mainly uses a dichotomy to obtain peak points of the first zero point and the first side lobe.
In a specific application example, the step S3 of the present invention specifically includes:
as shown in FIG. 4, AF in one direction, ρ/2 represents the 3dB point, ρ is the 3dB resolution, r I Is the first zero point, r P Is the first side lobe peak point. Wherein:
1. the 3dB resolution is defined as the 3dB width of AF, and can be expressed and calculated by the following equation:
wherein the method comprises the steps ofAF amplitude representing 3dB point, +.>The AF amplitude of the main lobe peak point is represented.
2. PSLR is defined as the ratio of the first side lobe peak to the main lobe peak in dB, and can be calculated as:
wherein the method comprises the steps ofAF amplitude representing peak point of main lobe, +.>The AF magnitude of the first side lobe peak point is represented.
3. ISLR is defined as the energy ratio of the side lobe to the main lobe in dB, and can be calculated as expressed in the following equation:
wherein the method comprises the steps ofRepresenting total energy->Representing the total energy of the main lobe, whereRepresenting the total energy of the side lobes.
It can be seen from fig. 2 that the AF calculated based on SVD has a small error compared with the AF calculated based on numerical method, but the current method for calculating AF has the highest accuracy, so from fig. 2 (b), we can see that the AF calculated based on SVD has a high accuracy, and the error is negligible compared with the numerical method.
It can be seen from fig. 3 (a) that the first derivative curve of AF calculated using SVD substantially coincides with the first derivative curve of AF calculated using numerical method, whereas the error of calculating the first derivative of AF based on SVD method is small and negligible as can be seen from the error image of fig. 3 (b).
From fig. 4, the main lobe and side lobe of AF, peak point of the first side lobe, etc. can be seen, and fig. 4 can facilitate analysis and calculation of three quality parameters.
As can be seen from fig. 5, the orbit of the satellite can be regarded as approximately a linear trajectory in a short time, and changes from approximately a linear trajectory to a nonlinear trajectory as the observation time increases.
As can be seen from fig. 6 (c), the error of both calculation methods is within 2%, and the error in the vast area is below 1%, indicating that on this track, the accuracy error of calculating AF based on SVD and calculating AF using numerical methods is negligible.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the invention without departing from the principles thereof are intended to be within the scope of the invention as set forth in the following claims.
Claims (4)
1. The synthetic aperture radar image quality evaluation method based on the decomposition theory is characterized by comprising the following steps:
step S1: SVD is used for rapidly obtaining accurate AF for the complex expression of the ambiguity function AF; the SVD is a singular value decomposition method and is used for solving the coupling problem of the distance direction and the azimuth direction in AF;
step S2: the prior information is obtained, and a first zero point, a first side lobe peak value point and a 3dB point are obtained through a numerical method;
step S3: according to the first zero point, the first side lobe peak point and the 3dB point obtained in the step S2, three quality parameters are obtained: ISLR, PSLR,3dB resolution;
in the step S2, the method includes:
step S201: obtaining an approximate range of the parameter; calculating an approximate range of the three quality points using a sliding window method; for a given window w s ＝[a 1 ,b 1 ]If at a 1 Where the slope of AF is greater than zero, and at b 1 The slope at which is less than zero, the window range is the range of the first side lobe peak; if the window startsThe window range is the range of the first zero point if the AF slope of (a) is less than zero and the AF slope at the end of the window is greater than zero; after the first zero point is calculated, the 3dB point is positioned between the main lobe peak point and the first zero point; if the windows are incorrect, the window range w needs to be updated s ＝[a 1 ,b 1 ]+Δl, where Δl is the length of the sliding window; continuing the operation after updating the window range;
step S202: calculating three points through a numerical method in the approximate range of the three points; calculating 3dB resolution to obtain the length of the sliding window; determining the range of three quality points through a sliding window; the slope according to AF is equal to zero at the peak value of the first side lobe, namely the first derivative of AF; the characteristic of jumping at the first zero point, calculating the peak point of the first side lobe and the first zero point by using a dichotomy; is equal to at 3dB according to AFThe 3dB point is calculated using a dichotomy.
2. The method for evaluating image quality of synthetic aperture radar based on decomposition theory according to claim 1, wherein said step S1 comprises:
step S101: introducing a small number of sampling points, performing singular value decomposition on the sampling points, and decoupling the distance and the azimuth;
step S102: mathematical deduction is carried out, AF is fitted into a high-order polynomial of distance and azimuth variables, double integral in AF is converted into product of two single integral, and finally the obtained AF expression is in the form of product of two single integral.
3. The method for evaluating image quality of synthetic aperture radar based on decomposition theory according to claim 1, wherein the length of the sliding window is set to one tenth of 3dB resolution.
4. A synthetic aperture radar image quality assessment method according to any one of claims 1-3, wherein said step S3 specifically comprises:
the 3dB resolution is defined as the 3dB width of AF, expressed and calculated by the following equation:
wherein the method comprises the steps ofAF amplitude representing 3dB point, +.>AF amplitude representing the peak point of the main lobe;
PSLR is defined as the ratio of the first side lobe peak to the main lobe peak in dB calculated as:
wherein the method comprises the steps ofAF amplitude representing peak point of main lobe, +.>An AF amplitude value representing a peak point of the first side lobe;
ISLR is defined as the energy ratio of the side lobe to the main lobe in dB, calculated as expressed in the following equation:
wherein the method comprises the steps ofRepresenting total energy->Representing the total energy of the main lobe, wherein +.>Representing the total energy of the side lobes, ρ/2 representing the 3dB point, ρ being the 3dB resolution, r I Is the first zero point, r P Is the first side lobe peak point.
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