CN101666879B - Method for improving resolution of linear-array three-dimensional imaging synthetic aperture radars - Google Patents

Abstract

The invention provides a resolution fusion method of linear array three-dimensional imaging synthetic aperture radar, which uses two linear array three-dimensional imaging synthetic aperture radars with orthogonal motion trajectories to image the same area, and then adopts discrete wavelet transform technology to convert The obtained two images are fused to obtain a high-resolution linear array three-dimensional imaging synthetic aperture radar image. The invention has the advantage of realizing the high-resolution imaging of the linear array three-dimensional imaging synthetic aperture radar by using a shorter array antenna, and solving the problem of low resolution of the cut track of the image obtained by the linear array three-dimensional imaging synthetic aperture radar. The invention can be widely used in the fields of synthetic aperture radar imaging, earth remote sensing, geological surveying and mapping, and the like.

Description

A Method of Improving the Resolution of Linear Array 3D Imaging Synthetic Aperture Radar

technical field

The invention belongs to the technical field of radar, in particular to the technical field of linear array three-dimensional imaging synthetic aperture radar (LASAR) imaging.

Background technique

Linear array three-dimensional imaging synthetic aperture radar (LASAR) is a new type of synthetic aperture radar system that fixes the linear array antenna on a moving platform to synthesize a two-dimensional planar array and perform three-dimensional imaging. Linear array three-dimensional imaging synthetic aperture radar can realize the ability of imaging three-dimensional ground which cannot be realized by single-antenna synthetic aperture radar at present, and has become a research hotspot in the field of synthetic aperture radar. According to the inventor's knowledge and published documents, for example: J.Klare, A.Brenner, J.Ender, "A New Airborne Radar for 3D Imaging-Image Formation using the ARTINO Principle-", EUSAR, Dresden, Germany, 2006. BASSEM R.MAHAFZA, MITCH SAJJADI "Three-dimensional SAR imaging using linear array in transverse motion" IEEEtransaction on aerospace and electronic system VOL 32, NO.1JANUARY 1996, due to the limitation of the length of the array antenna, the linear array three-dimensional imaging synthetic aperture radar obtained The tangent track resolution of the image is generally smaller than the along track direction resolution. In order to improve the resolution of linear array 3D imaging synthetic aperture radar, the corresponding resolution fusion technology must be studied. According to the knowledge of the present inventors, there is no published technical literature on the resolution fusion method of linear array three-dimensional imaging synthetic aperture radar.

Contents of the invention

In order to overcome the problem that the tangent track resolution of images obtained by the existing linear array 3D imaging synthetic aperture radar is generally smaller than the resolution along the track direction, the present invention provides a method for improving the resolution of the linear array 3D imaging synthetic aperture radar. The method of the invention can obtain the high-resolution line array three-dimensional imaging synthetic aperture radar image after the fusion of the orthogonal track three-dimensional imaging synthetic aperture radar.

In order to describe content of the present invention conveniently, at first do following term definition:

Definition 1. Linear Array 3D Imaging Synthetic Aperture Radar (LASAR)

Linear array three-dimensional imaging synthetic aperture radar (LASAR) is a new type of synthetic aperture radar system that fixes the linear array antenna on a moving platform to synthesize a two-dimensional planar array and perform three-dimensional imaging. See literature for details: R.Giret, H.Jeuland, P.Enert, "A Study of a 3D-SAR Concept for aMillimeter-Wave Imaging Radar onboard an UAV", European Radar Conference, 2004, pp 201-204.. Due to the limitation of the length of the array antenna, the tangent-track resolution of the images obtained by linear-array 3D imaging synthetic aperture radar is generally smaller than the along-track resolution.

Definition 2. Linear array 3D imaging synthetic aperture radar image

Linear array 3D imaging synthetic aperture radar image refers to the data obtained after imaging processing of linear array 3D imaging synthetic aperture radar data, which includes the distribution of scattering coefficients at different positions in space. See literature for details: J.Klare, A.Brenner, J.Ender, "A New Airborne Radar for 3D Imaging-Image Formation using the ARTINO Principle-", EUSAR, Dresden, Germany, 2006. The length and width of the image can be obtained from the linear array three-dimensional imaging synthetic aperture radar image, which are recorded as P and Q respectively.

Definition 3. Orthogonal track three-dimensional imaging synthetic aperture radar

Orthogonal track three-dimensional imaging synthetic aperture radar means that two linear array three-dimensional imaging synthetic aperture radars fly along mutually perpendicular motion tracks, and the track directions are respectively recorded as x direction and y direction, and the synthetic aperture direction of synthetic aperture radar SAR-A is along In the x direction, the image formed by the synthetic aperture radar SAR-A has a higher resolution in the x direction, and the y direction is the real aperture direction of the radar SAR-A, and the resolution in the y direction is lower. Synthetic Aperture Radar (SAR-B) is just the opposite. See attached drawing 1 for its working principle diagram, and refer to the literature for the working process of three-dimensional imaging synthetic aperture radar with orthogonal trajectory: J.Klare, A.Brenner, J.Ender, "A New Airborne Radar for 3D Imaging-Image Formation using the ARTINO Principle-", EUSAR, Dresden, Germany, 2006.

Definition 4. Low-resolution linear array 3D imaging synthetic aperture radar image in x(y) direction

Two linear array 3D imaging synthetic aperture radar images can be obtained by using the orthogonal track 3D imaging synthetic aperture radar, one of which has a high resolution in the y direction and a low resolution in the x direction, called the x direction The low-resolution linear array 3D imaging SAR image is denoted as G ^x ; the other linear array 3D imaging SAR image has high x-direction resolution and low y-direction resolution, which is called y-direction low-resolution linear array Three-dimensional imaging synthetic aperture radar image, denoted as G ^y .

Definition 5. One-dimensional discrete wavelet decomposition and reconstruction

For one-dimensional signal f _j+1 (n), its fast orthogonal wavelet transform relationship is as follows:

Fast orthogonal wavelet decomposition:

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>$

Among them, * means convolution, and n means discrete signal points. h(2n) and g(2n) represent 1/2 sampling after low-pass h(n) (high-pass g(n)) filtering of the high-resolution approximation signal. g(n) is the high-pass filter corresponding to h(n).

Fast Orthogonal Wavelet Reconstruction:

The proof of the above formula is detailed in the literature Stephane Mallat, "A Wavelet Tour of Signalprocessing", [c] 2nd ed.Chap.VII, Academic press Elsevier Pte Ltd, 2003. Fast Orthogonal Wavelet Transform can be seen in Figure 2 in the form of a system block diagram.

Definition 6. Two-dimensional discrete wavelet decomposition and reconstruction

An image f _j+1 (n ₁ , n ₂ ) can be decomposed by discrete wavelet using the following formula:

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

${\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="no"\; filenames="H2008100459746E00012.png"\; state="\{\{state\}\}">no</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

是原图的低频系数矩阵，

和

分别是水平，垂直和对角线方向的高频系数矩阵。Among them, * means convolution. n ₁ and n ₂ respectively denote pixels in the horizontal and vertical dimensions of the two-dimensional image. h(n) is a low-pass filter and g(n) is the corresponding high-pass filter. h(2n ₁ ), h(2n ₂ ) represent the downsampling of the horizontal and vertical dimensions of the image after low-pass filtering, respectively, g(2n ₁ ), g(2n ₂ ) represent the downsampling of the image after high-pass filtering of the horizontal and vertical dimensions, respectively . after decomposition

is the low-frequency coefficient matrix of the original image,

and

are the high-frequency coefficient matrices for the horizontal, vertical and diagonal directions, respectively.

The method of wavelet reconstruction using the above coefficients is:

in:

The process of discrete wavelet decomposition and reconstruction is shown in Figure 3. For the method of discrete wavelet decomposition and reconstruction, see: StephaneMallat, "A Wavelet Tour of Signal processing", [c] 2nd ed.Chap.VII, Academic press Elsevier Pte Ltd, 2003, pp.221-314

Definition 7, Meyer wavelet:

构建而成。具体构建方法详见：StephaneMallat，“A Wavelet Tour of Signal processing”，[c]2nd ed.Chap.VII，Academic pressElsevier Pte Ltd，2003，

的表达式如下：The Meyer wavelet is composed of a low-pass filter

built. The specific construction method is detailed in: StephaneMallat, "A Wavelet Tour of Signal processing", [c]2nd ed.Chap.VII, Academic pressElsevier Pte Ltd, 2003,

The expression of is as follows:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ]</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; ]</span>\end{array}\right.$

The invention provides a method for improving the resolution of linear array three-dimensional imaging synthetic aperture radar, which comprises the following steps:

Step 1. Obtain a low-resolution SAR image

Using Orthogonal Trajectory 3D Imaging Synthetic Aperture Radar to Obtain Low Resolution Linear Array 3D Imaging Synthesis in X Direction

Aperture radar image G ^x and y direction low-resolution linear array three-dimensional imaging synthetic aperture radar image G ^y ;

Step 2. Perform discrete wavelet decomposition on the high-resolution dimension of the low-resolution image:

其中，h(2n)表示高分辨逼近信号通过低通滤波器h(n)滤波后对其进行1/2采样得到的信号，和

是对应的小波正交基下的分解系数，f_j+1(n)是在分辨率j+1下的离散表示形式；首先对y方向低分辨率线阵三维成像合成孔径雷达图像G^y进行x方向一维离散小波分解，得到低频系数矩阵

和水平方向高频系数矩阵

然后对x方向低分辨率线阵三维成像合成孔径雷达图像G^x进行y方向一维离散小波分解，得到低频系数矩阵

和垂直方向高频系数矩阵

其中，y方向和x方向的低分辨率线阵三维成像合成孔径雷达图像通过一维离散小波分解得到低频系数矩阵

是相同的，n₁、n₂分别表示二维图像的横维和纵维像素点；n₁、n₂的取值范围取决于二维图像的大小；Using Meyer wavelet, using one-dimensional wavelet decomposition formula

Among them, h(2n) represents the signal obtained by sampling the high-resolution approximation signal through the low-pass filter h(n) and then sampling it by 1/2, and

is the decomposition coefficient under the corresponding wavelet orthogonal basis, f _j+1 (n) is the discrete representation at the resolution j ⁺ 1; One-dimensional discrete wavelet decomposition in the x direction to obtain the low-frequency coefficient matrix

and the matrix of high-frequency coefficients in the horizontal direction

Then, the low-resolution line array 3D synthetic aperture radar image G ^x in the x direction is decomposed by one-dimensional discrete wavelet in the y direction to obtain the low-frequency coefficient matrix

and the matrix of high-frequency coefficients in the vertical direction

Among them, the low-resolution linear array three-dimensional imaging synthetic aperture radar image in the y direction and x direction is decomposed by one-dimensional discrete wavelet to obtain the low-frequency coefficient matrix

are the same, n ₁ and n ₂ represent the horizontal and vertical pixels of the two-dimensional image respectively; the value range of n ₁ and n ₂ depends on the size of the two-dimensional image;

Step 3, using the wavelet coefficients obtained in step 2 to perform discrete wavelet difference zero padding:

水平方向高频系数矩阵

和垂直方向高频系数矩阵

按照公式：Using the low frequency coefficient matrix

Horizontal High Frequency Coefficient Matrix

and the matrix of high-frequency coefficients in the vertical direction

According to the formula:

对应的系数矩阵

水平方向高频系数矩阵

对应的系数矩阵

垂直方向高频系数矩阵

对应的系数矩阵

Calculate the low frequency coefficient matrix

Corresponding coefficient matrix

Horizontal High Frequency Coefficient Matrix

Corresponding coefficient matrix

Vertical high frequency coefficient matrix

Corresponding coefficient matrix

Step 4, wavelet reconstruction to obtain the fused image:

对应的系数矩阵水平方向高频系数矩阵

对应的系数矩阵

垂直方向高频系数矩阵对应的系数矩阵

通过二维小波重构公式：Use the low frequency coefficient matrix obtained in step 3

Corresponding coefficient matrix Horizontal High Frequency Coefficient Matrix

Corresponding coefficient matrix

Vertical high frequency coefficient matrix Corresponding coefficient matrix

Reconstruct the formula by two-dimensional wavelet:

Calculate the high-resolution linear array 3D imaging synthetic aperture radar image after resolution fusion Where * means convolution, n ₁ and n ₂ represent pixels in the horizontal and vertical directions respectively, h(n ₁ ), g(n ₁ ) represent low-pass and high-pass filtering in the horizontal direction, h(n ₂ ), g(n ₂ ) represents low-pass and high-pass filtering in the longitudinal direction.

After the above operations, the fused high-resolution linear array three-dimensional imaging synthetic aperture radar image of the orthogonal trajectory can be obtained.

The innovation of the present invention lies in the problem that the resolution of the tangential track of the image obtained by the linear array three-dimensional imaging synthetic aperture radar is low, and the same area is imaged by using two linear array three-dimensional imaging synthetic aperture radars whose motion trajectories are orthogonal, and then The discrete wavelet transform technology is used to fuse the obtained two images to obtain a high-resolution linear array three-dimensional imaging synthetic aperture radar image. The invention solves the problem that the resolution of the cut track of the image obtained by the linear array three-dimensional imaging synthetic aperture radar is low.

The invention has the advantage of realizing the high-resolution imaging of the linear array three-dimensional imaging synthetic aperture radar by using a shorter array antenna. The invention can be applied to the fields of synthetic aperture radar imaging, earth remote sensing and the like.

Description of drawings

Figure 1 is a schematic diagram of the working principle of the three-dimensional imaging synthetic aperture radar with orthogonal trajectories

Among them, the synthetic aperture radar SAR-A and the synthetic aperture radar SAR-B respectively represent two linear array three-dimensional imaging synthetic aperture radars that move orthogonally; the synthetic aperture radar SAR-A and the synthetic aperture radar SAR-B move along the x and y directions respectively .

Fig. 2 is a flow chart of wavelet decomposition and reconstruction of one-dimensional signal. Where (a) is an exploded view, and (b) is a reconstructed view. Among them, "↓2" means 1/2 sampling "↑2" means padding in odd bits. h means low-pass filter, g means high-pass filter. a _i+1 represents the decomposed one-dimensional signal, a _i represents the low-frequency coefficient generated after the decomposition, and d _i represents the high-frequency coefficient generated after the decomposition.

Fig. 3 is a flowchart of wavelet decomposition and reconstruction of a two-dimensional image. Where (a) is an exploded view, and (b) is a reconstructed view. Among them, "↓2" means 1/2 sampling, and "↑2" means zero padding in odd bits. h represents a low-pass filter, and g represents a high-pass filter. a _i+1 represents the decomposed two-dimensional image, a _i represents the low-frequency coefficient matrix generated after decomposition, d ¹ _i represents the horizontal high-frequency coefficient matrix generated after decomposition, and d ² _i represents the vertical high-frequency coefficient matrix generated after decomposition , d ³ _i represent the diagonal high-frequency coefficient matrix generated after decomposition.

Fig. 4 is the original image of the linear array three-dimensional imaging synthetic aperture radar adopted in the specific embodiment

The black rectangles 1, 2, 3, and 4 in the figure respectively represent four scatter points that can be distinguished from each other.

Fig. 5 is the x-direction low-resolution linear array three-dimensional imaging synthetic aperture radar image adopted in the specific embodiment

The black rectangles 5 and 6 in the figure respectively represent the blurring of the image in the x direction due to the low resolution in the x direction.

Fig. 6 is the y-direction low-resolution linear array three-dimensional imaging synthetic aperture radar image adopted in the specific embodiment

The black rectangles 7 and 8 in the figure respectively represent the blurring of the image in the y direction due to the low resolution in the y direction.

Fig. 7 is a linear array three-dimensional imaging synthetic aperture radar image after fusion of image 3 and image 4 obtained by the method provided by the present invention

Rectangles 9, 10, 11, and 12 respectively represent four scatter points that can be distinguished from each other after adopting the present invention. It can be seen from Figures 4, 5, 6, and 7 that the resolution fusion method of the linear array 3D imaging SAR proposed by the present invention can improve the resolution of the linear array 3D imaging SAR image.

Fig. 8 is a flow chart of the method of the present invention

Detailed ways

The present invention mainly adopts the method of simulation experiment to verify, and all steps and conclusions are verified correctly on MATLAB7.0. The specific implementation steps are as follows:

Step 1. Perform discrete wavelet decomposition on the high-resolution dimension of the low-resolution image:

对y方向低分辨率线阵三维成像合成孔径雷达图像G^y进行x方向一维离散小波分解，得到低频系数矩阵

和垂直方向高频系数对 ${\tilde{d}}_j^2(n_1,n_2).$ Using the Meyer wavelet base, the y-direction one-dimensional discrete wavelet decomposition is performed on the x-direction low-resolution linear array three-dimensional imaging synthetic aperture radar image G ^x to obtain the low-frequency coefficient matrix and the horizontal direction high-frequency coefficient pair

Perform one-dimensional discrete wavelet decomposition in the x-direction on the low-resolution linear array three-dimensional imaging synthetic aperture radar image G ^y in the y-direction to obtain the low-frequency coefficient matrix

and vertical high-frequency coefficient pairs ${\tilde{d}}_j^2({\mathrm{no}}_1,{\mathrm{no}}_2).$

Step 2, wavelet reconstruction to obtain the fused image:

进行离散小波重构，得到融合后的图像

Use the coefficient matrix obtained in step 1

Perform discrete wavelet reconstruction to obtain the fused image

It can be seen from the specific embodiments of the present invention that the linear array 3D imaging synthetic aperture radar resolution fusion method provided by the present invention can fuse two images to obtain a high resolution linear array 3D imaging synthetic aperture radar image.

Claims (1)

1. a linear array three-dimensional imaging synthetic aperture radar resolution fusion method based on discrete wavelet transform, is characterized in that it comprises the following steps: Step 1. Obtain a low-resolution SAR image Obtain the low-resolution linear array three-dimensional imaging synthetic aperture radar image G in the x direction and the low-resolution linear array three-dimensional imaging synthetic aperture radar image G ^y in the ^y direction by using the orthogonal trajectory three-dimensional imaging synthetic aperture radar; Step 2. Perform discrete wavelet decomposition on the high-resolution dimension of the low-resolution image: Using Meyer wavelet, using one-dimensional wavelet decomposition formula

Among them, h(2n) represents the signal obtained by sampling the high-resolution approximation signal through the low-pass filter h(n) and then sampling it by 1/2,

and

is the decomposition coefficient under the corresponding wavelet orthogonal basis, f _j+1 (n) is the discrete representation at the resolution j ⁺ 1; One-dimensional discrete wavelet decomposition in the x direction to obtain the low-frequency coefficient matrix and the matrix of high-frequency coefficients in the horizontal direction

Then, the low-resolution line array 3D synthetic aperture radar image G ^x in the x direction is decomposed by one-dimensional discrete wavelet in the y direction to obtain the low-frequency coefficient matrix

and the matrix of high-frequency coefficients in the vertical direction

Among them, the low-resolution linear array three-dimensional imaging synthetic aperture radar image in the y direction and x direction is decomposed by one-dimensional discrete wavelet to obtain the low-frequency coefficient matrix

are the same, n ₁ and n ₂ represent the horizontal and vertical pixels of the two-dimensional image respectively; the value range of n ₁ and n ₂ depends on the size of the two-dimensional image; Step 3, using the wavelet coefficients obtained in step 2 to perform discrete wavelet difference zero padding: Using the low frequency coefficient matrix

Horizontal High Frequency Coefficient Matrix

and the matrix of high-frequency coefficients in the vertical direction

According to the formula:

Calculate the low frequency coefficient matrix

Corresponding coefficient matrix

Horizontal High Frequency Coefficient Matrix

Corresponding coefficient matrix

Vertical high frequency coefficient matrix

Corresponding coefficient matrix Step 4, wavelet reconstruction to obtain the fused image: Use the low frequency coefficient matrix obtained in step 3

Corresponding coefficient matrix

Horizontal High Frequency Coefficient Matrix

Corresponding coefficient matrix

Vertical high frequency coefficient matrix

Corresponding coefficient matrix

Reconstruct the formula by two-dimensional wavelet: Calculate the high-resolution linear array 3D imaging synthetic aperture radar image after resolution fusion

Where * means convolution, n ₁ and n ₂ represent pixels in the horizontal and vertical directions respectively, h(n ₁ ), g(n ₁ ) represent low-pass and high-pass filtering in the horizontal direction, h(n ₂ ), g(n ₂ ) represents low-pass and high-pass filtering in the longitudinal direction.

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