CN110320530B

CN110320530B - Terahertz sparse imaging design method based on matrix filling

Info

Publication number: CN110320530B
Application number: CN201910460367.4A
Authority: CN
Inventors: 丁丽; 李萍; 朱亦鸣; 吴淑娴; 张紫欣
Original assignee: University of Shanghai for Science and Technology
Current assignee: University of Shanghai for Science and Technology
Priority date: 2019-05-30
Filing date: 2019-05-30
Publication date: 2022-03-29
Anticipated expiration: 2039-05-30
Also published as: CN110320530A

Abstract

The invention proposes a terahertz sparse imaging design method based on matrix filling. First, based on a pseudo-random array, the echo matrix model S is solved; then based on the echo matrix model S, the terahertz echo of the target point in the sampling space is obtained, to obtain the echo matrix M ₀ ; judge the rank of the echo matrix M ₀ ; if the rank of the matrix M ₀ is greater than the preset threshold value, perform rank reduction processing on the echo matrix M ₀ , and then perform a rank reduction process based on the matrix M 0 Filling theory, reconstruct the missing data of the echo matrix M ₀ , perform target imaging inversion on the echo matrix M ₁ to obtain an image; finally make a judgment on the imaging performance of the image; if the performance index of the imaging performance cannot meet the preset value, then the echo matrix model S is iteratively optimized. The invention solves the problem that the acquisition time is too long or the cost of the full array is too high under the condition of the classical sampling theorem; at the same time, it solves the problem that the traditional imaging algorithm has high side lobes and cannot obtain a clear target image.

Description

Terahertz sparse imaging design method based on matrix filling

Technical Field

The invention belongs to the technical field of terahertz three-dimensional sparse imaging, and particularly relates to a terahertz sparse imaging design method based on matrix filling.

Background

Terahertz waves (THz waves) generally refer to electromagnetic waves with the frequency within the range of 0.1THz-10THz (the wavelength is 3mm-30pm), the frequency range of the THz waves is in the transition region from macroscopic electronics to microscopic photonics, and the THz waves have unique physical characteristics and important research value. Terahertz imaging is one of the important application fields of terahertz waves. Based on the characteristics of safety, high resolution, penetrability and the like of terahertz waves, terahertz imaging has unique advantages: in contrast to infrared and optical imaging, terahertz imaging can penetrate non-polar materials such as clothing, wood, and plastics: compared with radio frequency and microwave imaging, terahertz imaging can often acquire images with higher spatial resolution: compared with radiographic imaging, terahertz imaging with milliwatt-level power is generally considered harmless to human bodies. Terahertz imaging technology applied to human body security inspection can be divided into an active type and a passive type according to whether a terahertz source exists or not. Passive imaging uses a bolometer to detect terahertz waves emitted by the human body to form an image of the surface of the human body. Because terahertz waves radiated by a human body are very weak, the contrast of an imaging result of passive imaging is often low, and the image is not clear enough; in active imaging, an antenna is generally used to emit terahertz waves at the milliwatt level, which penetrate through clothes on the surface of a human body and then reflected terahertz signals are measured to obtain images on the surface of the human body. Active imaging not only has high image contrast, but also can obtain higher azimuth resolution by a synthetic aperture method. The active terahertz imaging technology can be used for human body safety detection in short distance in places such as airports, subway stations and the like. One of the most common methods for active terahertz imaging is to use a synthetic aperture radar technology, increase the length of a synthetic aperture by moving or array expansion, sample the length of the synthetic aperture to obtain a large number of terahertz echo signals, and achieve high-resolution imaging by means of digital focusing.

However, as the length of the synthetic aperture increases, the sampling interval of the sub-wavelength is limited according to the Nyquist sampling theorem, so that on one hand, the cost of the acquisition time is increased, and the real-time performance of the system is reduced; on the other hand, the number of array elements is increased, and the processing and preparation difficulty of the transmission network is increased due to the contradiction between the physical size of the device and the sub-wavelength, so that the investment of economic cost is greatly improved. Therefore, how to ensure high-resolution imaging performance by reducing the number of required spatial sampling sample points at a certain synthetic aperture length becomes an important research topic.

Disclosure of Invention

The invention aims to provide a terahertz sparse imaging design method based on matrix filling, which aims to solve the technical problems in the prior art, can realize clear inversion of a target under the condition of low sampling cost and has great practical value. In order to achieve the purpose, the invention adopts the following technical scheme:

a terahertz sparse imaging design method based on matrix filling comprises the following steps:

step A: solving an echo matrix model S based on a conventional pseudo-random array type, such as a spiral type, a Chinese character 'mi' type or an annular type;

and B: obtaining terahertz echoes of a target point in a sampling space based on an echo matrix model S to obtain an echo matrix M₀；

And C: for the echo matrix M₀Judging the rank of the obtained data; if matrix M₀Is greater than a preset threshold value, the echo matrix M is processed₀Performing rank reduction treatment;

step D: reconstructing the echo matrix M based on a matrix filling method₀To obtain an echo matrix M of the complete sampling space₁；

Step E: for echo matrix M₁Performing target imaging inversion to obtain an image;

step F: judging the imaging performance of the image; if the performance index of the imaging performance can not meet the preset value, performing the step A based on a limiting condition; otherwise, ending.

Preferably, in step F, the performance indicators include peak-to-side lobe ratio and structural similarity.

Preferably, the defining conditions include the number of array elements, basic data amount required for matrix filling, and filling relative error value.

Preferably, in step a, the pseudo-random pattern is a spiral, a zigzag, or a circular pattern.

Preferably, in step C, the method of the rank reduction processing includes a singular value decomposition method (SVD), a STAP method, and a KA-RR method.

Preferably, in step D, the matrix filling method is singular value threshold algorithm (SVT), Augmented Lagrange Multiplier (ALM) or Fixed Point Continuation Algorithm (FPCA).

Preferably, in step E, the method for inversion of target imaging comprises a range migration algorithm, a range-doppler algorithm or a back-projection algorithm.

Preferably, in step a, a terahertz imaging system is used to transmit a terahertz signal to an object to be imaged, a terahertz echo of a target point is acquired, and an echo matrix model S sampled Q times is obtained.

Compared with the prior art, the invention has the advantages that:

1) the pseudo-random sampling scheme for sparse sampling is provided, and the problems of overlong acquisition time or too high cost of a full-array under the condition of a classical sampling theorem are solved;

2) the sparse imaging method based on matrix filling is provided, and the problems that a traditional imaging algorithm is high in sidelobe and cannot acquire a clear target image are solved.

Drawings

Fig. 1 is a flowchart of a terahertz sparse imaging method based on matrix filling according to an embodiment of the present invention;

fig. 2 is a scene diagram of the echo matrix model S obtained in fig. 1.

1-observation space, 2-sampling space, 3-terahertz imaging system, 4-strong scattering point, 5-scattering echo and 6-emission signal.

Detailed Description

The matrix-fill based terahertz sparse imaging method of the present invention will be described in more detail below with reference to schematic drawings, in which preferred embodiments of the present invention are shown, it being understood that a person skilled in the art may modify the invention described herein while still achieving the advantageous effects of the present invention. Accordingly, the following description should be construed as broadly as possible to those skilled in the art and not as limiting the invention.

As shown in fig. 1, aiming at the problem that the signal acquisition cost is too high or the sampling time is too long under the guidance of the classical nyquist sampling law, a terahertz sparse imaging design method based on matrix filling is disclosed, which comprises the following steps a to F, specifically as follows:

step A: solving an echo matrix model S based on a conventional pseudo-random array type, such as a spiral type, a Chinese character 'mi' type or an annular type; the pseudo-random array replaces a conventional uniform undersampling array to complete the optimization design of the conventional sampling array; a non-uniformly distributed pseudo-random array type is selected, so that the space sparsity of sampled data and the accuracy of full-array data recovery based on a small number of samples are guaranteed, and a determined pseudo-random sparse sampling mode or an array space distribution model is obtained. The specific optimization method comprises the following steps: firstly, based on a conventional pseudo-random model S, a terahertz imaging system 3 is used for transmitting terahertz waves (transmitting signals 6) to an object to be imaged, terahertz echoes (scattering echoes 5) of a target point, namely a strong scattering point 4 are obtained, a pseudo-random array type of Q-time sampling is obtained, and then an echo matrix model S in an observation space 1 is optimized and solved through intelligent optimization algorithms such as a genetic algorithm and a particle swarm algorithm and an iterative optimization mode. As shown in fig. 2, x, y, and z respectively represent a horizontal azimuth direction, a vertical azimuth direction, and a distance direction.

And B: obtaining terahertz echoes of a target point in the sampling space 2 based on the echo matrix model S to obtain an echo matrix M₀；M₀Containing echo data of a partially sampled volume.

And C: for echo matrix M₀Judging the rank of the obtained data; if the matrix M is₀Is greater than a preset threshold value, the echo matrix M is processed₀Performing rank reduction treatment; since the imaging target in the context of near-field SAR may not have strong scattering properties or strong correlation of the echo data, the partial echo data acquired in step B may not have low rank characteristics (if M is₀Is an L × N complex matrix, low rank index rank (M)₀)<<min (L, N)), so it is necessary to do with M₀The rank of (2) is judged, and the judgment result has the following two conditions: one situation is an echo matrix M₀The self rank is low, and the full sampling space echo data can be recovered with high accuracy directly by the matrix filling method in the step D;another situation is the echo matrix M₀The rank of the data is high, which affects the filling performance and filling efficiency of the matrix to a certain extent, so that rank reduction preprocessing can be performed on the two-dimensional sampling data under each frequency point by using methods such as Singular Value Decomposition (SVD), STAP and KA-RR, and then missing data is reconstructed, namely step D.

Step D: reconstructing an echo matrix M based on a matrix filling method₀To obtain an echo matrix M of the complete sampling space₁(ii) a Common matrix filling methods are singular value threshold algorithm (SVT), Augmented Lagrange Multiplier (ALM), stationary point continuation algorithm (FPCA), and the like.

Step E: for echo matrix M₁Target imaging inversion is performed to acquire an image. The target imaging inversion method comprises a range migration algorithm, a range-Doppler algorithm or a back projection algorithm.

Step F: judging the imaging performance of the image; if the performance index of the imaging performance of the image cannot meet the preset value, performing step A based on a limiting condition, namely performing further iterative optimization on the echo matrix model S, and finally obtaining a sparse sampling imaging method with low sampling rate and low side lobe level; otherwise, the design is finished. The performance index comprises a peak sidelobe ratio and a structural similarity. The limiting conditions include the number of array elements, the basic data amount required by matrix filling and the filling relative error value.

The terahertz imaging method is mainly applied to the field of high-frequency-band imaging, such as terahertz imaging, can realize clear inversion of a target under the condition of low sampling cost, and has a great practical value. The theoretical basis of the invention is as follows: according to the electromagnetic scattering property of the target, the echo signals can be generally regarded as superposition of echo signals of a few strong scattering points in a scanning range, and the redundancy and the sparsity are realized. On the basis, the method is expected to break through the limitation of the Nyquist sampling theorem, samples the original signal at a lower sampling rate, namely reconstructs the original signal by utilizing effective information in echo data, and can realize terahertz three-dimensional sparse imaging by combining the existing SAR imaging algorithm. The theory of recovering the original signal by using the missing data can be mainly divided into two types: matrix filling and compressed sensing. However, in the existing SAR imaging studies, there are several limitations to the application of the matrix filling technique. Firstly, there is no definite limit to the minimum data size that can be reconstructed by matrix filling, and in order to ensure reconstruction performance, researchers still have a large sampled data size; secondly, the adopted scanning mode or array configuration is random, which is relatively limited in practical application, so that a determined pseudo-random configuration is sought, the performance requirement of matrix filling can be met, and the array type can be determined; thirdly, echo data acquired by SAR imaging may be close to full rank, so in this case rank reduction preprocessing is required on the data.

In summary, in the terahertz sparse imaging method based on matrix filling provided by the embodiment of the invention, a pseudo-random sampling scheme for sparse sampling is provided, so that the problems of too long acquisition time or too high cost of a full-array under the condition of a classical sampling theorem are solved; furthermore, a sparse imaging method based on a matrix filling theory is provided, and the problems that a traditional imaging algorithm is high in sidelobe and cannot acquire a clear target image are solved.

The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. a terahertz sparse imaging design method based on matrix filling, is characterized in that, comprises the steps:

Step A: Solve the echo matrix model S based on the pseudo-random formation;

Step B: Based on the echo matrix model S, obtain the terahertz echo of the target point in the sampling space to obtain the echo matrix M ₀ ;

Step C: Judging the rank of the echo matrix M ₀ ; if the rank of the matrix M ₀ is greater than a preset threshold value, perform rank reduction processing on the echo matrix M ₀ ;

Step D: based on matrix filling, reconstruct the missing data of the echo matrix M ₀ to obtain the echo matrix M ₁ of the complete sampling space;

Step E: perform target imaging inversion on the echo matrix M ₁ to acquire an image;

Step F: Judging the imaging performance of the image; if the performance index of the imaging performance cannot meet the preset value, proceed to Step A based on the limited condition; otherwise, end.

2 . The terahertz sparse imaging design method based on matrix filling according to claim 1 , wherein, in step F, the performance indicators include peak sidelobe ratio and structural similarity. 3 .

3 . The terahertz sparse imaging design method based on matrix filling according to claim 1 , wherein the limiting conditions include the number of array elements, the basic data amount required for matrix filling, and the relative error value of filling. 4 .

4 . The terahertz sparse imaging design method based on matrix filling according to claim 1 , wherein, in step A, the pseudo-random model is a spiral type, a square shape or a ring type. 5 .

5 . The terahertz sparse imaging design method based on matrix filling according to claim 1 , wherein, in step C, the rank reduction processing method includes singular value decomposition method, STAP method and KA-RR method. 6 .

6. The terahertz sparse imaging design method based on matrix filling according to claim 1, wherein in step D, the matrix filling method is a singular value threshold algorithm, an augmented Lagrange multiplier method or Fixed point continuation algorithm.

7. The terahertz sparse imaging design method based on matrix filling according to claim 1, characterized in that, in step E, the method of target imaging inversion comprises range migration algorithm, range Doppler algorithm or back projection algorithm.

8. The terahertz sparse imaging design method based on matrix filling according to claim 1, characterized in that, in step A, first use a terahertz imaging system to transmit a terahertz wave signal to the object to be imaged, and obtain the terahertz wave signal of the target point. The Hertz echo is obtained, and the echo matrix model S of Q times sampling is obtained.