WO2019010679A1 - 一种基于降维稀疏表示的主动式场景三维信息获取方法 - Google Patents

一种基于降维稀疏表示的主动式场景三维信息获取方法 Download PDF

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WO2019010679A1
WO2019010679A1 PCT/CN2017/092826 CN2017092826W WO2019010679A1 WO 2019010679 A1 WO2019010679 A1 WO 2019010679A1 CN 2017092826 W CN2017092826 W CN 2017092826W WO 2019010679 A1 WO2019010679 A1 WO 2019010679A1
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scene
dimensional
sparse representation
signal
active
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陈崇雨
林倞
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Sun Yat Sen University
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Sun Yat Sen University
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/003—Bistatic radar systems; Multistatic radar systems
    • 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
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
    • G01S15/06—Systems determining the position data of a target
    • G01S15/42—Simultaneous measurement of distance and other co-ordinates
    • 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
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88—Sonar systems specially adapted for specific applications
    • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging

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  • the present invention relates to the field of digital signal processing methods, and more particularly to a method for acquiring active scene three-dimensional information based on reduced-dimensional sparse representation.
  • the traditional three-point positioning method achieves the acquisition of the three-dimensional position information of a single target by analyzing the time when the target echo reaches different measurement points. Although the number of sensors required for this method is larger than the target number, its application is still very extensive.
  • the multi-input multi-output radar system achieves simultaneous positioning of multiple targets by deploying the transmitting end and the receiving end at different locations. However, such systems require a high degree of directionality for the transmitted signal and the number of targets that can be detected is still no greater than the number of sensors deployed.
  • the invention provides a method for acquiring a three-dimensional information of an active scene based on a dimensionality reduction sparse representation, which can acquire a three-dimensional position of multiple targets in a scene by deploying a transmitter and a small number of one-dimensional detection signal receivers, or Obtain the three-dimensional structure of the detected scene.
  • a method for acquiring active scene three-dimensional information based on dimensionality reduction sparse representation includes the following steps:
  • step S1 is:
  • the transmitting end and the receiving end of the system are both oriented toward an open area, and only one object whose size is not larger than h 1 ⁇ h 2 ⁇ h 3 is activated, and the transmitting end transmits a detecting signal s, which is recorded by each receiving end.
  • the waveform of a single reflected signal, the received waveform is recorded as s 1 , s 2 , ..., s n , where n is the number of receiving ends, and after the received waveform is recorded, the calibration of the system is completed.
  • step S2 is:
  • the transmitting end and the receiving end are both directed to the detected scene, when the target information in the scene is to be acquired, step S21 is started; when the three-dimensional structure of the scene is to be acquired, step S22 is started;
  • S22 Send a sounding signal s to the scene, and record the signals y 1 , y 2 , . . . , y n received by each receiving end.
  • step S3 is:
  • S31 Divide the detected scene into a plurality of voxels of size h 1 ⁇ h 2 ⁇ h 3 , and establish a sparse representation dictionary D 1 , D 2 , . . . , D n , where the jth column of the i th dictionary D i
  • the element is the waveform that the i-th receiving end should receive when the element is the object of the jth element, and can be approximated by shifting to s i at the corresponding position;
  • step S32 Constructing a general sparse representation dictionary And overall received signal
  • the dictionary D is a matrix of p ⁇ q
  • the noise level ⁇ D of the dictionary and the noise level ⁇ s of the received signal are estimated, if and At the same time, step S33 is started, otherwise step S34 is started, wherein the threshold value ⁇ is taken as 0.05;
  • the matrix W is a unit matrix; if the structure information of the scene is acquired, the matrix W is a transformation matrix that makes Wx sparse.
  • the present invention has the following advantages:
  • the invention combines a plurality of one-dimensional active detection signals acquired synchronously to realize three-dimensional positioning of objects in the detected scene or three-dimensional reconstruction of the scene structure. Simultaneous three-dimensional positioning of multiple targets in the scene or three-dimensional reconstruction of the scene geometry can be achieved by an active detection system equipped with one transmitting end and multiple receiving ends.
  • the sparse representation model of the present invention is further transformed into a dimensionally reduced sparse representation model.
  • the proposed method breaks through the requirements of the number of sensors in the traditional three-point positioning method in the problem of multi-target simultaneous positioning.
  • the proposed method In the acquisition of three-dimensional information of the scene, the proposed method only needs multiple one-dimensional signal sensors. It can be derived into a variety of high-efficiency, low-cost, scalable active detection schemes; the dimensionality reduction model of the proposed method can handle the high noise level well.
  • Figure 1 is a flow chart of the method of the present invention
  • FIG. 2 is a schematic diagram of setting up an indoor positioning scene
  • Figure 3 shows the coefficients solved by different models
  • Figure 4 shows the scene target information reconstructed by different models.
  • a method for acquiring a three-dimensional information of an active scene based on a reduced-dimensional sparse representation includes the following steps:
  • step S1 is:
  • the transmitting end and the receiving end of the system are both oriented toward an open area, and only one object whose size is not larger than h 1 ⁇ h 2 ⁇ h 3 is activated, and the transmitting end transmits a detecting signal s, which is recorded by each receiving end.
  • the waveform of a single reflected signal, the received waveform is recorded as s 1 , s 2 , ..., s n , where n is the number of receiving ends, and after the received waveform is recorded, the calibration of the system is completed.
  • step S2 The specific process of step S2 is:
  • the transmitting end and the receiving end are both directed to the detected scene, when the target information in the scene is to be acquired, step S21 is started; when the three-dimensional structure of the scene is to be acquired, step S22 is started;
  • S22 Send a sounding signal s to the scene, and record the signals y 1 , y 2 , . . . , y n received by each receiving end.
  • step S3 The specific process of step S3 is:
  • S31 Divide the detected scene into a plurality of voxels of size h 1 ⁇ h 2 ⁇ h 3 , and establish a sparse representation dictionary D 1 , D 2 , . . . , D n , where the jth column of the i th dictionary D i
  • the element is the waveform that the i-th receiving end should receive when the element is the object of the jth element, and can be approximated by shifting to s i at the corresponding position;
  • step S32 Constructing a general sparse representation dictionary And overall received signal
  • the dictionary D is a matrix of p ⁇ q
  • the noise level ⁇ D of the dictionary and the noise level ⁇ s of the received signal are estimated, if and At the same time, step S33 is started, otherwise step S34 is started, wherein the threshold value ⁇ is taken as 0.05;
  • the scene size is 10m ⁇ 10m ⁇ 4m, which is evenly divided into 3200 voxels (the voxel size is 0.5m ⁇ 0.5m ⁇ 0.5m), and the sound propagation speed is Set to 350m/s and the system sampling rate is 7000 samples/second.
  • the axis from the corner of the room and place the emitter at the origin.
  • four non-coplanar receivers are placed with coordinates (10, 10, 4), (6.5, 10, 2.5), (10, 6.5, 2.5) and (10, 10, 0.5).
  • the x solved by the model (1) is shown in Fig. 3(a), and the x obtained by the model (2) is shown in Fig. 3(b).
  • the red line in the figure represents the true coefficient of the signal, and the blue line represents the estimated coefficient. Since the received signal contains noise, the coefficient estimated by the model (1) is not very accurate. In contrast, the coefficient recovered by model (2) is closer to the true value, and the visible model (2) is more suitable for the case of higher noise level.
  • the left picture is the real scene
  • the middle picture is the 3D target recovered from the solution result of the model (1)
  • the right picture is the 3D target recovered by the model (2) solution result.
  • Visible model (2) is more suitable for restoring real 3D targets when there is noise.

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  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
  • Electromagnetism (AREA)

Abstract

一种基于降维稀疏表示的主动式场景三维信息获取方法，该方法对同步采集的多个一维主动探测信号进行联合处理，实现被探测场景内物体的三维定位或者场景结构的三维重建，通过配备有一个发射端和多个接收端的主动探测系统，实现对场景中多个目标的同时三维定位或者对场景几何结构的三维重建。

Description

一种基于降维稀疏表示的主动式场景三维信息获取方法 技术领域
本发明涉及数字信号处理方法领域，更具体地，涉及一种基于降维稀疏表示的主动式场景三维信息获取方法。
背景技术
基于主动探测的目标定位与场景重建技术在交通、勘探和航空等领域有着广泛的应用，人们开发出了各种雷达设备来满足不同场景对探测的需求。传统的三点定位方法通过分析目标回波到达不同测量点的时间，实现了单个目标三维位置信息的获取。尽管该方法所需传感器的数量大于目标数量，但是其应用仍然十分广泛。多输入多输出雷达系统通过在不同的地点部署发射端和接收端，实现了多个目标的同时定位。然而，此类系统对发射信号的定向性要求较高，并且能探测的目标数量仍然不大于所部署的传感器数量。在不便部署雷达的室内场景，人们主要通过目标自身携带具有射频识别标签的设备来进行定位，通过分析到设备到不同传感器处的到达时间来获取物体的位置信息。对于自身不携带设备的目标，人们则需要在被检测场景周围以网格状地部署大量的传感器，通过传感器接收到物体发射信号的强弱来感知物体的位置信息。这种方法对于噪声十分敏感，而且无法同时获取多个物体的信息。并且大量传感器的布置成本较高，扩展性差。
发明内容
本发明提供一种基于降维稀疏表示的主动式场景三维信息获取方法，该方法通过部署一个发射器和少量的一维探测信号接收器，就可以获取场景中多个目标的三维位置，或者是获得被探测场景的三维结构。
为了达到上述技术效果，本发明的技术方案如下：
一种基于降维稀疏表示的主动式场景三维信息获取方法，包括以下步骤：
S1：对主动探测系统进行标定，其中，主动探测系统包括一个发射端和若干的一维探测信号接收端；
S2：对被探测场景进行探测，并采集一个探测周期内的多通道探测信号；
S3：根据标定结果和采集到的探测信号，建立和求解稀疏表示优化模型。
进一步地，所述步骤S1的具体过程是：
将系统的发射端与接收端都朝向一个空旷的区域，区域中只有一个尺寸不大于h1×h2×h3的物体，启动发射端发射一个探测信号s，记录每一个接收端所接收到的单个反射信号的波形，所接收到的波形记为s1、s2、…、sn，其中n为接收端的个数，记录完接收到的波形之后，对系统的标定完毕。
进一步地，所述步骤S2的具体过程是：
将多个接收端放置在不与发射端共面的位置，且与发射端间距不小于L，对于波速为v、持续时间为t的探测信号，令L≥vt；
令发射端和接收端都朝向被探测场景，当要获取场景中的目标信息时，启动步骤S21；当要获取场景三维结构时，启动步骤S22；
S21：对没有目标的场景发射一个探测信号s，记录每个接收端接收到的信号b1、b2、…、bn，当场景里面出现目标时，再对有目标的场景发射探测信号s，记录每个接收端接收到的信号z1、z2、…、zn，令y1＝z1-b1，y2＝z2-b2，…，yn＝zn-bn。
S22：对场景发射一个探测信号s，记录每个接收端接收到的信号y1、y2、…、yn。
进一步地，所述步骤S3的具体过程是：
S31：将被探测场景划分为多个尺寸为h1×h2×h3的体素，建立稀疏表示字典D1、D2、…、Dn，其中第i个字典Di的第j列元素为第j个体素有物体时第i个接收端应该接收到的波形，可用平移到对应位置上的si来近似；
S32：构造总体稀疏表示字典
Figure PCTCN2017092826-appb-000001
以及总体接收信号
Figure PCTCN2017092826-appb-000002
其中字典D为p×q的矩阵，并估计字典的噪声水平σD和接收信号的噪声水平σs，若
Figure PCTCN2017092826-appb-000003
并且
Figure PCTCN2017092826-appb-000004
时，启动步骤S33，否则启动步骤S34，其中阈值τ取0.05；
S33：建立并求解优化模型
Figure PCTCN2017092826-appb-000005
其中
Figure PCTCN2017092826-appb-000006
得到场景的三维信息Wx；
S34：令m＝min(p,q)，取适当的k，使得
Figure PCTCN2017092826-appb-000007
对字典D进行奇异值分解，得到D＝UΣVT；计算
Figure PCTCN2017092826-appb-000008
其中Uk是U的前k列，Vk是V的前k列，对角阵Σk是Σ的前k行和前k列的交集矩阵；建立并求降维稀疏表示优化模型
Figure PCTCN2017092826-appb-000009
其中
Figure PCTCN2017092826-appb-000010
得到场景的三维信息Wx。
进一步地，在步骤S33和S34中，如果是获取场景中的目标信息，则矩阵W为单位阵；如果是获取场景的结构信息，则矩阵W为使得Wx具有稀疏性的变换矩阵。
与现有技术相比，本发明具有以下优点：
本发明对同步采集的多个一维主动探测信号进行联合处理，实现被探测场景内物体的三维定位或者场景结构的三维重建。可以通过配备有一个发射端和多个接收端的主动探测系统，实现对场景中多个目标的同时三维定位或者对场景几何结构的三维重建。在本发明中，我们把被探测场景的三维信息按照体素来进行划分，从而将三维信息获取的问题重新建模为多个一维信号的解混叠问题，并且在稀疏表示的框架下转化为凸优化问题来进行求解。当接收信号噪声较大时，本发明稀疏表示模型进一步转化为降维稀疏表示模型。有关实验表明，在多目标同时定位的问题上，所提方法突破了传统三点定位法中对传感器数量的要求；在场景三维信息的获取上，所提方法只需要多个一维信号传感器，可以衍生为多种高效率、低成本、可扩展的主动探测方案；所提方法的降维模型可以很好处理噪声水平较高的情况。
附图说明
图1为本发明方法流程图；
图2为室内定位场景的设置示意图；
图3为不同模型求解出来的系数；
图4为不同模型所重建出来的场景目标信息。
具体实施方式
附图仅用于示例性说明，不能理解为对本专利的限制；
为了更好说明本实施例，附图某些部件会有省略、放大或缩小，并不代表实 际产品的尺寸；
对于本领域技术人员来说，附图中某些公知结构及其说明可能省略是可以理解的。
下面结合附图和实施例对本发明的技术方案做进一步的说明。
实施例1
如图1所示，一种基于降维稀疏表示的主动式场景三维信息获取方法，包括以下步骤：
S1：对主动探测系统进行标定，其中，主动探测系统包括一个发射端和若干的一维探测信号接收端；
S2：对被探测场景进行探测，并采集一个探测周期内的多通道探测信号；
S3：根据标定结果和采集到的探测信号，建立和求解稀疏表示优化模型。
进一步地，所述步骤S1的具体过程是：
将系统的发射端与接收端都朝向一个空旷的区域，区域中只有一个尺寸不大于h1×h2×h3的物体，启动发射端发射一个探测信号s，记录每一个接收端所接收到的单个反射信号的波形，所接收到的波形记为s1、s2、…、sn，其中n为接收端的个数，记录完接收到的波形之后，对系统的标定完毕。
步骤S2的具体过程是：
将多个接收端放置在不与发射端共面的位置，且与发射端间距不小于L，对于波速为v、持续时间为t的探测信号，令L≥vt；
令发射端和接收端都朝向被探测场景，当要获取场景中的目标信息时，启动步骤S21；当要获取场景三维结构时，启动步骤S22；
S21：对没有目标的场景发射一个探测信号s，记录每个接收端接收到的信号b1、b2、…、bn，当场景里面出现目标时，再对有目标的场景发射探测信号s，记录每个接收端接收到的信号z1、z2、…、zn，令y1＝z1-b1，y2＝z2-b2，…，yn＝zn-bn。
S22：对场景发射一个探测信号s，记录每个接收端接收到的信号y1、y2、…、yn。
步骤S3的具体过程是：
S31：将被探测场景划分为多个尺寸为h1×h2×h3的体素，建立稀疏表示字典D1、D2、…、Dn，其中第i个字典Di的第j列元素为第j个体素有物体时第i个 接收端应该接收到的波形，可用平移到对应位置上的si来近似；
S32：构造总体稀疏表示字典
Figure PCTCN2017092826-appb-000011
以及总体接收信号
Figure PCTCN2017092826-appb-000012
其中字典D为p×q的矩阵，并估计字典的噪声水平σD和接收信号的噪声水平σs，若
Figure PCTCN2017092826-appb-000013
并且
Figure PCTCN2017092826-appb-000014
时，启动步骤S33，否则启动步骤S34，其中阈值τ取0.05；
S33：建立并求解优化模型
Figure PCTCN2017092826-appb-000015
其中
Figure PCTCN2017092826-appb-000016
得到场景的三维信息Wx；
S34：令m＝min(p,q)，取适当的k，使得
Figure PCTCN2017092826-appb-000017
对字典D进行奇异值分解，得到D＝UΣVT；计算
Figure PCTCN2017092826-appb-000018
其中Uk是U的前k列，Vk是V的前k列，对角阵Σk是Σ的前k行和前k列的交集矩阵；建立并求降维稀疏表示优化模型
Figure PCTCN2017092826-appb-000019
其中
Figure PCTCN2017092826-appb-000020
得到场景的三维信息Wx。
在电脑上模拟了一个利用超声波进行室内定位的场景，场景大小为10m×10m×4m，被均匀的划分为3200个体素(体素大小为0.5m×0.5m×0.5m)，声音的传播速度设定为350m/s，系统采样率7000样本/秒。我们以房间的一个角为原点建立坐标轴，并在原点处放置发射器。另外放置四个不共面的接收器，坐标分别为(10，10，4)，(6.5，10，2.5)，(10，6.5，2.5)和(10，10，0.5)。
环境初始化之后，我们产生一个调幅脉冲信号作为探测信号，然后基于该探测信号，为各个接收端构造稀疏表示字典D1、…、Dn。首先，对无目标的场景进行了模拟探测。通过模拟该探测信号在室内的传播、衰减和反射，并加上高斯白噪声，我们可以计算出各个接收端应该接收到的背景反射信号，记录为b1、…、b4。然后，在场景中随机放置五个物体，再次模拟信号在室内的传播、衰减和反射，可以计算出各个接收端应该接收到的总体反射信号，记为z1、…、 z4。令y1＝z1-b1，y2＝z2-b2，…，y4＝z4-b4。构造总体稀疏表示字典
Figure PCTCN2017092826-appb-000021
以及总体接收信号
Figure PCTCN2017092826-appb-000022
我们分别通过建立稀疏表示模型
Figure PCTCN2017092826-appb-000023
和降维稀疏表示模型
Figure PCTCN2017092826-appb-000024
来求解场景的三维信息向量x。模型(1)求解出来的x如图3(a)所示，模型(2)求解出来的x如图3(b)图所示。图中红色的线代表信号的真实系数，蓝色的线代表估计的系数。由于接收信号中包含噪声，模型(1)估计出来的系数并不十分准确。相比之下，模型(2)恢复出来的系数更加接近真实值，可见模型(2)更适用于噪声水平较高的情况。通过重新排列x，使得x的元素排列到每个体素中，得到图4所示的3D目标定位结果。其中，左图是真实场景，中间图是根据模型(1)求解结果所恢复出来的3D目标，右图是模型(2)求解结果所恢复出来的3D目标。可见模型(2)在有噪声的时候更适用于恢复真实的3D目标。
相同或相似的标号对应相同或相似的部件；
附图中描述位置关系的用于仅用于示例性说明，不能理解为对本专利的限制；
显然，本发明的上述实施例仅仅是为清楚地说明本发明所作的举例，而并非是对本发明的实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明权利要求的保护范围之内。
Figure PCTCN2017092826-appb-000025

Claims (5)

  1. 一种基于降维稀疏表示的主动式场景三维信息获取方法，其特征在于，包括以下步骤：
    S1：对主动探测系统进行标定，其中，主动探测系统包括一个发射端和若干的一维探测信号接收端；
    S2：对被探测场景进行探测，并采集一个探测周期内的多通道探测信号；
    S3：根据标定结果和采集到的探测信号，建立和求解稀疏表示优化模型。
  2. 根据权利要求1所所述的基于降维稀疏表示的主动式场景三维信息获取方法，其特征在于，所述步骤S1的具体过程是：
    将系统的发射端与接收端都朝向一个空旷的区域，区域中只有一个尺寸不大于h1×h2×h3的物体，启动发射端发射一个探测信号s，记录每一个接收端所接收到的单个反射信号的波形，所接收到的波形记为s1、s2、…、sn，其中n为接收端的个数，记录完接收到的波形之后，对系统的标定完毕。
  3. 根据权利要求2所所述的基于降维稀疏表示的主动式场景三维信息获取方法，其特征在于，所述步骤S2的具体过程是：
    将多个接收端放置在不与发射端共面的位置，且与发射端间距不小于L，对于波速为v、持续时间为t的探测信号，令L≥vt；
    令发射端和接收端都朝向被探测场景，当要获取场景中的目标信息时，启动步骤S21；当要获取场景三维结构时，启动步骤S22；
    S21：对没有目标的场景发射一个探测信号s，记录每个接收端接收到的信号b1、b2、…、bn，当场景里面出现目标时，再对有目标的场景发射探测信号s，记录每个接收端接收到的信号z1、z2、…、zn，令y1＝z1-b1，y2＝z2-b2，…，yn＝zn-bn。
    S22：对场景发射一个探测信号s，记录每个接收端接收到的信号y1、y2、…、yn。
  4. 根据权利要求3所所述的基于降维稀疏表示的主动式场景三维信息获取方法，其特征在于，所述步骤S3的具体过程是：
    S31：将被探测场景划分为多个尺寸为h1×h2×h3的体素，建立稀疏表示字典D1、D2、…、Dn，其中第i个字典Di的第j列元素为第j个体素有物体时第i个 接收端应该接收到的波形，可用平移到对应位置上的si来近似；
    S32：构造总体稀疏表示字典
    Figure PCTCN2017092826-appb-100001
    以及总体接收信号
    Figure PCTCN2017092826-appb-100002
    其中字典D为p×q的矩阵，并估计字典的噪声水平σD和接收信号的噪声水平σs，若
    Figure PCTCN2017092826-appb-100003
    并且
    Figure PCTCN2017092826-appb-100004
    时，启动步骤S33，否则启动步骤S34，其中阈值τ取0.05；
    S33：建立并求解优化模型
    Figure PCTCN2017092826-appb-100005
    其中
    Figure PCTCN2017092826-appb-100006
    得到场景的三维信息Wx；
    S34：令m＝min(p,q)，取适当的k，使得
    Figure PCTCN2017092826-appb-100007
    对字典D进行奇异值分解，得到D＝UΣVT；计算
    Figure PCTCN2017092826-appb-100008
    其中Uk是U的前k列，Vk是V的前k列，对角阵Σk是Σ的前k行和前k列的交集矩阵；建立并求降维稀疏表示优化模型
    Figure PCTCN2017092826-appb-100009
    其中
    Figure PCTCN2017092826-appb-100010
    得到场景的三维信息Wx。
  5. 根据权利要求5所所述的基于降维稀疏表示的主动式场景三维信息获取方法，其特征在于，在步骤S33和S34中，如果是获取场景中的目标信息，则矩阵W为单位阵；如果是获取场景的结构信息，则矩阵W为使得Wx具有稀疏性的变换矩阵。
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