WO2017147774A1 - 一种可分离稀疏信号的压缩感知方法及其系统 - Google Patents

一种可分离稀疏信号的压缩感知方法及其系统 Download PDF

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WO2017147774A1
WO2017147774A1 PCT/CN2016/075135 CN2016075135W WO2017147774A1 WO 2017147774 A1 WO2017147774 A1 WO 2017147774A1 CN 2016075135 W CN2016075135 W CN 2016075135W WO 2017147774 A1 WO2017147774 A1 WO 2017147774A1
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sparse
signal
compressed
compression
sensing
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PCT/CN2016/075135
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French (fr)
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黄建军
康莉
谢丽娟
黄敬雄
梁钟尹
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深圳大学
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction

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  • the present invention relates to the field of signal processing, and in particular, to a compressed sensing method capable of separating sparse signals and a system thereof.
  • Compressed Sensing (CS) technology has become a research hotspot in the field of signal processing.
  • Compressed sensing technology requires that the compressed signal be sparse or nearly sparse under a single base set.
  • many signals may not be sparse or nearly sparse under a single base set. These signals usually contain more The sparse components under different base sets are the multi-base set sparse signals, such as the target part and the background part in the infrared small target image signal.
  • some components of the signal may not only be useless in subsequent processing, but may even adversely affect the signal processing process, such as the clutter portion of the radar signal.
  • problems there will be the following problems:
  • the signal can be represented as a sparse signal under a single base set and compressed, then the obtained compression measure is mixed with the sparse components of the original signal, and the signal-to-noise ratio is low, which is not only conducive to compression.
  • the compression measurement is directly used in the domain to realize the processing of the signal, and the overall speed of the signal recovery is slowed down;
  • an object of the present invention is to provide a compressed sensing method capable of separating sparse signals and a system thereof, which aims to solve the problem that the signal recovery speed is slow and the processing process is inflexible and scalable in the subsequent processing in the prior art. Not a strong problem.
  • the invention provides a compressed sensing method capable of separating sparse signals, the method comprising:
  • some or all of the sparse signal components are respectively subjected to compression sensing to obtain corresponding compression measurement values.
  • the method further includes:
  • the resulting plurality of compression measurements are combined to form a new compression measurement.
  • the method further includes:
  • This new compressed measurement is transmitted over the network using the network.
  • the method further includes:
  • the receiving end receives a new compressed measurement value transmitted through the network, and splits the new compressed measurement value to obtain a compressed measurement value of each of the compressed sparse signals.
  • the method further includes:
  • the obtained compressed measurement values of each of the compressed sparse signals are separately processed.
  • the present invention also provides a compressed sensing system capable of separating a sparse signal, the system comprising:
  • a signal decomposition module configured to perform signal decomposition on the separable sparse signal, and obtain a sparse signal component under a plurality of different base sets after being decomposed;
  • the compressed sensing module is configured to perform compressed sensing on some or all of the sparse signal components according to actual requirements to obtain a corresponding compressed measurement value.
  • the system further comprises:
  • the quantity combination module is configured to combine the obtained plurality of compression measurements to form a new compression measurement.
  • the system further comprises:
  • a network transmission module for performing network transmission of the new compressed measurement value by using a network.
  • the system further comprises:
  • the value splitting module is configured to receive a new compressed measurement value transmitted through the network, and split the new compressed measurement value to obtain a compressed measurement of each of the compressed sparse signals value.
  • the system further comprises:
  • the processing module is respectively configured to separately process the compressed measurement values of each of the acquired sparse signals according to actual requirements.
  • the technical solution provided by the invention breaks the traditional idea of treating a signal as a sparse signal of a single base set, but expresses the signal in the form of a sum of sparse signal components under a plurality of different base sets, and expands the compressible sensing signal and range. .
  • the sparse components can be separately compressed and sensed as needed, thereby improving the speed of signal recovery in the subsequent processing, and making the processing more flexible and more scalable.
  • FIG. 1 is a flowchart of a compressed sensing method capable of separating a sparse signal according to an embodiment of the present invention
  • FIG. 2 is a general block diagram of a compressed sensing method capable of separating sparse signals according to an embodiment of the present invention
  • FIG. 3 is a block diagram of a compression sensing method for an infrared small target image signal according to an embodiment of the present invention
  • FIG. 4 is a block diagram of another method for compressing sensing of an infrared small target image signal according to an embodiment of the present invention.
  • FIG. 5 is a schematic diagram showing the internal structure of a compressed sensing system 10 capable of separating sparse signals according to an embodiment of the present invention.
  • a specific embodiment of the present invention provides a compressed sensing method capable of separating a sparse signal, and the method mainly includes the following steps:
  • the compressed sensing method capable of separating sparse signals breaks the traditional idea of treating a signal as a single base set sparse signal, but represents a signal in the form of a sum of sparse signal components under a plurality of different base sets. Expanded compressible sensing signals and range. After the signal is decomposed, the sparse components can be separately compressed and sensed as needed, thereby improving the speed of signal recovery in the subsequent processing, and making the processing more flexible and more scalable.
  • FIG. 1 is a flowchart of a compressed sensing method capable of separating sparse signals according to an embodiment of the present invention.
  • step S11 the decomposable sparse signal is subjected to signal decomposition, and after decomposing, sparse signal components under a plurality of different base sets are obtained.
  • the separable sparse signal refers to a signal that can be represented as a sum of sparse signal components under a plurality of different sets of bases.
  • ⁇ 1 , ⁇ 2 ... ⁇ p are a plurality of different base sets of the R N space, and ⁇ 1 , ⁇ 2 ... ⁇ p are coefficient vectors under the corresponding base set, if it satisfies
  • the sparse signal, x i , i 1, ..., p is a sparse component corresponding to the base set ⁇ i , since the separable sparse signal x contains sparse signal components under a plurality of different base sets, the separable sparse signal is first The signal x is decomposed.
  • the separable sparse signal x is decomposed into x 1 , x 2 , . . . , x p , and the signal decomposition can be implemented in various ways, such as filtering, transforming, and the like.
  • step S12 some or all of the sparse signal components are respectively subjected to compression sensing according to actual requirements to obtain corresponding compression measurement values.
  • an observation matrix is used. (M 1 , M 2 , ..., M q ⁇ N,, 0 ⁇ q ⁇ p), for some or all of the sparse signal components x 1 , x 2 , ..., x q , 0 ⁇ q ⁇ p separately performs compression sensing, and obtains the corresponding compression measurement value after compression
  • the process of performing compressed sensing on some or all of the sparse signal components according to actual needs can be expressed as:
  • the corresponding sparse signals x 1 ', x 2 ', ..., x q ', q ⁇ p can be restored, and then they are phased. Plus, get the final recovery signal x'.
  • the compressed sensing method of the separable sparse signal of the present invention further includes:
  • the receiving end receives a new compressed measurement value transmitted through the network, and splits the new compressed measurement value to obtain a compressed measurement value of each of the compressed sparse signals;
  • the obtained compressed measurement values of each of the compressed sparse signals are separately processed.
  • the compressed sensing method capable of separating sparse signals breaks the traditional idea of treating a signal as a single base set sparse signal, but represents a signal as a sparse signal component under a plurality of different base sets.
  • the sum of the forms expands the compressible sensing signal and range.
  • the sparse components can be separately compressed and sensed as needed, thereby improving the speed of signal recovery in the subsequent processing, and making the processing more flexible and more scalable.
  • the infrared small target image signal is taken as an example to illustrate the practical application process of the separable sparse signal compression sensing method:
  • the task of signal processing is only for target detection tracking, then only the target sparse component can be compressed, and since the small target occupies only one or a few pixels in the image, it is sparse in the spatial domain, so compression The amount of data measured will be smaller, given matrix Compressing the target sparse component,
  • the overall processing is shown in block 4.
  • the present invention proposes two specific processing methods based on the separable sparse signal compression sensing method for the infrared small target video signal, and the method firstly performs the compression sensing on the infrared small target image signal.
  • the target signal and the background signal are obtained, and then processed according to the actual signal processing task: processing mode 1, compressing all the sparse signal components separately, and then transmitting through the network, and finally recovering the original infrared small target image.
  • processing method 2 only compresses the target image, and then uses the compression measurement to perform target detection without restoring the original image.
  • the invention can be applied to scenes for compressive sensing of any separable sparse signal, such as radar signals, infrared small target image signals, medical detection signals, and at the same time, the present invention has been successfully applied to the infrared small target image signal detection and tracking process.
  • Infrared small target detection and tracking technology is the key technology of infrared guidance, search tracking and infrared warning system.
  • the research on infrared small target detection method has important military significance and practical value for improving the defense ability of infrared system, effective counterattack capability and effective killing ability of infrared weapon equipment system.
  • the infrared small target image signal processing method adopted by the invention can not only directly adopt the target compression measurement to realize infrared small target detection in the compressed domain without restoring the original image, and can also realize asynchronous recovery of the background and the foreground, so that the recovery process It's simpler and faster.
  • the embodiment of the present invention further provides a compressed sensing system 10 capable of separating a sparse signal, which mainly includes:
  • the signal decomposition module 11 is configured to perform signal decomposition on the separable sparse signal, and obtain a sparse signal component under a plurality of different base sets after being decomposed;
  • the compressed sensing module 12 is configured to perform compressed sensing on some or all of the sparse signal components according to actual requirements to obtain a corresponding compressed measurement value.
  • the compressed sensing system 10 capable of separating sparse signals breaks the traditional idea of treating a signal as a sparse signal of a single base set, but represents a signal as a sum of sparse signal components under a plurality of different base sets.
  • the form expands the compressible sensing signal and range. After the signal is decomposed, the sparse components can be separately compressed and sensed as needed, thereby improving the speed of signal recovery in the subsequent processing, and making the processing more flexible and more scalable.
  • the compressed sensing system 10 that can separate the sparse signals mainly includes a signal decomposition module 11 and a compression sensing module 12.
  • the signal decomposition module 11 is configured to perform signal decomposition on the separable sparse signal, and obtain a sparse signal component under a plurality of different base sets after being decomposed.
  • the separable sparse signal refers to a signal that can be represented as a sum of sparse signal components under a plurality of different sets of bases.
  • ⁇ 1 , ⁇ 2 ... ⁇ p are a plurality of different base sets of the R N space, and ⁇ 1 , ⁇ 2 ... ⁇ p are coefficient vectors under the corresponding base set, if it satisfies
  • the sparse signal, x i , i 1, ..., p is a sparse component corresponding to the base set ⁇ i , since the separable sparse signal x contains sparse signal components under a plurality of different base sets, the separable sparse signal is first The signal x is decomposed.
  • the separable sparse signal x is decomposed into x 1 , x 2 , . . . , x p , and the signal decomposition can be implemented in various ways, such as filtering, transforming, and the like.
  • the compressed sensing module 12 is configured to perform compressed sensing on some or all of the sparse signal components according to actual requirements to obtain a corresponding compressed measurement value.
  • an observation matrix is used. (M 1 , M 2 , ..., M q ⁇ N,, 0 ⁇ q ⁇ p), for some or all of the sparse signal components x 1 , x 2 , ..., x q , 0 ⁇ q ⁇ p separately performs compression sensing, and obtains the corresponding compression measurement value after compression
  • the process of performing compressed sensing on some or all of the sparse signal components according to actual needs can be expressed as:
  • the corresponding sparse signals x 1 ', x 2 ', ..., x q ', q ⁇ p can be restored, and then they are phased. Plus, get the final recovery signal x'.
  • the separable signal-capable compression sensing system 10 of the present invention further includes: a value combination module, a network transmission module, a magnitude splitting module, and a separate processing module, none of which are shown in FIG. 5. .
  • the quantity combination module is configured to combine the obtained plurality of compression measurements to form a new compression measurement.
  • a network transmission module for performing network transmission of the new compressed measurement value by using a network.
  • the value splitting module is configured to receive a new compressed measurement value transmitted through the network, and split the new compressed measurement value to obtain a compressed measurement of each of the compressed sparse signals value.
  • the processing module is respectively configured to separately process the compressed measurement values of each of the acquired sparse signals according to actual requirements.
  • the compressed sensing system 10 capable of separating sparse signals breaks the traditional idea of treating a signal as a sparse signal of a single base set, but represents a signal as a sum of sparse signal components under a plurality of different base sets.
  • the form expands the compressible sensing signal and range. After the signal is decomposed, the sparse components can be separately compressed and sensed as needed, thereby improving the speed of signal recovery in the subsequent processing, and making the processing more flexible and more scalable.
  • each unit included is only divided according to functional logic, but is not limited to the above division, as long as the corresponding function can be implemented; in addition, the specific name of each functional unit is also They are only used to facilitate mutual differentiation and are not intended to limit the scope of the present invention.

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Abstract

本发明提供了一种可分离稀疏信号的压缩感知方法，包括：对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。本发明还提供一种可分离稀疏信号的压缩感知系统。本发明打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量之和的形式，扩大了可压缩感知信号和范围，信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。

Description

一种可分离稀疏信号的压缩感知方法及其系统 技术领域
本发明涉及信号处理领域，尤其涉及一种可分离稀疏信号的压缩感知方法及其系统。
背景技术
近年来，压缩感知(Compressed Sensing，CS)技术成为了信号处理领域中的研究热点。压缩感知技术要求被压缩的信号在某单个基集下是稀疏或者近似稀疏的，然而在实际处理过程中发现，许多信号在单个基集下可能并非是稀疏或者近似稀疏的，这些信号通常包含多个不同基集下的稀疏成分，即为多基集稀疏信号，如红外小目标图像信号中的目标部分与背景部分。同时，信号中某些成分在后续的处理过程中不仅可能是无用的，甚至会对信号处理的过程造成不良影响，如雷达信号中的杂波部分。对于这一类信号，将会存在以下问题：
(1)、若信号能被表示成某单个基集下的稀疏信号并对其进行压缩，那么所获得的压缩量测混杂了原始信号的各稀疏分量，信噪比低，不仅不利于在压缩域中直接采用压缩量测实现对信号的处理，而且会导致信号恢复的整体速度变慢；
(2)、若信号在单个基集下为非稀疏信号，那么便不能采用传统的压缩感知技术对信号进行处理。
发明内容
有鉴于此，本发明的目的在于提供一种可分离稀疏信号的压缩感知方法及其系统，旨在解决现有技术中在后续处理过程中信号恢复的速度较慢并且处理过程不灵活、扩展性不强的问题。
本发明提出一种可分离稀疏信号的压缩感知方法，所述方法包括：
对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
优选的，所述方法还包括：
将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值。
优选的，所述方法还包括：
利用网络将这一个新的压缩量测值进行网络传输。
优选的，所述方法还包括：
接收端接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值。
优选的，所述方法还包括：
根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
另一方面，本发明还提供一种可分离稀疏信号的压缩感知系统，所述系统包括：
信号分解模块，用于对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
压缩感知模块，用于根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
优选的，所述系统还包括：
量值组合模块，用于将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值。
优选的，所述系统还包括：
网络传输模块，用于利用网络将这一个新的压缩量测值进行网络传输。
优选的，所述系统还包括：
量值拆分模块，用于接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值。
优选的，所述系统还包括：
分别处理模块，用于根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
本发明提供的技术方案打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量之和的形式，扩大了可压缩感知信号和范围。信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。
附图说明
图1为本发明一实施方式中可分离稀疏信号的压缩感知方法流程图；
图2为本发明一实施方式中可分离稀疏信号的压缩感知方法总体框图；
图3为本发明一实施方式中一种红外小目标图像信号的压缩感知方法框图；
图4为本发明一实施方式中另一种红外小目标图像信号的压缩感知方法框图；
图5为本发明一实施方式中可分离稀疏信号的压缩感知系统10的内部结构示意图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅 仅用以解释本发明，并不用于限定本发明。
本发明具体实施方式提供了一种可分离稀疏信号的压缩感知方法，所述方法主要包括如下步骤：
S11、对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
S12、根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
本发明提供的一种可分离稀疏信号的压缩感知方法打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量之和的形式，扩大了可压缩感知信号和范围。信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。
以下将对本发明所提供的一种可分离稀疏信号的压缩感知方法进行详细说明。
请参阅图1，为本发明一实施方式中可分离稀疏信号的压缩感知方法流程图。
在步骤S11中，对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量。
在本实施方式中，可分离稀疏信号是指能够被表示成多个不同基集下的稀疏信号分量之和形式的信号。
在本实施方式中，对于信号x∈RN，若其可被表示成
x＝x1+x2+...+xp＝Ψ1θ1+Ψ2θ2+...+Ψpθp,p≥2；
其中Ψ1,Ψ2...Ψp为RN空间的多个不同基集，θ1,θ2...θp为对应基集下的系数向量，若它满足||θ1||0+||θ2||0+...+||θp||0<<N,(||·||0表示向量中的非零元素个数)，那么称信号x为可分离稀疏信号，xi,i＝1,...,p为对应于基集Ψi的稀疏分量，由于可分离稀疏信号x包含多个不同基集下的稀疏信号分量，因此首先将可分离稀疏信号x进 行分解，如图2所示，可分离稀疏信号x被分解为x1,x2,...,xp，其中信号分解的实现方式可以有多种，如滤波、变换等。
在步骤S12中，根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
在本实施方式中，在可分离稀疏信号分解后，采用观测矩阵
Figure PCTCN2016075135-appb-000001
(M1,M2,...,Mq<<N,，0<q≤p)，对所得的部分或全部稀疏信号分量x1,x2,...,xq,0<q≤p分别进行压缩感知，压缩后获得对应的压缩量测值
Figure PCTCN2016075135-appb-000002
其中，根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知的过程可被表示为：
Figure PCTCN2016075135-appb-000003
同时，对每一个压缩量测值，根据不同的字典及重构算法，即可恢复相应的稀疏信号x1',x2',...,xq',q≤p，再将它们相加，获得最终的恢复信号x'。
在本实施方式中，在步骤S12之后，本发明的可分离稀疏信号的压缩感知方法还包括：
将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值；
利用网络将这一个新的压缩量测值进行网络传输；
接收端接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值；
根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
本发明提供的一种可分离稀疏信号的压缩感知方法打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量 之和的形式，扩大了可压缩感知信号和范围。信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。
在本实施方式中，此处以红外小目标图像信号为例说明可分离稀疏信号压缩感知方法的实际应用过程：
红外小目标图像信号可被表示成f＝fb+ft，其中，f∈RN为红外小目标图像信号经过行堆叠之后的向量形式，fb∈RN为背景部分，ft∈RN为目标部分，由于背景部分变化缓慢，空间相关性大，因此fb在变换域(如傅里叶域、小波域)中具有稀疏性，而目标部分变化较快，空间相关性小，所以fb在空间域中为稀疏信号，假定
Figure PCTCN2016075135-appb-000004
为某变换域中的一组基，
Figure PCTCN2016075135-appb-000005
为空间域中的一组基，那么以上公式可被表示成f＝Ψbθb+Ψtθt，其中θb，θt为对应基集下的系数，满足||θb||0+||θt||0<<N，按照可分离稀疏信号压缩感知方法，对红外小目标图像信号f进行分解，得到两个不同基集下的稀疏信号fb，ft，接下来将从两个方面说明对分解后的稀疏信号的具体处理方式。
(1)全部稀疏分量压缩感知(q＝p)
若实际后续处理过程需要恢复出原始红外小目标图像信号，那么此时应对背景稀疏分量和前景稀疏分量分别进行压缩感知。给定矩阵
Figure PCTCN2016075135-appb-000006
(Mb,Mt<<N)，那么信号压缩感知的过程可被表示为
Figure PCTCN2016075135-appb-000007
其中，
Figure PCTCN2016075135-appb-000008
为背景信号压缩量测，
Figure PCTCN2016075135-appb-000009
为目标信号压缩量测。通过网络传输，拆分后，根据背景压缩量测以及前景压缩量测，采用不同的重构算法对它们进行异步恢复，最后经过加法器得到最终的恢复图像f'，整体处理框图如图3所示。
(2)部分稀疏分量压缩感知(0<q<p)
若信号处理的任务仅仅是为了进行目标检测跟踪，那么可仅对目标稀疏分 量进行压缩，且由于小目标在图像中仅占一个或几个像素点，在空间域中便具有稀疏性，因此压缩量测的数据量会更小，给定矩阵
Figure PCTCN2016075135-appb-000010
对目标稀疏分量进行压缩，
yt＝Φtft＝ΦtΨtθt；
得到目标压缩量测值
Figure PCTCN2016075135-appb-000011
再通过网络发送、传输、接收到达处理端，最后可直接使用目标压缩量测实现压缩域中的目标检测跟踪，整体处理框图4所示。
在本实施方式中，本发明针对红外小目标视频信号，提出了基于可分离稀疏信号压缩感知方法的两种具体处理方法，该方法在对红外小目标图像信号进行压缩感知前，首先对它进行了分解，得到目标信号及背景信号，再根据实际信号处理任务对它们进行处理：处理方式一，对全部的稀疏信号分量分别进行压缩、再通过网络传输等，最终恢复出原始的红外小目标图像信号；处理方式二，仅对目标图像进行压缩，再利用压缩量测在不恢复原始图像的情况下进行目标检测。
本发明可应用于对任何可分离稀疏信号进行压缩感知的场景，如雷达信号、红外小目标图像信号、医学检测信号，同时，本发明目前已成功应用于红外小目标图像信号检测跟踪过程当中。红外小目标检测跟踪技术是红外制导、搜索跟踪和红外预警系统的关键技术。红外小目标检测方法的研究，对提高红外系统的防御能力、有效反击能力以及红外武器装备系统的有效杀伤能力具有重要的军事意义和实用价值。本发明采用的红外小目标图像信号处理方法不仅能够直接采用目标压缩量测在不恢复原始图像的情况下实现压缩域中红外小目标检测，还能够对背景以及前景实现异步恢复，使得恢复的过程更加简单、快速。
本发明具体实施方式还提供一种可分离稀疏信号的压缩感知系统10，主要包括：
信号分解模块11，用于对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
压缩感知模块12，用于根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
本发明提供的一种可分离稀疏信号的压缩感知系统10，打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量之和的形式，扩大了可压缩感知信号和范围。信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。
请参阅图5，所示为本发明一实施方式中可分离稀疏信号的压缩感知系统10的结构示意图。在本实施方式中，可分离稀疏信号的压缩感知系统10主要包括信号分解模块11以及压缩感知模块12。
信号分解模块11，用于对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量。
在本实施方式中，可分离稀疏信号是指能够被表示成多个不同基集下的稀疏信号分量之和形式的信号。
在本实施方式中，对于信号x∈RN，若其可被表示成
x＝x1+x2+...+xp＝Ψ1θ1+Ψ2θ2+...+Ψpθp,p≥2；
其中Ψ1,Ψ2...Ψp为RN空间的多个不同基集，θ1,θ2...θp为对应基集下的系数向量，若它满足||θ1||0+||θ2||0+...+||θp||0<<N,(||·||0表示向量中的非零元素个数)，那么称信号x为可分离稀疏信号，xi,i＝1,...,p为对应于基集Ψi的稀疏分量，由于可分离稀疏信号x包含多个不同基集下的稀疏信号分量，因此首先将可分离稀疏信号x进行分解，如图2所示，可分离稀疏信号x被分解为x1,x2,...,xp，其中信号分解的实现方式可以有多种，如滤波、变换等。
压缩感知模块12，用于根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
在本实施方式中，在可分离稀疏信号分解后，采用观测矩阵
Figure PCTCN2016075135-appb-000012
(M1,M2,...,Mq<<N,，0<q≤p)，对所得的部分或全部稀疏 信号分量x1,x2,...,xq,0<q≤p分别进行压缩感知，压缩后获得对应的压缩量测值
Figure PCTCN2016075135-appb-000013
其中，根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知的过程可被表示为：
Figure PCTCN2016075135-appb-000014
同时，对每一个压缩量测值，根据不同的字典及重构算法，即可恢复相应的稀疏信号x1',x2',...,xq',q≤p，再将它们相加，获得最终的恢复信号x'。
在本实施方式中，本发明的可分离稀疏信号的压缩感知系统10还包括：量值组合模块、网络传输模块、量值拆分模块以及分别处理模块，这些模块均未在图5中示出。
量值组合模块，用于将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值。
网络传输模块，用于利用网络将这一个新的压缩量测值进行网络传输。
量值拆分模块，用于接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值。
分别处理模块，用于根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
本发明提供的一种可分离稀疏信号的压缩感知系统10，打破了将信号视为单个基集稀疏信号的传统思路，而是把信号表示成多个不同基集下的稀疏信号分量之和的形式，扩大了可压缩感知信号和范围。信号分解后可根据需要对各稀疏分量单独进行压缩感知，从而提高后续处理过程中信号恢复的速度，并且使得处理过程更加灵活，扩展性更强。
值得注意的是，上述实施例中，所包括的各个单元只是按照功能逻辑进行划分的，但并不局限于上述的划分，只要能够实现相应的功能即可；另外，各功能单元的具体名称也只是为了便于相互区分，并不用于限制本发明的保护范围。
另外，本领域普通技术人员可以理解实现上述各实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，相应的程序可以存储于一计算机可读取存储介质中，所述的存储介质，如ROM/RAM、磁盘或光盘等。
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，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，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种可分离稀疏信号的压缩感知方法，其特征在于，所述方法包括：
    对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
    根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
  2. 如权利要求1所述的可分离稀疏信号的压缩感知方法，其特征在于，所述方法还包括：
    将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值。
  3. 如权利要求2所述的可分离稀疏信号的压缩感知方法，其特征在于，所述方法还包括：
    利用网络将这一个新的压缩量测值进行网络传输。
  4. 如权利要求3所述的可分离稀疏信号的压缩感知方法，其特征在于，所述方法还包括：
    接收端接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值。
  5. 如权利要求4所述的可分离稀疏信号的压缩感知方法，其特征在于，所述方法还包括：
    根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
  6. 一种可分离稀疏信号的压缩感知系统，其特征在于，所述系统包括：
    信号分解模块，用于对可分离稀疏信号进行信号分解，并在分解后得到多个不同基集下的稀疏信号分量；
    压缩感知模块，用于根据实际需求对部分或者全部稀疏信号分量分别进行压缩感知，以得到对应的压缩量测值。
  7. 如权利要求6所述的可分离稀疏信号的压缩感知系统，其特征在于，所 述系统还包括：
    量值组合模块，用于将得到的多个压缩量测值进行组合，以形成一个新的压缩量测值。
  8. 如权利要求7所述的可分离稀疏信号的压缩感知系统，其特征在于，所述系统还包括：
    网络传输模块，用于利用网络将这一个新的压缩量测值进行网络传输。
  9. 如权利要求8所述的可分离稀疏信号的压缩感知系统，其特征在于，所述系统还包括：
    量值拆分模块，用于接收经过网络传输后的一个新的压缩量测值，并将所述一个新的压缩量测值进行拆分，以得到被压缩的每一个稀疏信号的压缩量测值。
  10. 如权利要求9所述的可分离稀疏信号的压缩感知系统，其特征在于，所述系统还包括：
    分别处理模块，用于根据实际需求对获取到的被压缩的每一个稀疏信号的压缩量测值分别进行处理。
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CN104485966A (zh) * 2014-12-01 2015-04-01 北京邮电大学 一种基于信号分解的压缩感知处理和信号重构方法

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CN103472450A (zh) * 2013-09-18 2013-12-25 哈尔滨工业大学 基于压缩感知的非均匀空间构形分布式sar动目标三维成像方法
CN104485966A (zh) * 2014-12-01 2015-04-01 北京邮电大学 一种基于信号分解的压缩感知处理和信号重构方法

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