CN109547961B - A Compressed Sensing Coding and Decoding Method for Large Data Volumes in Wireless Sensor Networks - Google Patents
A Compressed Sensing Coding and Decoding Method for Large Data Volumes in Wireless Sensor NetworksDownload PDFInfo
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Abstract
Description
Translated fromChinese技术领域technical field
本发明属于数据处理技术领域，具体涉及一种无线传感网络中大数据量压缩感知编解码方法。The invention belongs to the technical field of data processing, and in particular relates to a large-data-volume compressed sensing encoding and decoding method in a wireless sensor network.
背景技术Background technique
无线传感器测试网络采集的数据大部分为温度、湿度、振动、位移、声音等自然界中的一维数据。无线传感器网络中的数据压缩编码主要针对这类一维信号开展。压缩编码之所以可以做到数据压缩，实质上利用了无线传感器网络的数据相关性。这种相关性包括时间相关性和空间相关性。因此，相应的压缩算法也可以分为：基于时间相关性的数据压缩算法，基于空间相关性的数据压缩算法，以及基于时空相关性的数据压缩算法。Most of the data collected by the wireless sensor test network is one-dimensional data in nature, such as temperature, humidity, vibration, displacement, and sound. Data compression coding in wireless sensor networks is mainly carried out for such one-dimensional signals. The reason why compression coding can achieve data compression is that it uses the data correlation of wireless sensor networks in essence. This correlation includes temporal correlation and spatial correlation. Therefore, the corresponding compression algorithms can also be divided into: data compression algorithms based on time correlation, data compression algorithms based on spatial correlation, and data compression algorithms based on space-time correlation.
这些典型的数据压缩算法和设计思路多数仅考虑了数据的冗余性，没有考虑无线传输中的不稳定性和丢包现象。为此，luo和Lee等人将压缩感知算法引入无线传感器网络领域，在成功剔除了数据空间冗余的同时保证了数据对丢包的不敏感性。Xiong L等人结合小波变换，通过压缩感知算法剔除了数据的时空冗余。但是这些算法需要较高维度的测量信号保证数据的重构精度，影响了数据的压缩率和终端显示的实时性。Most of these typical data compression algorithms and design ideas only consider data redundancy, but do not consider instability and packet loss in wireless transmission. To this end, Luo and Lee et al. introduced the compressed sensing algorithm into the field of wireless sensor networks, which successfully eliminated the data space redundancy and ensured the data insensitivity to packet loss. Combined with wavelet transform, Xiong L et al. removed the spatial and temporal redundancy of data through compressed sensing algorithm. However, these algorithms require higher-dimensional measurement signals to ensure data reconstruction accuracy, which affects the data compression rate and the real-time display of the terminal.
发明内容SUMMARY OF THE INVENTION
有鉴于此，本发明的目的是提供一种无线传感网络中大数据量压缩感知编解码方法，可以提高数据重构的实时性和精度，节约了网络的传输带宽。In view of this, the purpose of the present invention is to provide a large data volume compressed sensing encoding and decoding method in a wireless sensor network, which can improve the real-time performance and accuracy of data reconstruction and save the transmission bandwidth of the network.
一种数据压缩感知编解码方法，包括如下步骤：A data compression sensing encoding and decoding method, comprising the following steps:
步骤一，对原始信号进行稀疏变换和分级：Step 1, sparse transformation and classification of the original signal:
步骤1)、将原始信号进行稀疏转换，计算原始信号的稀疏表示α；Step 1), sparsely transform the original signal, and calculate the sparse representation α of the original signal;
步骤2)、初始化残差信号的稀疏表示αr＝α；Step 2), initialize the sparse representation of the residual signal αr =α;
步骤3)、计算第1级分信号的稀疏表示，具体为：Step 3), calculating the sparse representation of the first level signal, specifically:
针对残差的稀疏表示αr中的每个元素，判断元素值是否大于或等于σmax(αr)，其中，分量系数σ根据实际情况确定，取值为0-1之间的小数：For each element in the sparse representation αr of the residual, determine whether the element value is greater than or equal to σmax(αr ), where the component coefficient σ is determined according to the actual situation and takes a decimal value between 0 and 1:
如果是，将该元素值赋值给当前级分信号对应位置；再将残差αr中的该元素的值置为0；If so, assign the element value to the corresponding position of the current fractional signal; then set the value of the element in the residual αr to 0;
如果否，将当前级分信号与该元素对应位置的值置为0；If not, set the value of the current fraction signal and the corresponding position of the element to 0;
遍历残差αr中的所有元素后，得到当前级分信号稀疏表示的各元素值，以及更新后的残差的稀疏表示αr；获得当前级分信号的稀疏度；After traversing all the elements in the residual αr , obtain the value of each element of the sparse representation of the current fractional signal, and the sparse representation αr of the updated residual; obtain the sparsity of the current fractional signal;
步骤4)、利用当前残差，按照步骤3)的方法分解得到下一级分信号；以此类推，直至分解级数达到设定阈值或者残差信号的p范数小于设定阈值；Step 4), using the current residual, decompose to obtain the next fractional signal according to the method of step 3); and so on, until the decomposition level reaches the set threshold or the p-norm of the residual signal is less than the set threshold;
步骤二，信号逐级编码压缩：Step 2, signal coding and compression step by step:
随机生成一个M×N维的伯努利随机矩阵，作为总的测量矩阵Φ；其中，N表示原始信号的维数；M的取值根据最后一级分信号的稀疏度Kn确定：M≥cKnlog(N/Kn)，其中c值根据信号的先验知识确定；Randomly generate an M×N-dimensional Bernoulli random matrix as the total measurement matrix Φ; where N represents the dimension of the original signal; the value of M is determined according to the sparsity Kn of the last stage signal: M≥ cKn log(N/Kn ), where the value of c is determined from prior knowledge of the signal;
则第i级分信号对应的测量矩阵Φi为总测量矩阵Φ的前Mi行数据；Then the measurement matrix Φi corresponding to the i-th fractional signal is the data of the first Mi rows of the total measurement matrix Φ;
利用各级分信号对应的测量矩阵对各级分信号的稀疏表示进行编码压缩，得到编码信号；The sparse representation of each fraction signal is encoded and compressed by using the measurement matrix corresponding to each fraction signal to obtain a coded signal;
步骤三，对完成编码的各级分信号，从第一级开始进行顺序传输；收到一级分信号的编码信号后，确定该级分信号的维度，即该级分信号对应的测量矩阵的行数；从总测量矩阵Φ中提取出该级分信号对应的测量矩阵；将编码数据和测量矩阵输入到匹配追踪算法OMP中，输出还原信号的稀疏表示αi’；Step 3: Perform sequential transmission from the first stage on the encoded signals of each fraction; after receiving the encoded signal of the fractional signal, determine the dimension of the fractional signal, that is, the dimension of the measurement matrix corresponding to the fractional signal. The number of rows; the measurement matrix corresponding to the fractional signal is extracted from the total measurement matrix Φ; the encoded data and the measurement matrix are input into the matching pursuit algorithm OMP, and the sparse representation αi ' of the output restored signal;
步骤四、设已完成第j级分信号编码数据的还原，则重构后的原始信号为：Step 4. Suppose that the restoration of the jth-level signal encoded data has been completed, then the reconstructed original signal is:
其中，Ψ表示步骤一中对原始信号进行稀疏转换的稀疏基。Among them, Ψ represents the sparse basis for the sparse transformation of the original signal in step 1.
较佳的，M＝cKnlog(N/Kn)，其中c取3。Preferably, M=cKn log(N/Kn ), where c is 3.
本发明具有如下有益效果：The present invention has the following beneficial effects:
采用以稀疏基下信号稀疏表示大小对信号进行逐级分解的方法，主信号包含在前几级的信号中，而次要信号则级数较为靠后，白噪声信号等噪声信号一般被分解至剩余残差中消除。有效的保护了我们所需的有效信号，并且弱化了噪声信号，提高了信号的准确性。The signal is decomposed step-by-step based on the sparse representation of the signal under the sparse base. The main signal is included in the signals of the first few stages, while the secondary signal is in the later stages. Noise signals such as white noise signals are generally decomposed into The remaining residuals are eliminated. It effectively protects the effective signal we need, weakens the noise signal, and improves the accuracy of the signal.
对稀疏化的信号进行分级压缩编码，分解后的信号在数据总量上大大降低，并且可提高重构的实时性和精度。By performing hierarchical compression coding on the sparse signal, the total amount of data of the decomposed signal is greatly reduced, and the real-time performance and accuracy of reconstruction can be improved.
设计了一个总测量矩阵Mmax×N，每一级分信号的测量矩阵作为该测量矩阵的子矩阵，不保存多余的测量矩阵，降低了硬件资源的使用率。A total measurement matrix Mmax×N is designed, and the measurement matrix of each sub-signal is used as a sub-matrix of the measurement matrix, and redundant measurement matrices are not saved, which reduces the utilization rate of hardware resources.
在单个分信号的编码数据传输完成后，便可以对原始信号进行重构并输出。随着重构完成的分信号越多，级数越高，原始信号的细节信息越多，失真越小。这种逐级重构的方式有别于传统的信号重构，不用接收完成所有压缩编码信息便可进行重构信号的输出，网络中首先传输级数低的分信号编码，因此首先重构出来的是稀疏向量系数最大的分信号，而后不断的累加级数较高的分信号，实现细节的修正，提高了数据传输的实时性。After the encoded data of a single sub-signal is transmitted, the original signal can be reconstructed and output. As more sub-signals are reconstructed, the higher the number of stages, the more detailed information of the original signal, and the smaller the distortion. This step-by-step reconstruction method is different from the traditional signal reconstruction. The reconstructed signal can be output without receiving all the compression and encoding information. The network first transmits the sub-signal encoding with the lower level, so the reconstruction is performed first. It is the sub-signal with the largest sparse vector coefficient, and then the sub-signal with higher series is continuously accumulated to realize the correction of details and improve the real-time performance of data transmission.
附图说明Description of drawings
图1为本发明的一种无线传感网络中大数据量压缩感知编解码方法流程图。FIG. 1 is a flowchart of a method for encoding and decoding a large amount of data compressed sensing in a wireless sensor network according to the present invention.
图2为本发明的基于稀疏向量系数的分解过程流程图。FIG. 2 is a flow chart of the decomposition process based on sparse vector coefficients of the present invention.
图3为本发明的分级重构信号流程图。FIG. 3 is a flow chart of the hierarchically reconstructed signal of the present invention.
具体实施方式Detailed ways
下面结合附图并举实施例，对本发明进行详细描述。The present invention will be described in detail below with reference to the accompanying drawings and embodiments.
本发明提出了一种无线传感网络中大数据量压缩感知编解码方法，如图1所示，该方法包含如下步骤：The present invention proposes a large data volume compressive sensing encoding and decoding method in a wireless sensor network, as shown in FIG. 1 , the method includes the following steps:
步骤一，对原始信号进行稀疏变换和分级：Step 1, sparse transformation and classification of the original signal:
以稀疏基下信号稀疏表示大小对信号进行分解，并通过控制分量系数σ的大小来控制每层分信号的稀疏表示大小的范围。稀疏表示是指信号经过稀疏变换的值。首先从总信号中分解出最主要、最稀疏的信号，之后从残差中分解出较次要的信号，依次类推。最开始分解出的信号是稀疏的，而随着分解的逐级进行，信号的稀疏性会越来越差，能量也会越来越小，剩余最后的残差信号被忽略；The signal is decomposed according to the size of the sparse representation of the signal under the sparse basis, and the range of the size of the sparse representation of each layer of sub-signals is controlled by controlling the size of the component coefficient σ. The sparse representation refers to the value of the signal that has been sparsely transformed. The most important and sparsest signals are first decomposed from the total signal, then the lesser ones are decomposed from the residuals, and so on. The signal decomposed at the beginning is sparse, and as the decomposition progresses step by step, the sparseness of the signal will become worse and the energy will become smaller and smaller, and the remaining final residual signal is ignored;
具体的按照公式(1)进行信号稀疏化；Specifically, the signal is sparsed according to formula (1);
式中，X为N×1维原始信号，Ψ为N×N维的稀疏基，α为N×1维的信号，是原始信号在稀疏基Ψ下的稀疏表示，r为N×1维剩余残差；Xi表示分解得到的第i级分信号；αi为N×1维的信号，是各级分信号在稀疏基Ψ下的稀疏表示，αr为N×1维的信号，是残差信号在稀疏基Ψ下的稀疏表示。In the formula, X is the N×1-dimensional original signal, Ψ is the N×N-dimensional sparse basis, α is the N×1-dimensional signal, which is the sparse representation of the original signal under the sparse basis Ψ, and r is the N×1-dimensional residual Residual; Xi represents the i-th sub-signal obtained by decomposition; αi is the N×1-dimensional signal, which is the sparse representation of each sub-signal under the sparse basis Ψ, and αr is the N×1-dimensional signal, which is A sparse representation of the residual signal in a sparse basis Ψ.
本发明采用自适应阈值法定义每一级分信号中αi元素的取值范围：The present invention adopts the adaptive threshold method to define the value range of the αi element in each fractional signal:
σ·max(αr)≤αi(n)≤max(αr) (2)σ·max(αr )≤αi (n)≤max(αr ) (2)
分量系数σ根据实际情况确定，取值为0-1之间的小数；式(2)表示第i级分信号中αi元素的取值范围是当前残差(即分解得到第i-1级分信号后得到的残差)的αr元素中取值σ·max(αr)到max(αr)的值。The component coefficient σ is determined according to the actual situation, and the value is a decimal between 0-1; formula (2) indicates that the value range of the αi element in the i-th level signal is the current residual (that is, the i-1 level is obtained by decomposition In the αr element of the residual obtained after dividing the signal, the value σ·max(αr ) to max(αr ) is taken.
如图2所示，具体信号的分解步骤如下：As shown in Figure 2, the specific signal decomposition steps are as follows:
步骤1)、首先将原始信号进行稀疏转换，计算原始信号的稀疏表示α。Step 1): First, the original signal is sparsely transformed, and the sparse representation α of the original signal is calculated.
步骤2)、初始化残差信号的稀疏表示αr＝α，分解级数为i＝1。Step 2), initialize the sparse representation of the residual signal αr =α, and the decomposition level is i=1.
步骤3)、计算第i级分信号的稀疏表示αi，具体为：Step 3), calculate the sparse representation αi of the i-th grade signal, specifically:
针对残差αr中的每个元素，判断元素值是否大于或等于σmax(αr)：For each element in the residual αr , determine whether the element value is greater than or equal to σmax(αr ):
如果是，将该元素值赋值给当前级分信号对应位置，即αi(j)＝αr(j)；再将残差αr中的该元素的值置为0，即α'r(j)＝0；If yes, assign the element value to the corresponding position of the current fractional signal, that is, αi (j)=αr (j); then set the value of this element in the residual αr to 0, that is, α'r ( j)=0;
如果否，将当前级分信号与该元素对应位置的值置为0；If not, set the value of the current fraction signal and the corresponding position of the element to 0;
遍历残差αr中的所有元素后，得到当前级分信号各元素值，以及更新后的残差αr；获得当前级分信号的稀疏度Ki；After traversing all elements in the residual αr , obtain the value of each element of the current fractional signal, and the updated residual αr ; obtain the sparsity Ki of the current fractional signal;
步骤4)、利用当前残差，按照步骤3)的方法分解得到下一级分信号；以此类推，直至分解级数达到设定阈值n或者残差信号的p范数小于设定阈值。Step 4), using the current residual, decompose to obtain the next fractional signal according to the method of step 3); and so on, until the decomposition level reaches the set threshold n or the p-norm of the residual signal is less than the set threshold.
原始信号稀疏变换和分级后，原始信号被分解为各级的信号稀疏表示α1,α2,α3…αn。按该方法分解的信号，其主信号包含在前几级的信号中，而次要信号则级数较为靠后，而白噪声信号等噪声信号一般被分解至剩余残差中消除。After the original signal is sparsely transformed and graded, the original signal is decomposed into signal sparse representations of various levels α1 , α2 , α3 . . . αn . The main signal of the signal decomposed by this method is included in the signals of the previous stages, while the secondary signal is in the later stage, and the noise signal such as white noise signal is generally decomposed into the residual residual to eliminate.
步骤二，信号逐级编码压缩：Step 2, signal coding and compression step by step:
本发明选用伯努利随机矩阵作为信号编码的测量矩阵，测量矩阵为一个与稀疏基不相关的矩阵；利用测量矩阵对信号进行编码压缩过程如式(3)The present invention selects Bernoulli random matrix as the measurement matrix of signal coding, and the measurement matrix is a matrix irrelevant to the sparse basis; the process of encoding and compressing the signal by the measurement matrix is as shown in formula (3)
yi＝Φi⊙αi (3)yi =Φi ⊙αi (3)
式中αi表示第i级分信号的稀疏表示，Φi是第i级分信号对应的测量矩阵；y1,y2,y3…yn是压缩后的各级分信号，大小为Mi×1维；行数Mi的取值与该级分信号的稀疏度相等，稀疏度越小，行数Mi的值就可以取的越小，压缩的效果就越好。但是行数不能无限制的减少，一般来说，需要大于某一下限。where αi represents the sparse representation of the i-th sub-signal, Φi is the measurement matrix corresponding to the i-th sub-signal; y1 , y2 , y3 ......i ×1 dimension; the value of the number of rows Mi is equal to the sparsity of the fractional signal. The smaller the sparsity is, the smaller the value of the number of rows Mi can be, and the better the compression effect is. However, the number of rows cannot be reduced indefinitely. Generally speaking, it needs to be larger than a certain lower limit.
伯努利随机矩阵的行数满足下式才能较好的还原原始信号，The number of rows of the Bernoulli random matrix satisfies the following formula to restore the original signal better,
M≥cKlog(N/K) (4)M≥cKlog(N/K) (4)
其中c值根据信号的先验知识确定，一般取3；K值是该信号的稀疏度。The c value is determined according to the prior knowledge of the signal, and generally takes 3; the K value is the sparsity of the signal.
各级分信号的稀疏度(K)是不相同的，往往级数越低的分信号越稀疏，测量矩阵所需的行数越小。若为每级分信号单独定义测量矩阵，容易造成硬件资源的浪费。本发明中，为了不保存多余的测量矩阵，随机生成一个M×N维的伯努利随机矩阵，作为总的测量矩阵Φ；其中，M的取值由最后一级分信号(设为第n级)的稀疏度Kn决定。The sparsity (K) of each sub-signal is different, and the sub-signal with a lower series is often more sparse, and the number of rows required for the measurement matrix is smaller. If the measurement matrix is defined separately for each level of signal, it is easy to cause waste of hardware resources. In the present invention, in order not to save redundant measurement matrices, an M×N-dimensional Bernoulli random matrix is randomly generated as the total measurement matrix Φ; wherein, the value of M is determined by the last stage signal (set as the nth level) is determined by the sparsity Kn .
该测量矩阵Φ是一个足够大的伯努利随机矩阵。每一级分信号的测量矩阵作为该测量矩阵的子矩阵，其矩阵的列数与总测量矩阵相同，而行数则是根据各级分信号所需行数Mi，从总测量矩阵Φ第一行起到第Mi行止，进行选取。The measurement matrix Φ is a sufficiently large Bernoulli random matrix. The measurement matrix of each fractional signal is used as a sub-matrix of the measurement matrix, and the number of columns of the matrix is the same as that of the total measurement matrix, and the number of rows is based on the number of rows Mi required for each fractional signal, from the total measurement matrix Φ. One line to theMith line ends, select.
步骤三，对完成编码的各级分信号，从第一级开始进行传输，在单个分信号的编码数据yi传输完成后，便可以对原始信号进行重构并输出，具体为：In step 3, the encoded sub-signals are transmitted from the first stage, and after the encoded datayi of a single sub-signal is transmitted, the original signal can be reconstructed and output, specifically:
对于接收的第i级分信号的编码数据yi(MiX1维数据)，确定该级分信号的维度，即该级分信号对应的测量矩阵的行数Mi；从测量矩阵Φ中选择前Mi行数据，即得到测量矩阵Φi。将编码数据yi和测量矩阵Φi输入OMP重构算法，输出还原信号的稀疏表示α′i。For the coded datayi (Mi×1 dimension data) of the received i-th fractional signal, determine the dimension of the fractional signal, that is, the number of rows Mi of the measurement matrix corresponding to the fractional signal; select the first M from the measurement matrix Φi rows of data, that is, the measurement matrix Φi is obtained. The encoded datayi and the measurement matrix Φi are input into the OMP reconstruction algorithm, and the sparse representation α′i of the restored signal is output.
随着重构完成的分信号越多，级数越高，原始信号的细节信息越多，失真越小。这种逐级重构的方式有别于传统的信号重构，不用接收完成所有压缩编码信息便可进行重构信号的输出。其逐级重构过程如图3所示。网络中首先传输级数低的分信号编码，因此首先重构出来的是稀疏向量系数最大的分信号，而后不断的累加级数较高的分信号，实现细节的修正；设完成第j级分信号的重构，则原始信号重构如式(5)：As more sub-signals are reconstructed, the higher the number of stages, the more detailed information of the original signal, and the smaller the distortion. This step-by-step reconstruction method is different from the traditional signal reconstruction, and the output of the reconstructed signal can be carried out without receiving all the compressed and encoded information. The step-by-step reconstruction process is shown in Figure 3. In the network, the sub-signal encoding with the low level is first transmitted, so the sub-signal with the largest sparse vector coefficient is reconstructed first, and then the sub-signal with a higher level is continuously accumulated to realize the correction of details; The reconstruction of the signal, the original signal reconstruction is as formula (5):
综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
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