CN109817229B - Single-bit audio compression transmission and reconstruction method assisted by superposition characteristic information - Google Patents

Single-bit audio compression transmission and reconstruction method assisted by superposition characteristic information Download PDF

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CN109817229B
CN109817229B CN201910193583.7A CN201910193583A CN109817229B CN 109817229 B CN109817229 B CN 109817229B CN 201910193583 A CN201910193583 A CN 201910193583A CN 109817229 B CN109817229 B CN 109817229B
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卿朝进
万东琴
阳庆瑶
蔡斌
郭奕
张岷涛
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Xihua University
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Abstract

本发明公开了叠加特征信息辅助的单比特音频压缩传输与重构方法，步骤S1：对稀疏的音频信号进行特征处理，得到特征信息；步骤S2：对特征信息进行扩频处理，得到扩频特征向量；步骤S3：对稀疏的音频信号进行单比特压缩处理，得到1‑bit压缩信号；步骤S4：将扩频特征向量和1‑bit压缩信号进行加权叠加处理，得到发送信号；步骤S5：将发送信号发送出去，在接收端对发送信号接收，接收信号为带噪信号；步骤S6：对带噪信号进行恢复处理，得到恢复特征信息和恢复1‑bit压缩信息；步骤S7：利用恢复特征信息辅助重构算法，重构出稀疏音频信号，解决了在不增加传输系统频谱资源的情况下，有效提高单比特音频信号的重构精度。

Figure 201910193583

The invention discloses a single-bit audio compression transmission and reconstruction method assisted by superimposed feature information. Step S1: perform feature processing on sparse audio signals to obtain feature information; step S2: perform spectrum spread processing on the feature information to obtain spectrum spread features vector; Step S3: perform single-bit compression processing on the sparse audio signal to obtain a 1-bit compressed signal; Step S4: perform weighted superposition processing on the spread spectrum eigenvector and the 1-bit compressed signal to obtain a transmission signal; Step S5: add The transmission signal is sent out, and the transmission signal is received at the receiving end, and the received signal is a signal with noise; Step S6: recovering the signal with noise to obtain recovery feature information and recovery 1-bit compression information; Step S7: use the recovery feature information The auxiliary reconstruction algorithm reconstructs the sparse audio signal, and solves the problem of effectively improving the reconstruction accuracy of the single-bit audio signal without increasing the spectral resources of the transmission system.

Figure 201910193583

Description

叠加特征信息辅助的单比特音频压缩传输与重构方法A single-bit audio compression transmission and reconstruction method assisted by superimposed feature information

技术领域technical field

本发明涉及音频压缩传输与重构领域，特别是叠加特征信息辅助的单比特音频压缩传输与重构方法。The invention relates to the field of audio compression transmission and reconstruction, in particular to a single-bit audio compression transmission and reconstruction method assisted by superimposed feature information.

背景技术Background technique

压缩感知(Compressed sensing,CS)技术已广泛应用于音频信号处理领域，并已取得实质性进展。然而在实践中，对压缩信号编码前是需要对其量化的。为缓解AD转换器硬件压力，提升数据存储效率以及数据传输速率，进一步将单比特压缩感知应用于音频信号处理。Compressed sensing (CS) technology has been widely used in the field of audio signal processing and has made substantial progress. In practice, however, the compressed signal needs to be quantized before being encoded. In order to relieve the hardware pressure of the AD converter and improve the data storage efficiency and data transmission rate, single-bit compressed sensing is further applied to audio signal processing.

然而，现有的单比特压缩感知重构算法诸如固定点连续FPC(Fixed PointContinuation,FPC)算法、符号匹配追踪(Matching Sign Pursuit,MSP)算法、限制步长收敛(Restricted Step Shrinkage,RSS)算法、二进制迭代硬阈值(Binary Iterative HardThresholding,BIHT)算法，均不是专门针对稀疏音频信号的单比特重构而提出的，继而没有考虑音频信号的特殊性，未充分利用稀疏音频信号的非零元素位置索引，使稀疏音频信号的重构精度受到限制。However, existing single-bit compressive sensing reconstruction algorithms such as Fixed Point Continuation (FPC) algorithm, Matching Sign Pursuit (MSP) algorithm, Restricted Step Shrinkage (RSS) algorithm, Binary Iterative Hard Thresholding (BIHT) algorithms are not specially proposed for single-bit reconstruction of sparse audio signals, and then do not consider the particularity of audio signals, and do not fully utilize the non-zero element position index of sparse audio signals , which limits the reconstruction accuracy of sparse audio signals.

虽然现有研究提出利用信号的支撑集信息辅助单比特量化信号的重构，可进一步改善单比特压缩信号的重构性能。但是在传统的单比特压缩音频信号的传输过程，音频信号的支撑集信息的传输将会占用一定的频谱资源，增加传输成本。因此，需要一种有效的方法来缓解频谱资源和重构精度之间的矛盾。Although the existing research proposes to use the support set information of the signal to assist the reconstruction of the single-bit quantized signal, the reconstruction performance of the single-bit compressed signal can be further improved. However, in the traditional single-bit compressed audio signal transmission process, the transmission of the support set information of the audio signal will occupy a certain spectrum resource and increase the transmission cost. Therefore, an effective method is needed to alleviate the contradiction between spectrum resources and reconstruction accuracy.

发明内容SUMMARY OF THE INVENTION

为解决现有技术中存在的问题，本发明提供了叠加特征信息辅助的单比特音频压缩传输与重构方法，解决了在传统的单比特压缩音频信号的传输过程，音频信号的支撑集信息的传输将会占用一定的频谱资源，增加传输成本的问题，并有效改善音频信号的重构精度。In order to solve the problems existing in the prior art, the present invention provides a single-bit audio compression transmission and reconstruction method assisted by superimposed feature information, which solves the problem of the traditional single-bit compressed audio signal transmission process, the support set information of the audio signal. Transmission will occupy certain spectrum resources, increase the problem of transmission cost, and effectively improve the reconstruction accuracy of audio signals.

本发明采用的技术方案是：叠加特征信息辅助的单比特音频压缩传输与重构方法，方法包括如下步骤：The technical scheme adopted by the present invention is: a single-bit audio compression transmission and reconstruction method assisted by superimposed feature information, the method comprises the following steps:

步骤S1：对稀疏的音频信号进行特征处理，得到特征信息；Step S1: perform feature processing on the sparse audio signal to obtain feature information;

步骤S2：对特征信息进行扩频处理，得到扩频特征向量；Step S2: performing spread spectrum processing on the feature information to obtain a spread spectrum feature vector;

步骤S3：对稀疏的音频信号进行单比特压缩处理，得到1-bit压缩信号；Step S3: performing single-bit compression processing on the sparse audio signal to obtain a 1-bit compressed signal;

步骤S4：将扩频特征向量和1-bit压缩信号进行加权叠加处理，得到发送信号；Step S4: performing weighted superposition processing on the spread spectrum eigenvector and the 1-bit compressed signal to obtain a transmitted signal;

步骤S5：将发送信号发送出去，在接收端对发送信号接收，接收信号为带噪信号；Step S5: sending the transmitted signal, receiving the transmitted signal at the receiving end, and the received signal is a noisy signal;

步骤S6：对带噪信号进行恢复处理，得到恢复特征信息和恢复1-bit压缩信息；Step S6: recovering the noisy signal to obtain recovered feature information and recovered 1-bit compression information;

步骤S7：利用恢复特征信息辅助重构算法，重构出稀疏音频信号。Step S7: Reconstruct the sparse audio signal by using the restored feature information to assist the reconstruction algorithm.

优选地，步骤S1包括如下子步骤：Preferably, step S1 includes the following sub-steps:

步骤S11：设定稀疏音频信号x的稀疏度为K，长度为N；Step S11: set the sparsity of the sparse audio signal x as K and the length as N;

步骤S12：提取稀疏音频信号x的非零元素的位置索引，得到长度为K的支撑集合Ω；Step S12: extracting the position index of the non-zero element of the sparse audio signal x to obtain a support set Ω of length K;

步骤S13：在长度为K的支撑集合Ω中，找出稀疏音频信号x的前L1个幅度值最大元素的位置索引，得到长度为L2的部分支撑集合

Figure BDA0001995087620000021
其中，0≤L1≤K,L2＝L1；Step S13: In the support set Ω of length K, find the position index of the first L 1 elements with the largest amplitude value of the sparse audio signal x, and obtain a partial support set of length L 2
Figure BDA0001995087620000021
Wherein, 0≤L 1 ≤K, L 2 =L 1 ;

步骤S14：对长度为L2的部分支撑集合

Figure BDA0001995087620000022
进行编码调制，得到长度为L3的元素为1或-1的特征信息h，其中，L3＜M；Step S14: Partial support set with length L 2
Figure BDA0001995087620000022
Code modulation is performed to obtain feature information h with an element of length L 3 being 1 or -1, where L 3 <M;

步骤S14的编码调制为The code modulation of step S14 is

步骤S141：将长度为l的部分支撑集合

Figure BDA0001995087620000023
中的十进制数转化为r位的二进制数，转化后生成序列的长度为L，且L＝rl；Step S141: Assemble the partial supports of length l
Figure BDA0001995087620000023
The decimal number in is converted into a binary number of r bits, and the length of the generated sequence after conversion is L, and L=rl;

步骤S142：将序列中的元素“1”映射为“1”，将元素“0”映射为元素“-1”。Step S142: Map the element "1" in the sequence to "1", and map the element "0" to the element "-1".

优选地，步骤S3的单比特压缩处理的表达式为：Preferably, the expression of the single-bit compression process in step S3 is:

y＝sign(Φx)y=sign(Φx)

式中，y表示长度为M的1-bit压缩信号，Φ表示预先存储的M×N的测量矩阵Φ，x表示长度为N的稀疏音频信号。In the formula, y represents a 1-bit compressed signal of length M, Φ represents a pre-stored M×N measurement matrix Φ, and x represents a sparse audio signal of length N.

优选地，步骤S4包括如下子步骤：Preferably, step S4 includes the following sub-steps:

步骤S41：将长度为M的扩频特征信息H赋予权值为

Figure BDA0001995087620000031
将长度为M的1-bit压缩信号y赋予权值为
Figure BDA0001995087620000032
α为加权系数且满足0＜α＜1，Es为发送信号的能量；Step S41: assigning the weighted value of the spread spectrum feature information H of length M as
Figure BDA0001995087620000031
The 1-bit compressed signal y of length M is given the weight as
Figure BDA0001995087620000032
α is a weighting coefficient and satisfies 0<α<1, and E s is the energy of the transmitted signal;

步骤S42：将特征信息和1-bit压缩信号进行加权叠加处理，加权叠加处理的公式为Step S42: Perform weighted superposition processing on the feature information and the 1-bit compressed signal, and the formula for the weighted superposition processing is:

Figure BDA0001995087620000033
Figure BDA0001995087620000033

式中，H表示长度为M的扩频特征信息，y表示长度为M的1-bit压缩信号，z表示长度为M的发送信号，α为加权系数且满足0＜α＜1，Es为发送信号的能量。In the formula, H represents the spread spectrum feature information of length M, y represents the 1-bit compressed signal of length M, z represents the transmitted signal of length M, α is the weighting coefficient and satisfies 0<α<1, E s is The energy of the transmitted signal.

优选地，步骤S6包括如下子步骤：Preferably, step S6 includes the following sub-steps:

步骤S61：对发送信号进行解扩处理，所述解扩处理的表达式为Step S61: Perform despreading processing on the transmitted signal, and the expression of the despreading processing is:

Figure BDA0001995087620000034
Figure BDA0001995087620000034

式中，

Figure BDA0001995087620000035
表示长度为M的带噪信号，
Figure BDA0001995087620000036
式中，n为长度为M的噪声信号，Ph为解扩特征信息，QT为扩频矩阵Q的转置；In the formula,
Figure BDA0001995087620000035
represents a noisy signal of length M,
Figure BDA0001995087620000036
In the formula, n is the noise signal of length M, P h is the despreading feature information, and Q T is the transpose of the spreading matrix Q;

步骤S62：将解扩特征信息Ph进行硬判决操作，得到恢复特征信息

Figure BDA0001995087620000037
Step S62: Perform a hard decision operation on the despreading feature information P h to obtain restored feature information
Figure BDA0001995087620000037

步骤S63：将恢复特征信息

Figure BDA0001995087620000041
进行扩频处理，得到长度为M的恢复扩频特征信息
Figure BDA0001995087620000042
Step S63: feature information will be restored
Figure BDA0001995087620000041
Perform spread spectrum processing to obtain recovered spread spectrum feature information of length M
Figure BDA0001995087620000042

步骤S64：利用长度同为M的带噪信号

Figure BDA0001995087620000043
和恢复扩频特征信息
Figure BDA0001995087620000044
计算长度为M的解扩压缩信号Py，Step S64: Use the noisy signal with the same length as M
Figure BDA0001995087620000043
and recover the spread spectrum characteristic information
Figure BDA0001995087620000044
Calculate the despread compressed signal P y of length M,

Figure BDA0001995087620000045
Figure BDA0001995087620000045

步骤S65：将长度为M的解扩压缩信号Py进行硬判决操作，得到长度为M的1-bit压缩信号

Figure BDA0001995087620000046
Step S65: Perform a hard decision operation on the despreading and compressed signal Py with a length of M to obtain a 1-bit compressed signal with a length of M
Figure BDA0001995087620000046

优选地，步骤S2和步骤S63的扩频处理的表达式为：Preferably, the expression of the spread spectrum processing in step S2 and step S63 is:

H＝QhH=Qh

式中，Q为扩频矩阵大小为M×L且QTQ＝MIL，其中，L＜M，IL为L×L的单位矩阵，h为特征信息，H为扩频特征向量。In the formula, Q is the size of the spreading matrix M×L and Q T Q=MI L , where L<M, IL is the L×L unit matrix, h is the feature information, and H is the spreading feature vector.

优选地，步骤S62和步骤S65的硬判决处理的公式为Preferably, the formula of hard decision processing in step S62 and step S65 is:

Figure BDA0001995087620000047
Figure BDA0001995087620000047

式中，

Figure BDA0001995087620000048
为硬判决处理后的信号，长度为L3，Ph为解扩特征信息，长度为L3。In the formula,
Figure BDA0001995087620000048
is the signal after hard decision processing, the length is L 3 , and Ph is the despreading feature information, and the length is L 3 .

优选地，步骤S7包括如下步骤：Preferably, step S7 includes the following steps:

步骤S71：对恢复特征信息

Figure BDA0001995087620000049
进行解调解码处理，得到恢复部分支撑集合
Figure BDA00019950876200000410
Step S71: restore feature information
Figure BDA0001995087620000049
Perform demodulation and decoding processing to obtain the restored partial support set
Figure BDA00019950876200000410

步骤S72:利用恢复部分支撑集合

Figure BDA00019950876200000411
辅助，并结合重构算法，从长度为M的恢复1-bit压缩信号
Figure BDA00019950876200000412
中重构出长度为N的稀疏音频信号
Figure BDA00019950876200000413
Step S72: use the recovery part to support the set
Figure BDA00019950876200000411
Auxiliary, combined with reconstruction algorithm, recover 1-bit compressed signal from length M
Figure BDA00019950876200000412
A sparse audio signal of length N is reconstructed in
Figure BDA00019950876200000413

优选地，步骤S71的解码解调为Preferably, the decoding and demodulation of step S71 is

步骤S711：将长度为L的恢复特征信息

Figure BDA0001995087620000051
中的元素“1”映射为“1”，将元素“-1”映射为“0”；Step S711: restore the feature information whose length is L
Figure BDA0001995087620000051
The element "1" in is mapped to "1" and the element "-1" is mapped to "0";

步骤S712：将长度为L的序列中的每r个二进制数转化为一个十进制数，得到长度为l的恢复部分支撑集合

Figure BDA0001995087620000052
且L＝rl；Step S712: Convert every r binary numbers in the sequence of length L into a decimal number to obtain a restored partial support set of length l
Figure BDA0001995087620000052
and L=rl;

优选地，步骤S72的重构算法包括如下步骤：Preferably, the reconstruction algorithm of step S72 includes the following steps:

步骤S721：输入恢复1-bit压缩信号

Figure BDA0001995087620000053
测量矩阵Φ∈RM×N，稀疏度K，恢复部分支撑集
Figure BDA0001995087620000054
0＜l≤K，最大迭代次数iternum；Step S721: input and restore the 1-bit compressed signal
Figure BDA0001995087620000053
Measurement matrix Φ∈R M×N , sparsity K, recover partial support set
Figure BDA0001995087620000054
0<l≤K, the maximum number of iterations iternum;

步骤S722：初始化残差矢量x0＝ON×1，迭代次数t＝0；Step S722: Initialize the residual vector x 0 =ON ×1 , and the number of iterations t=0;

步骤S723：根据x、Φ、

Figure BDA0001995087620000055
和梯度计算公式
Figure BDA0001995087620000056
计算出βt+1；Step S723: According to x, Φ,
Figure BDA0001995087620000055
and gradient calculation formula
Figure BDA0001995087620000056
Calculate β t+1 ;

步骤S724：根据βt+1和硬阈值映射公式xt+1＝η(βt+1)，计算出xt+1；Step S724: Calculate x t+1 according to β t+1 and the hard threshold mapping formula x t+1 = η(β t+1 );

步骤S725：根据xt+1、βt+1、

Figure BDA0001995087620000057
和支撑集映射公式
Figure BDA0001995087620000058
计算出xt+1；Step S725: According to x t+1 , β t+1 ,
Figure BDA0001995087620000057
and support set mapping formula
Figure BDA0001995087620000058
Calculate x t+1 ;

式中，ξ(·)是支撑集映射操作符号，将集合

Figure BDA0001995087620000059
在矢量βt+1中索引的元素幅值赋给集合
Figure BDA00019950876200000510
在xt+1中的索引所在位置；In the formula, ξ( ) is the support set mapping operation symbol, and the set
Figure BDA0001995087620000059
The magnitude of the element indexed in the vector β t+1 is assigned to the set
Figure BDA00019950876200000510
the position of the index in x t+1 ;

步骤S726：计算非零元素的个数

Figure BDA00019950876200000511
令t＝t+1；Step S726: Calculate the number of non-zero elements
Figure BDA00019950876200000511
Let t=t+1;

其中，符号||·||0表示求向量的算子0范数Among them, the symbol ||·|| 0 means to find the operator 0 norm of the vector

步骤S727：判断若t＜iternum且nnz＞0，若是，返回步骤S723；若否，则进入步骤S728；Step S727: Determine if t<iternum and nnz>0, if yes, go back to Step S723; if not, go to Step S728;

步骤S728：根据计算出的xt+1再计算出xt+1＝U(Xt+1)，Step S728: Calculate x t+1 =U(X t+1 ) according to the calculated x t +1,

式中，U(v)＝v/||v||2，符号||·||2表示求向量的算子2范数；In the formula, U(v)=v/||v|| 2 , and the symbol ||·|| 2 represents the operator 2-norm of the vector;

步骤S729：根据xt+1，计算出稀疏音频信号

Figure BDA00019950876200000512
Step S729: Calculate the sparse audio signal according to x t+1
Figure BDA00019950876200000512

本发明叠加特征信息辅助的单比特音频压缩传输与重构方法的有益效果如下：The beneficial effects of the single-bit audio compression transmission and reconstruction method assisted by superimposing feature information of the present invention are as follows:

相比于传统的单比特压缩感知语音压缩，本发明考虑音频信号的特殊性，利用稀疏音频信号的非零元素的部分位置索引辅助重构，在不增加频谱开销的情况下，改善音频信号的重构精度。Compared with the traditional single-bit compressed sensing speech compression, the present invention considers the particularity of the audio signal, uses the partial position index of the non-zero element of the sparse audio signal to assist reconstruction, and improves the audio signal quality without increasing the spectrum overhead. Reconstruction accuracy.

附图说明Description of drawings

图1为本发明叠加特征信息辅助的单比特音频压缩传输与重构方法的流程图。FIG. 1 is a flow chart of the method for single-bit audio compression, transmission and reconstruction assisted by superimposed feature information according to the present invention.

具体实施方式Detailed ways

下面结合附图对本发明的实施例进行详细说明。The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

下面对本发明的具体实施方式进行描述，以便于本技术领域的技术人员理解本发明，但应该清楚，本发明不限于具体实施方式的范围，对本技术领域的普通技术人员来讲，只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内，这些变化是显而易见的，一切利用本发明构思的发明创造均在保护之列。The specific embodiments of the present invention are described below to facilitate those skilled in the art to understand the present invention, but it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes Such changes are obvious within the spirit and scope of the present invention as defined and determined by the appended claims, and all inventions and creations utilizing the inventive concept are within the scope of protection.

如图1所示，叠加特征信息辅助的单比特音频压缩传输与重构方法，方法包括如下步骤：As shown in Figure 1, the single-bit audio compression transmission and reconstruction method assisted by superimposed feature information, the method includes the following steps:

步骤S1：对稀疏的音频信号进行特征处理，得到特征信息；Step S1: perform feature processing on the sparse audio signal to obtain feature information;

步骤S2：对特征信息进行扩频处理，得到扩频特征向量；Step S2: performing spread spectrum processing on the feature information to obtain a spread spectrum feature vector;

步骤S3：对稀疏的音频信号进行单比特压缩处理，得到1-bit压缩信号；Step S3: performing single-bit compression processing on the sparse audio signal to obtain a 1-bit compressed signal;

步骤S4：将扩频特征向量和1-bit压缩信号进行加权叠加处理，得到发送信号；Step S4: performing weighted superposition processing on the spread spectrum eigenvector and the 1-bit compressed signal to obtain a transmitted signal;

步骤S5：将发送信号发送出去，在接收端对发送信号进行接收，接收信号为带噪信号；Step S5: sending the transmitted signal, receiving the transmitted signal at the receiving end, and the received signal is a noisy signal;

步骤S6：对带噪信号进行恢复处理，得到恢复特征信息和恢复1-bit压缩信息；Step S6: recovering the noisy signal to obtain recovered feature information and recovered 1-bit compression information;

步骤S7：利用恢复特征信息辅助重构算法，重构出稀疏音频信号。Step S7: Reconstruct the sparse audio signal by using the restored feature information to assist the reconstruction algorithm.

本实施方案的步骤S1包括如下子步骤：Step S1 of this embodiment includes the following sub-steps:

步骤S11：设定稀疏音频信号x的稀疏度为K，长度为N；Step S11: set the sparsity of the sparse audio signal x as K and the length as N;

步骤S12：提取稀疏音频信号x的非零元素的位置索引，得到长度为K的支撑集合Ω；Step S12: extracting the position index of the non-zero element of the sparse audio signal x to obtain a support set Ω of length K;

步骤S13：在长度为K的支撑集合Ω中，找出稀疏音频信号x的前L1个幅度值最大的位置索引，得到长度为L2的部分支撑集合

Figure BDA0001995087620000071
其中，0＜L1≤K,L2＝L1；Step S13: In the support set Ω of length K, find out the first L 1 position indices with the largest amplitude values of the sparse audio signal x, and obtain a partial support set of length L 2
Figure BDA0001995087620000071
Wherein, 0<L 1 ≤K, L 2 =L 1 ;

步骤S14：对长度为L2的部分支撑集合

Figure BDA0001995087620000072
进行编码调制，得到长度为L3的特征信息h，其中，L3＜M。Step S14: Partial support set with length L 2
Figure BDA0001995087620000072
Code modulation is performed to obtain feature information h of length L 3 , where L 3 <M.

本实施方案的步骤S1的稀疏音频信号是指离散音频信号经过时频变换方法从时域信号变换为频域信号，并根据掩蔽效应将低于掩蔽门限的信号幅度置为零，得到的稀疏音频信号。The sparse audio signal in step S1 of this embodiment refers to the sparse audio signal obtained by transforming the discrete audio signal from a time-domain signal into a frequency-domain signal through a time-frequency transform method, and setting the amplitude of the signal below the masking threshold to zero according to the masking effect. Signal.

本实施方案的L1根据工程经验设定，且满足0＜L1≤K；L 1 of this embodiment is set according to engineering experience, and satisfies 0<L 1 ≤K;

在本申请的实施例中，设：In the embodiments of this application, it is assumed that:

x＝[0,0,0,3.75,0,0,0,0,-2.67,0,0,0,0,0,-5.12,0,0,0,0,4.89,0,0,0,1.56,0,0,0,0]，可得：x=[0,0,0,3.75,0,0,0,0,-2.67,0,0,0,0,0,-5.12,0,0,0,0,4.89,0,0,0 ,1.56,0,0,0,0], we get:

稀疏度K＝5，支撑集合Ω＝{4,9,15,20,24}；Sparsity K=5, support set Ω={4, 9, 15, 20, 24};

设L1＝3，则x的前L1＝3个幅度值最大非零元素为{-5.12,4.89,3.75}，其对应的位置索引为{15,20,4}，因此构成的部分支撑集合

Figure BDA0001995087620000073
长度L2＝L1＝3；Set L 1 =3, then the first L 1 =3 maximum non-zero elements of amplitude value of x are {-5.12, 4.89, 3.75}, and the corresponding position index is {15, 20, 4}, so the partial support formed gather
Figure BDA0001995087620000073
length L 2 =L 1 =3;

步骤S14：对长度为L2的部分支撑集合

Figure BDA0001995087620000074
进行编码调制，得到长度为L3的特征信息h，其中，L3＜M。Step S14: Partial support set with length L 2
Figure BDA0001995087620000074
Code modulation is performed to obtain feature information h of length L 3 , where L 3 <M.

本实施方案的步骤S3的单比特压缩处理的表达式为：The expression of the single-bit compression process in step S3 of this embodiment is:

y＝sign(Φx)y=sign(Φx)

式中，y表示长度为M的1-bit压缩信号，Φ表示预先存储的M×N的测量矩阵Φ，x表示长度为N的稀疏音频信号。。In the formula, y represents a 1-bit compressed signal of length M, Φ represents a pre-stored M×N measurement matrix Φ, and x represents a sparse audio signal of length N. .

其中，本实施方案的sign(·)表示{1,-1}符号函数，即将大于0的数置为1，其余数置为-1。Wherein, sign(·) in this embodiment represents the {1,-1} sign function, that is, the number greater than 0 is set as 1, and the remaining number is set as -1.

本实施方案的步骤S4包括如下子步骤：Step S4 of this embodiment includes the following sub-steps:

步骤S41：长度为M的扩频特征信息H赋予权值为

Figure BDA0001995087620000081
将长度为M的1-bit压缩信号y赋予权值为
Figure BDA0001995087620000082
α为加权系数且满足0＜α＜1，Es为发送信号的能量；Step S41: The spread spectrum feature information H with a length of M is given a weight of
Figure BDA0001995087620000081
The 1-bit compressed signal y of length M is given the weight as
Figure BDA0001995087620000082
α is a weighting coefficient and satisfies 0<α<1, and E s is the energy of the transmitted signal;

步骤S42：将特征信息和1-bit压缩信号进行加权叠加处理，加权叠加处理的公式为

Figure BDA0001995087620000083
式中，H表示长度为M的扩频特征信息，y表示长度为M的1-bit压缩信号，z表示长度为M的发送信号，α为加权系数且满足0＜α＜1，Es为发送信号的能量。Step S42: Perform weighted superposition processing on the feature information and the 1-bit compressed signal, and the formula for the weighted superposition processing is:
Figure BDA0001995087620000083
In the formula, H represents the spread spectrum feature information of length M, y represents the 1-bit compressed signal of length M, z represents the transmitted signal of length M, α is the weighting coefficient and satisfies 0<α<1, E s is The energy of the transmitted signal.

本实施方案的步骤S6包括如下子步骤：Step S6 of this embodiment includes the following sub-steps:

步骤S61：对发送信号进行解扩处理，所述解扩处理的表达式为Step S61: Perform despreading processing on the transmitted signal, and the expression of the despreading processing is:

Figure BDA0001995087620000084
Figure BDA0001995087620000084

式中，

Figure BDA0001995087620000085
表示长度为M的带噪信号，
Figure BDA0001995087620000086
式中，n为长度为M的噪声信号，Ph为解扩特征信息，QT为扩频矩阵Q的转置；In the formula,
Figure BDA0001995087620000085
represents a noisy signal of length M,
Figure BDA0001995087620000086
In the formula, n is the noise signal of length M, P h is the despreading feature information, and Q T is the transpose of the spreading matrix Q;

步骤S62：将解扩特征信息Ph进行硬判决操作，得到恢复特征信息

Figure BDA0001995087620000087
Step S62: Perform a hard decision operation on the despreading feature information P h to obtain restored feature information
Figure BDA0001995087620000087

步骤S63：将恢复特征信息

Figure BDA0001995087620000088
进行扩频处理，得到长度为M的恢复扩频特征信息
Figure BDA0001995087620000089
Step S63: feature information will be restored
Figure BDA0001995087620000088
Perform spread spectrum processing to obtain recovered spread spectrum feature information of length M
Figure BDA0001995087620000089

步骤S64：利用长度同为M的带噪信号

Figure BDA0001995087620000091
和恢复扩频特征信息
Figure BDA0001995087620000092
计算长度为M的解扩压缩信号Py，Step S64: Use the noisy signal with the same length as M
Figure BDA0001995087620000091
and recover the spread spectrum characteristic information
Figure BDA0001995087620000092
Calculate the despread compressed signal P y of length M,

Figure BDA0001995087620000093
Figure BDA0001995087620000093

步骤S65：将长度为M的解扩压缩信号Py进行硬判决操作，得到长度为M的1-bit压缩信号

Figure BDA0001995087620000094
Step S65: Perform a hard decision operation on the despreading and compressed signal Py with a length of M to obtain a 1-bit compressed signal with a length of M
Figure BDA0001995087620000094

本实施方案中，步骤S2和步骤S63的扩频处理的表达式为：In this embodiment, the expressions of the spread spectrum processing in step S2 and step S63 are:

H＝QhH=Qh

式中，Q为扩频矩阵大小为M×L且QTQ＝MIL，其中，L＜M，IL为L×L的单位矩阵，h为特征信息，H为扩频特征向量。In the formula, Q is the size of the spreading matrix M×L and Q T Q=MI L , where L<M, IL is the L×L unit matrix, h is the feature information, and H is the spreading feature vector.

本实施方案中，步骤S62和步骤S65的硬判决处理的公式为In this embodiment, the formula of hard decision processing in step S62 and step S65 is:

Figure BDA0001995087620000095
Figure BDA0001995087620000095

式中，

Figure BDA0001995087620000096
为硬判决处理后的信号，长度为L3，Ph为解扩特征信息，长度为L3。In the formula,
Figure BDA0001995087620000096
is the signal after hard decision processing, the length is L 3 , and Ph is the despreading feature information, and the length is L 3 .

本实施方案的硬判决操作是将Ph中大于0的元素置为1，其余元素置为-1；The hard decision operation of this embodiment is to set the elements greater than 0 in P h to 1, and set the remaining elements to -1;

在本申请的实施例中，设：In the embodiments of this application, it is assumed that:

Ph＝[0.25,-0.36,1.58,-2.96,3.74,5.62,-0.02,1.23,0.85,-6.84]，对Ph进行硬判决操作，则得到恢复特征信息序列

Figure BDA0001995087620000097
P h =[0.25,-0.36,1.58,-2.96,3.74,5.62,-0.02,1.23,0.85,-6.84], perform a hard decision operation on P h , then get the recovered feature information sequence
Figure BDA0001995087620000097

本实施方案的步骤S7包括如下步骤：Step S7 of this embodiment includes the following steps:

步骤S71：对恢复特征信息

Figure BDA0001995087620000098
进行解调解码处理，得到恢复部分支撑集合
Figure BDA0001995087620000099
Step S71: restore feature information
Figure BDA0001995087620000098
Perform demodulation and decoding processing to obtain the restored partial support set
Figure BDA0001995087620000099

步骤S72:利用恢复部分支撑集合

Figure BDA0001995087620000101
辅助，并结合重构算法，从长度为M的恢复1-bit压缩信号
Figure BDA0001995087620000102
中重构出长度为N的稀疏音频信号
Figure BDA0001995087620000103
Step S72: use the recovery part to support the set
Figure BDA0001995087620000101
Auxiliary, combined with reconstruction algorithm, recover 1-bit compressed signal from length M
Figure BDA0001995087620000102
A sparse audio signal of length N is reconstructed in
Figure BDA0001995087620000103

本实施方案的步骤S14的编码调制为The code modulation in step S14 of this embodiment is:

步骤S141：将长度为l的部分支撑集合

Figure BDA0001995087620000104
中的十进制数转化为r位的二进制数，转化后生成序列的长度为L，且L＝rl；Step S141: Assemble the partial supports of length l
Figure BDA0001995087620000104
The decimal number in is converted into a binary number of r bits, and the length of the generated sequence after conversion is L, and L=rl;

步骤S142：将序列中的元素“1”映射为“1”，将元素“0”映射为元素“-1”。Step S142: Map the element "1" in the sequence to "1", and map the element "0" to the element "-1".

本实施方案的步骤S71的解码解调为The decoding and demodulation of step S71 in this embodiment is

步骤S711：将长度为L的恢复特征信息

Figure BDA0001995087620000105
中的元素“1”映射为“1”，将元素“-1”映射为“0”；Step S711: restore the feature information whose length is L
Figure BDA0001995087620000105
The element "1" in is mapped to "1" and the element "-1" is mapped to "0";

步骤S712：将长度为L的序列中的每r个二进制数转化为一个十进制数，得到长度为l的恢复部分支撑集合

Figure BDA0001995087620000106
且L＝rl；Step S712: Convert every r binary numbers in the sequence of length L into a decimal number to obtain a restored partial support set of length l
Figure BDA0001995087620000106
and L=rl;

本实施方案的步骤S72的重构算法包括如下步骤：The reconstruction algorithm in step S72 of this embodiment includes the following steps:

步骤S721：输入恢复1-bit压缩信号

Figure BDA0001995087620000107
测量矩阵Φ∈RM×N，稀疏度K，恢复部分支撑集合
Figure BDA0001995087620000108
最大迭代次数iternum；Step S721: input and restore the 1-bit compressed signal
Figure BDA0001995087620000107
Measurement matrix Φ∈R M×N , sparsity K, recover partial support set
Figure BDA0001995087620000108
the maximum number of iterations iternum;

步骤S722：初始化残差矢量x0＝ON×1，迭代次数t＝0；Step S722: Initialize the residual vector x 0 =ON ×1 , and the number of iterations t=0;

步骤S723：根据X、Φ、

Figure BDA0001995087620000109
和梯度计算公式
Figure BDA00019950876200001010
计算出βt+1；Step S723: According to X, Φ,
Figure BDA0001995087620000109
and gradient calculation formula
Figure BDA00019950876200001010
Calculate β t+1 ;

步骤S724：根据βt+1和硬阈值映射公式xt+1＝η(βt+1)，计算出xt+1；Step S724: Calculate x t+1 according to β t+1 and the hard threshold mapping formula x t+1 = η(β t+1 );

η(·)是硬阈值映射操作符号，即保留βt+1中前K个最大元素，其余元素置为0；η( ) is the hard threshold mapping operation symbol, that is, the first K largest elements in β t+1 are reserved, and the remaining elements are set to 0;

在本申请的实施例中，设：In the embodiments of this application, it is assumed that:

βt+1＝[-0.92,1.10,-7.02,4.33,10.36,5.48,-0.77,-2.25,3.66,5.90,6.75,6.96,9.09,-2.05,-1.41,-6.84,-3.49,-3.04,-2.64,1.22]，K＝10,可得出：β t+1 =[-0.92,1.10,-7.02,4.33,10.36,5.48,-0.77,-2.25,3.66,5.90,6.75,6.96,9.09,-2.05,-1.41,-6.84,-3.49,-3.04 ,-2.64,1.22], K=10, we can get:

xt+1＝[0,0,-7.02,4.33,10.36,5.48,0,0,3.66,5.90,6.75,6.96,9.09,0,0,-6.84,0,0,0,0]。x t+1 = [0,0,-7.02,4.33,10.36,5.48,0,0,3.66,5.90,6.75,6.96,9.09,0,0,-6.84,0,0,0,0].

步骤S725：根据xt+1、βt+1、

Figure BDA0001995087620000111
和支撑集映射公式
Figure BDA0001995087620000112
计算出xt+1；Step S725: According to x t+1 , β t+1 ,
Figure BDA0001995087620000111
and support set mapping formula
Figure BDA0001995087620000112
Calculate x t+1 ;

ξ(·)是支撑集映射操作符号，即将集合

Figure BDA0001995087620000113
在矢量βt+1中索引的元素幅值赋给集合
Figure BDA0001995087620000114
在xt+1中的索引所在位置；ξ( ) is the support set mapping operation symbol, that is, the set
Figure BDA0001995087620000113
The magnitude of the element indexed in the vector β t+1 is assigned to the set
Figure BDA0001995087620000114
the position of the index in x t+1 ;

在本申请的实施例中，设：In the embodiments of this application, it is assumed that:

Figure BDA0001995087620000115
依据上例，可得：
Figure BDA0001995087620000115
According to the above example, we can get:

xt+1＝[0,0,-7.02,4.33,10.36,5.48,0,0,3.66,5.90,6.75,6.96,9.09,-2.05,0,-6.84,0,0,0,0]。x t+1 = [0,0,-7.02,4.33,10.36,5.48,0,0,3.66,5.90,6.75,6.96,9.09,-2.05,0,-6.84,0,0,0,0].

步骤S726：计算非零元素的个数

Figure BDA0001995087620000116
令t＝t+1；Step S726: Calculate the number of non-zero elements
Figure BDA0001995087620000116
Let t=t+1;

其中，符号||·||0表示求向量的算子0范数；Among them, the symbol ||·|| 0 means to find the operator 0 norm of the vector;

步骤S727：判断若t＜iternum且nnz＞0，返回步骤S723；若否，则进入步骤S727；Step S727: It is judged that if t<iternum and nnz>0, go back to step S723; if not, go to step S727;

步骤S728：根据步骤计算出的S725的xt+1，再计算出xt+1＝U(xt+1)，Step S728: Calculate x t+1 =U(x t+1 ) according to the x t+1 calculated in step S725,

式中U(v)＝v/||v||2，符号||·||2表示求向量的算子2范数；where U(v)=v/||v|| 2 , the symbol ||·|| 2 represents the operator 2 norm of the vector;

步骤S729：根据xt+1，计算出稀疏音频信号

Figure BDA0001995087620000117
Step S729: Calculate the sparse audio signal according to x t+1
Figure BDA0001995087620000117

Claims (1)

1. A single-bit audio compression transmission and reconstruction method assisted by superposition characteristic information is characterized by comprising the following steps:
step S1: carrying out feature processing on the sparse audio signal to obtain feature information;
step S2: carrying out expansion processing on the feature information to obtain an expanded feature vector;
step S3: carrying out single-bit compression processing on the sparse audio vector to obtain a 1-bit compression signal;
step S4: carrying out weighted superposition processing on the expansion characteristic vector and the 1-bit compressed signal to obtain a sending signal;
step S5: sending out the sending signal;
step S6: carrying out recovery processing on a sending signal received by a receiving end to obtain recovery characteristic information and recovery 1-bit compression information;
step S7: carrying out auxiliary reconstruction algorithm processing on the recovery characteristic information to obtain a sparse audio signal;
the step S1 includes the following sub-steps:
step S11: setting the sparsity of a sparse audio signal X as K and the length as N;
step S12: extracting the position index of a non-zero element of the sparse audio signal X to obtain a support set omega with the length of K;
step S13: finding the front L of the sparse audio signal X in a support set omega of length K1Obtaining the position index with the maximum amplitude value and the length of L2Part of the supporting set of
Figure FDA0002621622750000011
Wherein 0 < L1≤K；
Step S14: for the length L2Part of the supporting set of
Figure FDA0002621622750000012
Code modulation is carried out to obtain the length L3Is 1 or-1, wherein L3＜M；
The expression of the single-bit compression processing of step S3 is:
y＝sign(Φx)
in the formula, y represents a 1-bit compressed signal, phi represents a pre-stored M multiplied by N measurement matrix phi, and x represents a sparse audio signal;
the step S4 includes the following sub-steps:
step S41: the extension characteristic information H with the length M is given a weight value of
Figure FDA0002621622750000021
The 1-bit compressed signal y is given a weight of
Figure FDA0002621622750000022
α is anWeight coefficient satisfying 0 < α < 1, EsEnergy of the transmitted signal;
step S42: the characteristic information and the 1-bit compressed signal are weighted and superposed, and the formula of the weighted superposition is
Figure FDA0002621622750000023
Wherein H represents a transmission signal Z having a length M, y represents a 1-bit compressed signal, α is a weighting coefficient and satisfies 0 < α < 1, and EsEnergy of the transmitted signal;
the step S6 includes the following sub-steps:
step S61: de-spreading the transmitted signal, the expression of the de-spreading process is
Figure FDA0002621622750000024
In the formula (I), the compound is shown in the specification,
Figure FDA0002621622750000025
it is indicated that the signal is transmitted,
Figure FDA0002621622750000026
where n is a noise signal of length M, PhFor despreading signature information, QTIs the transposition of the spreading matrix;
step S62: de-spread characteristic information PhPerforming hard decision operation to obtain recovery characteristic information
Figure FDA0002621622750000027
Step S63: the characteristic information will be recovered
Figure FDA0002621622750000028
Performing extension processing to obtain recovery spread spectrum characteristic information with length of M
Figure FDA0002621622750000029
Step S64: to noise signal of length M
Figure FDA00026216227500000210
And recovering spread spectrum signature information
Figure FDA00026216227500000211
Performing despreading and compression processing to obtain a despread and compressed signal P with length My，
Figure FDA0002621622750000031
Step S65: de-spread compressed signal P of length MyPerforming hard decision operation to obtain a 1-bit compressed signal with length of M
Figure FDA0002621622750000032
The expressions of the spreading processing of step S2 and step S63 are:
H＝Qh
wherein Q is a spreading matrix size of M × L and QTQ＝MILWherein L < M, ILThe matrix is an identity matrix of L × L, H is characteristic information, and H is an expansion characteristic vector;
the hard decision operation of step S62 and step S65 has the formula
Figure FDA0002621622750000033
In the formula (I), the compound is shown in the specification,
Figure FDA0002621622750000034
the signal is processed by hard decision, and y is a compressed signal;
the step S7 includes the following steps:
step S71: for the recovery of characteristic information
Figure FDA0002621622750000035
Code modulation processing is carried out to obtain a recovered part of the support set
Figure FDA0002621622750000036
Step S72, supporting the collection for the recovered part
Figure FDA0002621622750000037
Assisted and simultaneously recovering 1-bit compressed signal with length M
Figure FDA0002621622750000038
Reconstructing a sparse audio signal of length N
Figure FDA0002621622750000039
The coded modulation of step S14 and step S71 is
Step S141: assembling partial supports of length l "
Figure FDA00026216227500000310
Decimal elements in the sequence are converted into r-bit binary numbers, the length of a generated sequence after conversion is L, and L is rl;
step S142: mapping an element "1" in the sequence to "1", and mapping an element "0" to an element "-1";
the reconstruction algorithm of step S72 includes the following steps:
step S721: input recovery 1-bit compressed signal
Figure FDA0002621622750000041
Measurement matrix phi ∈ RM×NSparsity K, recovery of partial supporting set
Figure FDA0002621622750000042
Maximum number of iterations iternum;
step S722: initializing a residual vector x0＝ON×1The iteration time t is 0;
step S723: according to x, phi,
Figure FDA0002621622750000043
And gradient calculation formula
Figure FDA0002621622750000044
Calculate gradient βt+1；
Step S724, according to the gradient βt+1And hard threshold mapping formula xt+1＝η(βt+1) Calculating a hard threshold xt+1；
Step S725: calculating the number of non-zero elements
Figure FDA0002621622750000045
Wherein the symbol | | | purple0An operator 0 norm for calculating a vector is expressed, and t is t + 1;
step S726: if t is less than iternum and nnz is more than 0, returning to step S723; if not, go to step S727;
step S727: calculating x from tt+1＝U(xt+1)，
Wherein u (v) ═ v/| | v | | | grind2Symbol | | | non-conducting phosphor22, representing an operator 2 norm of the vector;
step S728: according to xt+1Computing a sparse audio signal
Figure FDA0002621622750000046
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