CN108880558A - A kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform - Google Patents
A kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform Download PDFInfo
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- 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
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Abstract
The present invention relates to a kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform, first, discrete cosine transform is carried out for single-frequency underwater sound signal, to obtain sparse expression, is constituted under corresponding condensation matrix primary condition for the element that gaussian random generates.Using dictionary matrix and condensation matrix correlation minimal construction objective function, and the condensation matrix optimized in conjunction with the optimizing of steepest gradient iteration, condensation matrix compresses single-frequency underwater sound signal, compressed signal is transmitted again, in receiving end, signal is restored in conjunction with orthogonal matching pursuit recovery algorithms.The present invention optimizes gaussian random matrix under steepest gradient optimizing strategy, and then obtains the condensation matrix of optimization.Since condensation matrix and dictionary matrix cross correlation are minimum, so that the optimization condensation matrix that the present invention generates has very big advantage to the recovery of sparse signal.
Description
Technical field
The invention belongs to marine acousticss and field of underwater acoustic signal processing, are related to a kind of underwater sound signal based on discrete cosine transform
Condensation matrix optimization method, compression and restorability of the condensation matrix of the optimization by raising to single-frequency underwater sound signal, is suitable for
The optimization of condensation matrix, ocean underwater sound data compression and recovery etc..
Background technique
The problems such as underwater sound data compression and recovery, which can all be attributed to, is expressed and is restored to sparse signal, based on to random
The dictionary matrix of the condensation matrix combination discrete cosine transform construction of generation is to carry out compression and sparse expression to underwater sound signal
Estimation.Currently, carrying out theoretical characteristics analysis to the tight frame between given dictionary matrix and its corresponding condensation matrix.Specific ginseng
See《Designing structured tight frames via an alternating projection method》, should
Text is published in for 2005《IEEE Transactions on Information Theory》51st phase, first page number 188.
The objective function building that the correlation of dictionary matrix and condensation matrix minimizes is detailed in《Optimized projections
for compressed sensing》It is published within this article 2007《IEEE Transactions on Signal
Processing》55th phase, first page number 5695.
Two matroids used in compressed sensing, including condensation matrix and dictionary matrix, compressive sensing theory are pointed out：It obtains
The adequate condition for obtaining unique sparse signal estimation is the limitation equidistant characteristics for meeting condensation matrix and dictionary matrix.However the limitation
Equidistant characteristics can not be verified directly in engineering, therefore switch to examine the correlation of condensation matrix and dictionary matrix minimum.Because
Cross-correlation can quantify to reflect limitation equidistant characteristics, make the correlation of condensation matrix and dictionary matrix is as minimum as possible can then protect
The probability of success for demonstrate,proving compressed sensing algorithm is bigger.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of underwater sound signal pressure based on discrete cosine transform
Contracting matrix optimizing method overcomes the corresponding compressed sensing algorithm of existing condensation matrix to restore the problems such as precision is limited.
Technical solution
A kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform, it is characterised in that steps are as follows：
Step 1：If Φ is condensation matrix, y is measurement signal, and x is underwater sound signal to be compressed, and wherein the dimension of Φ is M
× N, M < N, measurement process are：
Y=Φ x；
Step 2：Constructing objective function is：
Wherein, F norm is defined asI, j is the i row of A condensation matrix, j column；I is
Unit matrix；T is transposition；
Step 3：Given initial value is that the element being randomly generated constitutes Φ1, step parameter η, setting threshold value is for Th and repeatedly
Generation number K；
Step 4：Output information is set：Condensation matrix Φ after optimization；
Step 5：Initialization：Regularization1≤j≤N,H1=I；And there is A1=idct (ΦT)T；
Step 6：The number of iterations is set as L, according to following iterative iteration：
Wherein Th is set threshold value, and sign is sign function, and setting the number of iterations is K, is updated
WhereinTTo carry out transposition operation to matrix.
The Th is 0.3~0.6.
Beneficial effect
A kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform proposed by the present invention, firstly, being directed to
Single-frequency underwater sound signal carries out discrete cosine transform, is high to obtain sparse expression, under corresponding condensation matrix primary condition
This element being randomly generated is constituted.Using dictionary matrix and condensation matrix correlation minimal construction objective function, and combine steepest
The condensation matrix that gradient method iteration optimizing is optimized compresses condensation matrix to single-frequency underwater sound signal, then will be after compression
Signal transmitted, in receiving end, signal is restored in conjunction with orthogonal matching pursuit recovery algorithms.
The present invention is based on the iteration optimizing of steepest gradient, using steepest gradient to this black norm minimum of not Luo Beini
Realization is optimized, so that it is the smallest to realize that the compressed sensing of optimization better adapts to discrete cosine transform dictionary matrix correlation
Situation.It is different that the compressed sensing that is constituted of element is generated from gaussian random, and the present invention is not necessarily to underwater sound signal sparse characteristic and dilute
The priori knowledges such as degree are dredged, only iteration step length need to be set, in conjunction with steepest gradient, realize the compression square to optimization by adjusting thresholds
Battle array is estimated.
It has the beneficial effect that：The present invention is based on condensation matrixes and the minimum optimization aim of dictionary matrix correlation, most
Under heavy gradient method optimizing strategy, gaussian random matrix is optimized, and then obtains the condensation matrix of optimization.Due to condensation matrix
It is minimum with dictionary matrix cross correlation, so that the optimization condensation matrix that the present invention generates restores with very big sparse signal
Advantage.
Detailed description of the invention
Fig. 1 is that the condensation matrix of the method for the present invention optimization restores under different original signal signal-to-noise ratio from gaussian random matrix
Performance comparison figure.
Fig. 2 is that compressed sensing restoration result corresponding to the condensation matrix of original signal and the method for the present invention optimization compares
Figure.
Fig. 3 is that compressed sensing recovery signal corresponding to the optimization condensation matrix of original signal and the method for the present invention generation exists
Comparison diagram on frequency domain.
Fig. 4 is the condensation matrix and its corresponding lattice Lay that the condensation matrix that the method for the present invention generates and random element are constituted
Nurse matrix comparison diagram.
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described：
Referring to Fig.1, using 8PSK coding mode, in conjunction with Carrier Modulation, carrier frequency 1kHz, sample frequency 4kHz,
The signal-to-noise ratio for receiving original signal is set as 0 to 25dB, change step 5dB；In compression process, the line number of matrix is set as
64, columns 128, i.e. compression ratio are 2, and step parameter is that η is 0.1, and setting threshold value is that Th is 0.13 and the number of iterations L is 10,
The number of iterations K is 50.
(1) Φ is set as condensation matrix, y is measurement signal, and x is underwater sound signal to be compressed, and wherein the dimension of Φ is M × N,
M < N, specific measurement process are：
Y=Φ x (1)
(2) measuring process was complete system, was non-sparse signal, dictionary square in time domain for single carrier frequency underwater sound signal
Battle array use discrete cosine transform D, dimension be N × N, the dictionary expression under, underwater sound signal switch to can sparse expression signal.Its
In, the underwater sound signal of sparse expression is expressed as θ by A=Φ D, and therefore, the objective function of optimization problem is：
Wherein | | θ | |0Indicate the number of nonzero element, the direct solution of formula (2) is extremely complex, therefore is often converted into
Wherein | | θ | |1Indicate the sum of the absolute value of each element.
(3) then, the present invention is directed to optimize condensation matrix.It is first in view of traditional condensation matrix is limited to precision is restored
First defining gram matrix is：
G=ATA (4)
The target of optimization is to realize：
Wherein not this black norm of Luo Beini is defined as：I, j is A condensation matrix
I=64 row, j=128 column；I is unit matrix；T is transposition；
However, it is contemplated that Gtram matrix cross-correlation will not be 0, then it is revised as unit matrix as objective function：
Wherein Th is set threshold value, and sign is sign function.
(4) specific method of optimization condensation matrix is：
It is constituted 1. setting the initial value of condensation matrix as the element being randomly generated：Φ.Step parameter is η=0.1, and threshold value is arranged
For Th=0.13 and the number of iterations K=50.
2. output information：The condensation matrix Φ of optimization.
3. initializing：Regularization1≤j≤N,H1=I；And there is A1=idct (ΦT)T。
4. the number of iterations is set as L=10, according to following iterative iteration：
And objective matrix is updated to formula (6).Setting the number of iterations is K, is updated
By following iterative update condensation matrix：
When further changing compression factor, setting line number be 32, columns 128, using orthogonal matching pursuit algorithm into
The estimation of row sparse signal, the number of iterations are set as 16, and original signal and corresponding restoration result such as Fig. 2 (a) and 2 (b) are shown, institute
The mean square error obtained is 0.039.
For further investigate optimization condensation matrix caused by the present invention to restore signal frequency domain influence.To in Fig. 2
Signal do Fourier transformation, obtained original signal and restore signal spectrum result such as Fig. 3 (a) and 3 (b) shown in.It can see
The optimization matrix that the present invention generates out does not have an impact the frequency domain of signal during compression and recovery, this is because this hair
Optimization condensation matrix caused by bright is beneficial to compressed sensing to the Exact recovery of signal.
For show gaussian random generation element constitute condensation matrix and optimization condensation matrix difference, by the two
Condensation matrix Gtram matrix corresponding with its be illustrated respectively in (a) (b) (c) (d) of Fig. 4, there it can be seen that optimization
Gtram matrix corresponding to condensation matrix afterwards is more nearly than Gtram matrix corresponding to the condensation matrix that is randomly generated
Unit matrix.Illustrate that it has smaller cross correlation with dictionary matrix, so that explanation realizes cross-correlation to a certain extent
Property minimize optimization aim.
The present invention achieves apparent implementation result in the emulation that sparse signal compresses and restores, with classical Gauss with
The condensation matrix that machine generates is compared, and condensation matrix of the invention improves the recovery of current compressed sensing algorithm under certain condition
Precision.
Claims (2)
1. a kind of underwater sound signal condensation matrix optimization method based on discrete cosine transform, it is characterised in that steps are as follows：
Step 1：If Φ is condensation matrix, y is measurement signal, and x is underwater sound signal to be compressed, and wherein the dimension of Φ is M × N, M
< N, measurement process are：
Y=Φ x；
Step 2：Constructing objective function is：
Wherein, F norm is defined asI, j is the i row of A condensation matrix, j column；I is unit
Matrix；T is transposition；
Step 3：Given initial value is that the element being randomly generated constitutes Φ1, step parameter η, setting threshold value is Th and the number of iterations
K；
Step 4：Output information is set：Condensation matrix Φ after optimization；
Step 5：Initialization：Regularization1≤j≤N,H1=I；And there is A1=idct (ΦT)T；
Step 6：The number of iterations is set as L, according to following iterative iteration：
Wherein Th is set threshold value, and sign is sign function, and setting the number of iterations is K, is updated
Wherein T is to carry out transposition operation to matrix.
2. the underwater sound signal condensation matrix optimization method based on discrete cosine transform according to claim 1, it is characterised in that：
The Th is 0.3~0.6.
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| CN110912564A (en) * | 2019-11-19 | 2020-03-24 | 重庆邮电大学 | Image measurement matrix optimization method based on unit norm tight framework |
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| US20140006536A1 (en) * | 2012-06-29 | 2014-01-02 | Intel Corporation | Techniques to accelerate lossless compression |
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