CN103176946A - Sparse decomposition and denoising method facing block sparse signals - Google Patents

Abstract

The invention discloses a sparse decomposition and denoising method facing block sparse signals, and relates to the sparse decomposition and denoising method of the block sparse signals. The problems that in the field of signal denoising, an existing sparse decomposition algorithm is complex in calculation, and self cluster characteristics of the block sparse signals are not considered are mainly solved. The method includes the following steps: setting an original state value of each parameter in the sparse decomposition and denoising process facing the block sparse signals; finding a maximum related atom subblock; obtaining a matched subdictionary of sparse decomposition; obtaining a matched atom column sequence number set of the sparse decomposition; updating residual errors; judging whether the iteration l is smaller than a preset maximum iteration iterNum, if the judged result is yes, executing the step eight, and if not, executing the step seven; adding one to the iteration l, and returning to the step two; estimating sparse decomposition coefficient vectors; and compositing denoised signals. The sparse decomposition and denoising method facing the block sparse signals can be applied to the technical field of noise elimination and suppression of the block sparse signals.

Description

A kind of Its Sparse Decomposition denoising method of block-oriented sparse signal

Technical field

The noise that the invention belongs to signal is eliminated and suppresses technical field, is specifically related to the Its Sparse Decomposition denoising method of block-sparse signal.

Background technology

The purpose of signal denoising is abandon various interference and extract wanted signal from contain noisy data, and the unknown message that is hidden in signal for announcement provides powerful guarantee.The development of decades, make signal noise is eliminated with the research that suppresses theory and algorithm thereof and obtained certain achievement, multiple denoising method occurs, mainly contained the methods such as traditional filter method, Wei Na, Kalman filtering method, SVD decomposition method, wavelet decomposition method, Empirical mode decomposition, Independent component analysis, neural network and Its Sparse Decomposition.But different denoising methods is mostly effective for specific signal and noise, all has defective more or less, and along with the rising of signal complexity and the people harsh requirement to the signal degree of accuracy, a lot of traditional signal antinoise methods can not meet demand.Its Sparse Decomposition is having very large potentiality aspect the inhibition of signal noise and elimination, can realize more succinct, the flexible and adaptive rarefaction representation of signal based on the Its Sparse Decomposition of the former word bank of redundancy, so the Its Sparse Decomposition method is with a wide range of applications in the signal denoising field.

At present, be used for the noise elimination and with the Its Sparse Decomposition that suppresses, a lot of algorithms arranged, matching pursuit algorithm (Matching Pursuit wherein, MP) be the main flow algorithm of Its Sparse Decomposition, the thought principle is simple, is convenient to understand, and to compare its computation complexity minimum with other algorithms of Its Sparse Decomposition, but because the mistake completeness of former word bank causes calculated amount huge, so the high fatal problem that remains the MP algorithm of complexity.For the large problem of calculated amount, Chinese scholars has been carried out various improvement to the MP algorithm, such as quadrature coupling track algorithm (Orthogonal MP, OMP), the speed of MP algorithm that makes the OMP algorithm has improved a lot, but in face of the mass data of signal, the quality of existing Its Sparse Decomposition algorithm speed and restoring signal still can not be satisfactory.In addition, the emphasis of Its Sparse Decomposition research at present is the computing velocity of improving algorithm itself, research is seldom arranged for pending signal itself, namely seldom have or do not consider the architectural characteristic that signal itself is intrinsic, yet in reality, a lot of signals all have some special constructions, for example the nonzero value of block-sparse signal becomes piece to occur, and shows a bunch class feature, and perhaps the coefficient of signal under certain transform domain has the sparse bunch category feature of piece.

Summary of the invention

The present invention is in order to solve Its Sparse Decomposition algorithm calculation of complex in existing signal denoising field, not consider the problem of block-sparse signal bunch class feature itself, and proposes a kind of Its Sparse Decomposition denoising method of block-oriented sparse signal.The particular problem that the present invention will solve is described below:

Clean signal s is that length is the real number vector of M, namely

Putative signal s is polluted by white Gaussian noise n, and wherein n is that length is the column vector of M, namely

Noise level is characterized by signal to noise ratio (S/N ratio) (Signal to Noise Rate, SNR), and the relation of supposing noise and signal is additivity, and signals with noise is y=s+n, wherein

The initial signal to noise ratio (S/N ratio) of y is made as SNR ₀, wherein the snr computation formula is:

$\mathrm{SNR}=10\lg \left(\frac{\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{s}^2\left(i\right)}{\underset{i}{\overset{M}{\mathrm{\Σ}}}{(s\left(i\right)-y\left(i\right))}^2}\right)$

Signals with noise y is carried out Its Sparse Decomposition realize that the process of denoising is: signals with noise y is gathered D={d in given certain _n, n=1,2 ..., decompose on N}, wherein D is former word bank or dictionary, d _nBe atom, basic model is y=Dx, wherein Be coefficient vector, making the minimum x of zero coefficient values is namely required coefficient vector, and the namely linear combination with some atom minimum in D approaches clean signal s, and mathematic(al) representation is:

$s\≈\underset{\mathrm{\γ}\∈I_k}{\mathrm{\Σ}}{x}_{\mathrm{\γ}}{d}_{\mathrm{\γ}}$

Wherein, d _γSelected atom, I _kD _γThe subscript collection, k is the number of choosing atom, x _γBe the expression coefficient that each atom pair is answered, namely pick out a most sparse linear combination of expression and represent denoised signal from dictionary D, Its Sparse Decomposition method that Here it is realizes the basic thought of denoising;

The present invention is directed to the coefficient vector of the Its Sparse Decomposition s=Dx of clean signal s

Effective when having sparse bunch of class feature of piece, that is:

Wherein, N=m * d, m are the packet count of piece sparse coefficient vector x, and d is the sub-block length of x, x[j] (j=1 ..., m) be called a sub-block, suppose x[j] the isometric d of being, and the block sparsity of x is K, i.e. a sub-block x[j] in K is arranged at the most is not 0 euclideam norm, definition:

${\left|\right|x\left|\right|}_{\mathrm{2,0}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}I({\left|\right|x\[j\]\left|\right|}_2>0)$

Wherein, $I\left({\left|\right|x\[j\]\left|\right|}_2\right)=\{\begin{array}{c}1,{\left|\right|x\[j\]\left|\right|}_2>0\\ 0,\mathrm{otherwise}\end{array};$

Its Sparse Decomposition dictionary D is real number or the complex matrix of the capable N row of the M of a series of sparse base compositions, namely

D=[d ₁, d ₂, d ₃..., d _N], M＜N wherein, therefore that dictionary is redundancy is excessively complete, each column vector d of dictionary D _nThat length is that the complex vector located or real number of M is vectorial, namely

Be called an atom, each atom sequence number is designated as respectively 1,2, ..., N, in the present invention, dictionary D will guarantee that Its Sparse Decomposition coefficient x is that piece is sparse, D is different because of signal, for example the expression coefficient of multi-band signal on discrete cosine transform (Discrete Cosine Transform, DCT) base meets sparse bunch of class feature of piece, DCT dictionary atom producing method:

$d_n=\mathrm{\ω}\left(n\right){\[\cos \left(\frac{\mathrm{\π}(n-1)}{2N}\right),\cos \left(\frac{3\mathrm{\π}(n-1)}{2N}\right),...,\cos \left(\frac{\mathrm{\π}(2M-1)(n-1)}{2N}\right)\]}^T$

N=1 wherein, 2 ..., N, $\mathrm{\ω}\left(n\right)=\{\begin{array}{c}\frac{1}{\sqrt{N}},n=1\\ \sqrt{\frac{2}{N}},2\≤n\≤N\end{array};$

Set dictionary D and carry out accordingly the piece division by the piece sparse characteristic of coefficient vector x:

Wherein, every d of redundant dictionary D classifies one as, is total to m sub-block, and the sequence number of each atom sub-block is designated as respectively 1,2 ..., m, i.e. D[j] be j sub-block of dictionary;

The matrix representation forms of the Its Sparse Decomposition denoising model of block-oriented sparse signal is:

Thought of the present invention is that the linear combination of choosing some the most sparse atom sub-block from dictionary D approaches denoised signal, that is:

$s\≈\underset{\mathrm{\γ}\∈I_k}{\mathrm{\Σ}}x\[\mathrm{\γ}\]D\[\mathrm{\γ}\]$

Wherein, D[γ] be selected atom sub-block, I _KD[γ] sequence number subscript collection, K is the number of choosing the atom sub-block, x[γ] be coefficient sub-block corresponding to each atom sub-block;

The present invention is achieved by following proposal: a kind of Its Sparse Decomposition denoising method of block-oriented sparse signal, and the process of described method is:

The original state value of each parameter in the Its Sparse Decomposition denoising process of step 1, setting block-oriented sparse signal:

The set algorithm input: signals with noise y, redundant dictionary D, the piecemeal number m of piece sparse coefficient vector x and block sparsity K, maximum iteration time iterNum=K,

Initialization: the initial value r of residual error ₀=y, matched atoms sub-block sequence number initial value

, the former molecular matrix initial value that the matched atoms sub-block is corresponding

The atom row sequence number vector initial value that the matched atoms sub-block is corresponding

The initial value that mates sub-dictionary

Mate the corresponding atom row of sub-dictionary sequence number vector initial value

The initial value of iterations l is 1, the initial value of reconstructed blocks sparse coefficient vector x

Step 2, seek maximal correlation atom sub-block: calculate l(l 〉=1) residual error r during inferior iteration and after the l-1 time iteration _l-1The sub-block λ that mates most _l:

${\mathrm{\λ}}_l=\arg \underset{j}{\max }(\mathrm{norm}\left(\right|D^H\[j\]r_{l-1}\left|\right))$

Wherein, D[j] be j the atom sub-block of D, D ^H[j] is D[j] conjugate transpose, j=1,2 ..., m, λ _lThe corresponding piecemeal sequence number 1,2 of value ..., m, i.e. each sub-block D[j] conjugate transpose and previous step residual error r _l-1The vector that it is d that the phase multiplication obtains a length takes absolute value and asks 2 norms this vector, obtains m absolute norm value, and therefrom the piece of selective value maximum is namely and residual error r _l-1The sub-block of coupling, sub-block sequence number assignment to λ _l, sub-block λ _lCorresponding atom row sequence number assignment is given vector

Sub-block λ _lCorresponding former molecular matrix assignment is given

Step 3, obtain the sub-dictionary of coupling of Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding former molecular matrix With the sub-dictionary T of the coupling of the l-1 time iteration _l-1The union assignment to the sub-dictionary T of the coupling of l iteration _l, that is:

$T_l=T_{l-1}\∪D_{{\mathrm{\λ}}_l};$

Step 4, the matched atoms row sequence number set of obtaining Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding atom row sequence number vector

Atom row sequence number vector t with the l-1 time iteration _l-1The union assignment to the atom row sequence number of l iteration vector t _l, that is:

Step 5, renewal residual error: dictionary T according to the coupling that obtains in step 3 _l, calculate the residual error r after iteration the l time _lFor:

$r_l=y-T_l\left(T_l^{+}y\right)r_l$

Wherein,

Be T _lPseudo inverse matrix, namely

Step 6, judge that iterations l whether less than predefined maximum iteration time iterNum, judgment result is that to be, execution in step eight, and the determination result is NO, and execution in step seven;

Step 7, the value of iterations l is added 1, return to step 2;

Step 8, estimation Its Sparse Decomposition coefficient vector: according to the t that obtains in signals with noise y, step 4 _lWith the matrix that obtains in step 5

The reconstruct vector of computing block sparse vector x

For:

$\hat{x}\[t_l\]=T_l^{+}y;$

Step 9, synthetic denoised signal: by what obtain in step 8

Calculate denoised signal with dictionary D

$\hat{y}=D\hat{x}$

Finished surface is to the Its Sparse Decomposition denoising process of block-sparse signal.

The present invention includes following advantage:

1, utilize the each Iterative matching of piece sparse characteristic of signal itself to go out one group of atom by matching pursuit algorithm, saved the sparse approximate time of structure, improved matching efficiency;

2, the corresponding signals with noise y of piece sparse coefficient vector that is K for a block sparsity only needs K iteration can reconstruct the coefficient vector with piece sparse characteristic

The computational complexity of algorithm reduces;

3, take full advantage of the signal self character, improve the denoising effect of signal;

4, effectively eliminate and suppressed to have the noise of the block-sparse signal of bunch class feature.

Description of drawings

Fig. 1 is the process flow diagram of the Its Sparse Decomposition denoising method of the described a kind of block-oriented sparse signal of embodiment one; Fig. 2 be the method for the invention from the OMP algorithm under the DCT dictionary to the random equally distributed block-sparse signal of emulation amplitude the signal to noise ratio (S/N ratio) curve map during at different noise level; Fig. 3 be the method for the invention from the OMP algorithm under the DCT dictionary to the random equally distributed block-sparse signal of emulation amplitude the square error curve map during at different noise level; Fig. 4 be the method for the invention from the OMP algorithm under the DCT dictionary to multi-band signal the signal to noise ratio (S/N ratio) curve map during at different noise level; Fig. 5 be the method for the invention from the OMP algorithm under the DCT dictionary to multi-band signal the square error curve map during at different noise level.

Embodiment

Embodiment one, illustrate present embodiment below in conjunction with Fig. 1.A kind of Its Sparse Decomposition denoising method of block-oriented sparse signal, the process of described method is:

The original state value of each parameter in the Its Sparse Decomposition denoising process of step 1, setting block-oriented sparse signal:

The set algorithm input: signals with noise y, redundant dictionary D, the piecemeal number m of piece sparse coefficient vector x and block sparsity K, maximum iteration time iterNum=K,

Initialization: the initial value r of residual error ₀=y, matched atoms sub-block sequence number initial value The former molecular matrix initial value that the matched atoms sub-block is corresponding

The atom row sequence number vector initial value that the matched atoms sub-block is corresponding

The initial value that mates sub-dictionary

Mate the corresponding atom row of sub-dictionary sequence number vector initial value

The initial value of iterations l is 1, the initial value of reconstructed blocks sparse coefficient vector x

Step 2, seek maximal correlation atom sub-block: calculate l(l 〉=1) residual error r during inferior iteration and after the l-1 time iteration _l-1The sub-block λ that mates most _l:

${\mathrm{\λ}}_l=\arg \underset{j}{\max }(\mathrm{norm}\left(\right|D^H\[j\]r_{l-1}\left|\right))$

Wherein, D[j] be j the atom sub-block of D, D ^H[j] is D[j] conjugate transpose, j=1,2 ..., m, λ _lThe corresponding piecemeal sequence number 1,2 of value ..., m, i.e. each sub-block D[j] conjugate transpose and previous step residual error r _l-1The vector that it is d that the phase multiplication obtains a length takes absolute value and asks 2 norms this vector, obtains m absolute norm value, and therefrom the piece of selective value maximum is namely and residual error r _l-1The sub-block of coupling, sub-block sequence number assignment to λ _l, sub-block λ _lCorresponding atom row sequence number assignment is given vector

Sub-block λ _lCorresponding former molecular matrix assignment is given

Step 3, obtain the sub-dictionary of coupling of Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding former molecular matrix

With the sub-dictionary T of the coupling of the l-1 time iteration _l-1The union assignment to the sub-dictionary T of the coupling of l iteration _l, that is:

$T_l=T_{l-1}\∪D_{{\mathrm{\λ}}_l};$

Step 4, the matched atoms row sequence number set of obtaining Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding atom row sequence number vector

Atom row sequence number vector t with the l-1 time iteration _l-1The union assignment to the atom row sequence number of l iteration vector t _l, that is:

Step 5, renewal residual error: dictionary T according to the coupling that obtains in step 3 _l, calculate the residual error r after iteration the l time _lFor:

$r_l=y-T_l\left(T_l^{+}y\right)r_l$

Wherein, Be T _lPseudo inverse matrix, namely

Step 6, judge that iterations l whether less than predefined maximum iteration time iterNum, judgment result is that to be, execution in step eight, and the determination result is NO, and execution in step seven;

Step 7, the value of iterations l is added 1, return to step 2;

Step 8, estimation Its Sparse Decomposition coefficient vector: according to the t that obtains in signals with noise y, step 4 _lWith the matrix that obtains in step 5

The reconstruct vector of computing block sparse vector x

For:

$\hat{x}\[t_l\]=T_l^{+}y;$

Step 9, synthetic denoised signal: by what obtain in step 8 Calculate denoised signal with dictionary D

$\hat{y}=D\hat{x}$

Finished surface is to the Its Sparse Decomposition denoising process of block-sparse signal.

Embodiment two, present embodiment are further illustrating the step 1 in the Its Sparse Decomposition denoising method of the described a kind of block-oriented sparse signal of embodiment one, presetting maximum iteration time iterNum in step 1 is K, and wherein K is the block sparsity of piece sparse coefficient vector x.

Embodiment three, present embodiment are to the further illustrating of the step 2 in the Its Sparse Decomposition denoising method of the described a kind of block-oriented sparse signal of embodiment one, in step 2 with each sub-block D[j of dictionary] with residual error r _l-1The phase multiplication finds and residual error r by the sub-block of selecting absolute norm value maximum _l-1The one group of atom that mates most

Be checking effect of the present invention, with method of the present invention and orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm compares experiment: be applied to respectively meet in the signal denoising of piece sparse characteristic, signal to noise ratio snr between more resulting denoised signal and clean signal, square error (Mean Square Error, MSE) respectively.In experimentation, adopt respectively the signal and the multi-band signal that transform to time domain by the random equally distributed sparse coefficient vector of amplitude to test: given sparse coefficient vector length N, block count m and block sparsity K, random selected K sub-block, assignment is the random equally distributed data point of amplitude on this K sub-block respectively, namely obtain required emulation testing piece sparse coefficient vector, transform to time domain by dictionary D and be original signal s; The multi-band signal model as shown in the formula:

$s\left(t\right)=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\sqrt{E_{i}B}\sin c\left(B(t-{\mathrm{\τ}}_i)\right)\cos \left(2\mathrm{\π}{f}_i(t-{\mathrm{\τ}}_i)\right)$

Sinc (x)=sin (π x)/(π x) wherein, source signal s (t) comprises 3 pairs of frequency bands, number of frequency bands K=6.B is the source signal maximum bandwidth, and experiment arranges B=50MHz, E _iBe the energy of each frequency band, E _i={ 1,2,3}, τ _iBe time migration, τ _i={ 0.40.70.2} μ secs.For each frequency band, carrier frequency fi is evenly distributed on [f _NYQ/ 2, f _NYQ/ 2], f _NYQBe Nyquist sampling rate, f _NYQ=10GHz.

In the experimentation of present embodiment, adopt the DCT base to produce DCT redundant dictionary D as atom, denoising experiment for multi-band signal arranges dictionary line number M=10000, columns N=20000, piecemeal number m=200, block sparsity K=6, denoising experiment for simulate signal arranges M=1000, N=2000, piecemeal number m=200, block sparsity K=6.All suppose the initial signal to noise ratio snr of signals with noise for two kinds of experimental signals ₀Be followed successively by-20 ,-15 ,-10 ..., 20dB is for each noise level SNR ₀OMP algorithm and the inventive method are moved respectively 100 times, calculate average signal-to-noise ratio SNR and the square error MSE of every kind of algorithm, SNR represents the degree of noise remove, the larger denoising effect of SNR value is better, MSE represents the difference degree of denoised signal and clean signal, and the less denoising effect of MSE value is better.

In the inventive method, the process of computational algorithm evaluation index SNR and MSE is:

One, input tape noise cancellation signal y=s+n, the initial signal to noise ratio (S/N ratio) of default y and s is followed successively by SNR ₀=-20 ,-15 ,-10 ..., 20dB;

Two, the method for the invention obtains denoised signal

Calculate with following two formulas

And the SNR between s and MSE:

$\mathrm{SNR}=101g\left(\frac{\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{s}^2\left(n\right)}{\underset{n}{\overset{N}{\mathrm{\Σ}}}{(s\left(n\right)-\hat{y}\left(n\right))}^2}\right)$

$\mathrm{MSE}=\frac{1}{N}\underset{n}{\overset{N}{\mathrm{\Σ}}}{(s\left(n\right)-\hat{y}\left(n\right))}^2$

Three, to every kind of denoising method at different noise level SNR ₀Upward move respectively 100 times, and calculate respectively SNR and MSE, get its mean value and do the algorithm performance evaluation index.

Experimental result such as Fig. 2 are to shown in Figure 5, wherein Fig. 2 and Fig. 3 be the method for the invention from the OMP algorithm under the DCT dictionary to the emulation block-sparse signal denoising result during at different noise level, Fig. 4 and Fig. 5 be the method for the invention from the OMP algorithm under the DCT dictionary to multi-band signal the denoising result during at different noise level.Be with in Fig. 2 to Fig. 5 The curve of mark is for adopting the denoising effect curve of the described method of present embodiment, band

The curve of mark is for adopting the denoising effect curve of OMP method.As seen from the figure, for simulate signal and actual multi-band signal, the SNR of the described method of present embodiment has significantly raising than the OMP method, MSE has significantly reduction, i.e. any class signal no matter, as long as meet bunch class feature of block-sparse signal in transform domain, all can utilize the inventive method effectively to carry out denoising.

Claims (3)

1. the Its Sparse Decomposition denoising method of a block-oriented sparse signal is characterized in that it realizes by following steps:

The original state value of each parameter in the Its Sparse Decomposition denoising process of step 1, setting block-oriented sparse signal:

The set algorithm input: signals with noise y, redundant dictionary D, the piecemeal number m of piece sparse coefficient vector x and block sparsity K, maximum iteration time iterNum=K,

Initialization: the initial value r of residual error ₀=y, matched atoms sub-block sequence number initial value

The former molecular matrix initial value that the matched atoms sub-block is corresponding

The atom row sequence number vector initial value that the matched atoms sub-block is corresponding

The initial value that mates sub-dictionary Mate the corresponding atom row of sub-dictionary sequence number vector initial value

The initial value of iterations l is 1, the initial value of reconstructed blocks sparse coefficient vector x

Step 2, seek maximal correlation atom sub-block: calculate l(l 〉=1) residual error r during inferior iteration and after the l-1 time iteration _l-1The sub-block λ that mates most _l:

${\mathrm{\λ}}_l=\arg \underset{j}{\max }(\mathrm{norm}\left(\right|D^H\[j\]r_{l-1}\left|\right))$

Wherein, D[j] be j the atom sub-block of D, D ^H[j] is D[j] conjugate transpose, j=1,2 ..., m, λ _lThe corresponding piecemeal sequence number 1,2 of value ..., m, i.e. each sub-block D[j] conjugate transpose and previous step residual error r _l-1The vector that it is d that the phase multiplication obtains a length takes absolute value and asks 2 norms this vector, obtains m absolute norm value, and therefrom the piece of selective value maximum is namely and residual error r _l-1The sub-block of coupling, sub-block sequence number assignment to λ _l, sub-block λ _lCorresponding atom row sequence number assignment is given vector

Sub-block λ _lCorresponding former molecular matrix assignment is given

Step 3, obtain the sub-dictionary of coupling of Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding former molecular matrix With the sub-dictionary T of the coupling of the l-1 time iteration _l-1The union assignment to the sub-dictionary T of the coupling of l iteration _l, that is:

$T_l=T_{l-1}\∪D_{{\mathrm{\λ}}_l};$

Step 4, the matched atoms row sequence number set of obtaining Its Sparse Decomposition: with the sub-block λ that obtains in step 2 _lCorresponding atom row sequence number vector

Atom row sequence number vector t with the l-1 time iteration _l-1The union assignment to the atom row sequence number of l iteration vector t _l, that is:

Step 5, renewal residual error: dictionary T according to the coupling that obtains in step 3 _l, calculate the residual error r after iteration the l time _lFor:

$r_l=y-T_l\left(T_l^{+}y\right)r_l$

Wherein, Be T _lPseudo inverse matrix, namely

Step 6, judge that iterations l whether less than predefined maximum iteration time iterNum, judgment result is that to be, execution in step eight, and the determination result is NO, and execution in step seven;

Step 7, the value of iterations l is added 1, return to step 2;

Step 8, estimation Its Sparse Decomposition coefficient vector: according to the t that obtains in signals with noise y, step 4 _lWith the matrix that obtains in step 5 The reconstruct vector of computing block sparse vector x

For:

$\hat{x}\[t_l\]=T_l^{+}y;$

Step 9, synthetic denoised signal: by what obtain in step 8

Calculate denoised signal with dictionary D

$\hat{y}=D\hat{x}$

Finished surface is to the Its Sparse Decomposition denoising process of block-sparse signal.

2. the Its Sparse Decomposition denoising method of a kind of block-oriented sparse signal as claimed in claim 1, it is characterized in that presetting in step 1 maximum iteration time iterNum is K, wherein K is the block sparsity of piece sparse coefficient vector x.

3. the Its Sparse Decomposition denoising method of a kind of block-oriented sparse signal as claimed in claim 1 is characterized in that in step 2 each the sub-block D[j with dictionary] with residual error r _l-1The phase multiplication finds and residual error r by the sub-block of selecting absolute norm value maximum _l-1The one group of atom that mates most

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