CN103257856A - Signal receiver based self-adaptive OMP (orthogonal matching pursuit) method - Google Patents

Abstract

The invention discloses a signal receiver based self-adaptive OMP (orthogonal matching pursuit) method, firstly deduces and illustrates sparse decomposition and secondarily introduces a signal receiver based self-adaptive OMP method. By learning from relevant methods, the problems about large calculation amount and long calculation period are discovered, so that selection of atoms in an atomic library is handled, and treatment of a single atom is changed into treatment of an atom set. Further, iterations are reduced, so signal sparse representation can be obtained within a short time, speed of signal sparsity is increased and the signal receiver based self-adaptive OMP method can be well applied in practice.

Description

A kind of self-adaptation OMP method based on signal receiver

Technical field

The present invention relates to the signal process field, wherein mainly is the invention based on the relevant sparse decomposition method of signal receiver in the compression sampling theory, specifically, relates to a kind of self-adaptation OMP method based on signal receiver.

Background technology

The generation of compressed sensing theory has improved the speed that signal is handled greatly, rely on its outstanding performance, make it obtain development at full speed, but, as a theory of just having risen, must there be many weak points in it, and it is perfect still to need experts and scholars constantly it to be carried out, and one of them emphasis is exactly the research of sparse decomposition.

Nowadays the development of sparse decomposition mainly is exactly the development of algorithm, because at different situations, with a kind of algorithm outstanding demand that also can't satisfy all situations again, the common progress of multiple algorithm makes this theory of compressed sensing obtain application more and more widely, and the core of algorithm is exactly the foundation of former word bank, former word bank is exactly the base in original the decomposition in fact, but it is unique so lost some important attribute of base because of it, seeking a kind of new former word bank will be the basic of sparse decomposition development, so this paper is after having fully understood existing classic algorithm, it is improved, make it adapt to different characteristics of signals.

The method of sparse decomposition has a lot, they design at different situations, except the MP method of classics, many OMP methods in addition of using now, it is exactly the orthogonal matching pursuit method, it is to have carried out and must improve in the MP method, it has solved the problem that atom may be non-orthogonal in the MP method, because after choosing atom, the OMP method has been carried out orthogonalization process by the Gram-Schmidt method to it, and then signal carried out projection on atom, after so continuous projection, obtain the linear combination of selected atom, then, there is certain problem in this method, be to carry out one by one when choosing atom, so algorithm have certain defective in computing time, and also underaction on the adaptability of this algorithm, like this, by study a kind of adaptive quadrature match tracing method that can be applicable in the signal receiver has been proposed.

Summary of the invention

The technical problem to be solved in the present invention provides a kind of self-adaptation OMP method based on signal receiver, and its selection to atom is changed into the set of selecting specific atom, makes to reduce on its calculated amount, thereby has improved the efficient of signal receiver.

The present invention realizes goal of the invention by following technological means:

A kind of self-adaptation OMP method based on signal receiver is characterized in that, may further comprise the steps:

(1) initialization: order

u ₁=p ₁/ || p ₁|| 1, I=s, j=1, k=1 improves former word bank;

(2) atom in the former word bank is sorted:

${<R}^{K-1},{{g_r}_k}_1>\&GreaterEqual;<R^{K-1},{{g_r}_k}_2>\&GreaterEqual;...\&GreaterEqual;<R^{K-1},{{g_r}_k}_n>$

(3) son of choosing preceding I item maximum is marked, and forms set, namely

$S_k=\{{r_k}_1,{r_k}_2,{r_k}_3....{r_k}_I\}$

(4) will gather unification then:

C _k=f _k-1∪S _k

Wherein, f _K-1It is the signal indication after last projection finishes.

(5) atom of choosing is carried out orthogonalization process, by the definition of quadrature as can be known, if { β ₁, β ₂, β ₃.... β _nBe { α ₁, α ₂, α ₃.... α _nOrthogonalization after base, then can obtain:

${\mathrm{\&beta;}}_k={\mathrm{\&alpha;}}_k-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_1>}{<{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_1>}{\mathrm{\&beta;}}_1-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_2>}{<{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_2>}{\mathrm{\&beta;}}_2-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_{k-1}>}{<{\mathrm{\&beta;}}_{k-1},{\mathrm{\&beta;}}_{k-1}>}{\mathrm{\&beta;}}_{k-1}$

Identical principle, the atom of before choosing is

Make the atom after the orthogonalization be By orthogonalized definition, can obtain the expression formula of the atom after the new orthogonalization:

$u_k={g_r}_k-\frac{<{g_r}_k,u_1>}{<u_1,u_1>}{u}_1-\frac{<{g_r}_k,u_2>}{<u_2,u_2>}{u}_2-\frac{<{g_r}_k,u_{k-1}>}{<u_{k-1},u_{k-1}>}{u}_{k-1}$

(6) the signal residual error is calculated, the residual error that makes signal is γ, then can obtain its expression formula:

${\mathrm{\&gamma;}}_k=f-\underset{I\&Element;C_k}{\mathrm{\&Sigma;}}<f,u_I>u_I$

(7) restrictive condition is set: this step is by to residual error γ _kJudgement realize, if

|| γ _k‖≤σ then stops iteration, and wherein σ is the threshold value that arranges before the iteration, otherwise, change step (8);

(8) size of the last residual error of the current residual sum of judgement is if current residual error is greater than or equal to last residual error, that is:

||r _k|| ₂≥||r _k-1‖ ₂

Then initialized condition is upgraded, done following processing: j is increased by 1, I is increased s doubly, with the mathematical way expression namely be

j=j+1

j=j+1

I=j×s

Wherein s is the initial value of the I that arranges, and along with after j adds, the scope of I also will increase like this, thereby the scope of the maximum atom of I item also increases before selection, commentaries on classics step (2);

Diminishing if current residual error less than the residual error of last time, is exactly residual error, illustrating that the atom of current several maximums can satisfy the condition of decomposition, that is:

|| r _k|| ₂＜|| r _K-1‖ ₂Change step (1).

Compared with prior art, advantage of the present invention and good effect are: the present invention is based on the OMP method, itself still possesses the advantage of OMP method, improve and do not destroy this one-piece construction, compared to the MP method, it is selecting to have carried out orthogonalized processing behind the required atom of projection, and this can have bigger precision when making the sparse decomposition of the signal of back, for the follow-up signal that reconstructs has more accurately been laid good basis; When selecting atom, be not that single atom is selected, because the selection of single atom can strengthen operand, thereby influenced operation time, this algorithm is that several atoms of a maximum are selected, and then the set of atom done required subsequent treatment, like this, just can guarantee the quick of time, improve the efficient of projection; The number of atom set is not definite by artificial control, but be adaptive to signal characteristics own, after the user gives initial value to method, this method can change by judgement after the iteration by adaptive carrying out, and the process that changes is exactly an adaptive process, if initial value is suitable, just can the rarefaction signal with iteration number of times seldom; Method is used very flexible, accurately can finish the Sparse Decomposition of Signal process at short notice to the assurance of iteration thresholding, and if carry out basis for estimation with iterations, only needs to change simple parameters just can accomplish; The renewal of former word bank can liberalization, can select different former word banks well at different letters, so just can better obtain sparse resolution characteristic, save time simultaneously, and disposed a kind of former word bank at time varying signal in the invention, produce new characteristic item by it being carried out linear frequency modulation control, can better improve signal receiver efficient.

Description of drawings

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is whole-sample block scheme of the present invention.

Embodiment

Below in conjunction with accompanying drawing and preferred embodiment the present invention is done further to describe in detail.

Referring to Fig. 1 and Fig. 2, improved method is based on the OMP method, selection principle to atom in the OMP method is to get maximum, like this because the number of choosing restriction at every turn, processing speed can be relatively slow when processing comprises the very big signal of quantity of information to make the OMP method, add in the MP method, many orthogonalized steps of a step, also atom to be done normalized, these all make its big heavy discount in efficient, so restricted the application that further develops of OMP method, and follow-on algorithm is once chosen I maximum atom, the operation to atom has been become the operation of pair set, like this, optimum condition is exactly to lack the step of half than the OMP method, also can reduce naturally on the time a lot, will more be of practical significance more than using.

And at time frequency signal, I have carried out certain improvement to the former word bank of method, the former word bank of Gabor is by to the Gaussian function time shift, stretches, and obtains after the frequency displacement conversion, it is also bad to the drop shadow effect of the signal of time-frequency, therefore, this wherein, I have added a linear frequency modulation conversion to former word bank, see to be exactly that the back of signal is increased quadratic term intuitively, its quadratic term coefficient is exactly that frequency modulation is sparse, and like this, the MP algorithm after the improvement will have the good treatment effect to the signal near nature more.

The former word bank of original Gabor: $g\left(t\right)=\frac{1}{\sqrt{s}}g\left(\frac{t-u}{s}\right)\cos (\mathrm{vt}+\mathrm{\&omega;})$

The former word bank of modified Gabor: $g\left(t\right)=\frac{1}{\sqrt{s}}g\left(\frac{t-u}{s}\right)\cos (\mathrm{vt}+\mathrm{\&omega;}+\mathrm{\&beta;}{t}^2)$

Former word bank after the improvement can better be sampled to time frequency signal, and feasible signal sampling machine based on this method has better application to be worth, and can carry out sampling processing to most signals in the reality.

The present invention includes following steps:

(1) initialization: order U1=p ₁/ || p ₁‖, I=s, j=1, k=1 improves former word bank;

(2) atom in the former word bank is sorted:

$<R^{K-1},{{g_r}_k}_1>\&GreaterEqual;<R^{K-1},{{g_r}_k}_2>\&GreaterEqual;...\&GreaterEqual;<R^{K-1},{{g_r}_k}_n>$

(3) son of choosing preceding I item maximum is marked, and forms set, namely

$S_k=\{{r_k}_1,{r_k}_2,{r_k}_3....{r_k}_I\}$

(4) will gather unification then:

C _k=f _k-1∪S _k

Wherein, f _K-1It is the signal indication after last projection finishes.

(5) atom of choosing is carried out orthogonalization process, by the definition of quadrature as can be known, if { β ₁, β ₂, β ₃.... β _nBe { α ₁, α ₂, α ₃.... α _nOrthogonalization after base, then can obtain:

${\mathrm{\&beta;}}_k={\mathrm{\&alpha;}}_k-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_1>}{<{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_1>}{\mathrm{\&beta;}}_1-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_2>}{<{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_2>}{\mathrm{\&beta;}}_2-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_{k-1}>}{<{\mathrm{\&beta;}}_{k-1},{\mathrm{\&beta;}}_{k-1}>}{\mathrm{\&beta;}}_{k-1}$

Identical principle, the atom of before choosing is Make the atom after the orthogonalization be

By orthogonalized definition, can obtain the expression formula of the atom after the new orthogonalization:

$u_k={g_r}_k-\frac{<{g_r}_k,u_1>}{<u_1,u_1>}{u}_1-\frac{<{g_r}_k,u_2>}{<u_2,u_2>}{u}_2-\frac{<{g_r}_k,u_{k-1}>}{<u_{k-1},u_{k-1}>}{u}_{k-1}$

(6) the signal residual error is calculated, the residual error that makes signal is γ, then can obtain its expression formula:

${\mathrm{\&gamma;}}_k=f-\underset{I\&Element;C_k}{\mathrm{\&Sigma;}}<f,u_I>u_I$

(7) restrictive condition is set: this step is by to residual error γ _kJudgement realize, if

|| γ _k‖≤σ then stops iteration, and wherein σ is the threshold value that arranges before the iteration, and is generally all very little very little.If satisfied this condition, illustrate that Sparse Decomposition of Signal finishes, and good degree of rarefication arranged that we need proceed iteration and decompose if do not satisfy condition, and change step (8);

(8) size of the last residual error of the current residual sum of judgement is if current residual error is greater than or equal to last residual error, that is:

||r _k|| ₂≥||r _k-1‖ ₂

Then initialized condition is upgraded, done following processing: j is increased by 1, I is increased s doubly, with the mathematical way expression namely be

j=j+1

j=j+1

I=j×s

Wherein s is the initial value of the I that arranges, and along with after j adds, the scope of I also will increase like this, thereby the scope of the maximum atom of I item also increases before selection, commentaries on classics step (2);

Diminishing if current residual error less than the residual error of last time, is exactly residual error, illustrating that the atom of current several maximums can satisfy the condition of decomposition, that is:

|| r _k‖ ₂＜|| r _K-1‖ ₂This time, we only needed the continuation iteration just can finally make it satisfy the termination numerical value that we arrange, and changeed step (1).

Claims (1)

1. the self-adaptation OMP method based on signal receiver is characterized in that, may further comprise the steps:

(1) initialization: order

U1=p ₁/ || p ₁|| 1, I=s, j=1, k=1 improves former word bank;

(2) atom in the former word bank is sorted:

$<R^{K-1},{{g_r}_k}_1>\&GreaterEqual;<R^{K-1},{{g_r}_k}_2>\&GreaterEqual;...\&GreaterEqual;<R^{K-1},{{g_r}_k}_n>$

(3) son of choosing preceding I item maximum is marked, and forms set, namely

$S_k=\{{r_k}_1,{r_k}_2,{r_k}_3....{r_k}_I\}$

(4) will gather unification then:

C _k=f _k-1∪S _k

Wherein, f _K-1It is the signal indication after last projection finishes.

(5) atom of choosing is carried out orthogonalization process, by the definition of quadrature as can be known, if { β ₁, β ₂, β ₃.... β _nBe { α ₁, α ₂, α ₃.... α _nOrthogonalization after base, then can obtain:

${\mathrm{\&beta;}}_k={\mathrm{\&alpha;}}_k-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_1>}{<{\mathrm{\&beta;}}_1,{\mathrm{\&beta;}}_1>}{\mathrm{\&beta;}}_1-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_2>}{<{\mathrm{\&beta;}}_2,{\mathrm{\&beta;}}_2>}{\mathrm{\&beta;}}_2-\frac{<{\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_{k-1}>}{<{\mathrm{\&beta;}}_{k-1},{\mathrm{\&beta;}}_{k-1}>}{\mathrm{\&beta;}}_{k-1}$

Identical principle, the atom of before choosing is

Make the atom after the orthogonalization be

By orthogonalized definition, can obtain the expression formula of the atom after the new orthogonalization:

$u_k={g_r}_k-\frac{<{g_r}_k,u_1>}{<u_1,u_1>}{u}_1-\frac{<{g_r}_k,u_2>}{<u_2,u_2>}{u}_2-\frac{{{<g}_r}_k,u_{k-1}>}{<u_{k-1},u_{k-1}>}{u}_{k-1}$

(6) the signal residual error is calculated, the residual error that makes signal is γ, then can obtain its expression formula:

${\mathrm{\&gamma;}}_k=f-\underset{I\&Element;C_k}{\mathrm{\&Sigma;}}<f,u_I>u_I$

(7) restrictive condition is set: this step is by to residual error γ _kJudgement realize, if || γ _k||≤σ then stops iteration, and wherein σ is the threshold value that arranges before the iteration, otherwise, change step (8);

(8) size of the last residual error of the current residual sum of judgement is if current residual error is greater than or equal to last residual error, that is:

||r _k|| ₂≥||r _k-1‖ ₂

Then initialized condition is upgraded, done following processing: j is increased by 1, I is increased s doubly, with the mathematical way expression namely be

j=j+1

j=j+1

I=j×s

Wherein s is the initial value of the I that arranges, and along with after j adds, the scope of I also will increase like this, thereby the scope of the maximum atom of I item also increases before selection, commentaries on classics step (2);

Diminishing if current residual error less than the residual error of last time, is exactly residual error, illustrating that the atom of current several maximums can satisfy the condition of decomposition, that is:

|| r _k|| ₂＜|| r _K-1‖ ₂Change step (1).

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