CN105281780A - Variable step size regularized adaptive compressed sampling matching pursuit method - Google Patents
Variable step size regularized adaptive compressed sampling matching pursuit method Download PDFInfo
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Abstract
The invention provides a variable step size regularized adaptive compressed sampling matching pursuit method, specifically relates to a reconstruction method based on compressed sensing, and a solution aims at the prior two problems in the regularized orthogonal matching pursuit (ROMP) method. One of the problems is that the sparseness K is difficult to be obtained in reality, then the method provides that the adaptive idea of the sparse adaptive matching pursuit (SAMP) is applied in ROMP; the other problem is that once an atom which is selected in a support set will not able be deleted, then the method provides that the backtrack idea of the compressed sampling matching pursuit (CoSaMP) is applied in ROMP. In addition, the method adopts a stage orthogonal matching pursuit (StOMP) idea to set the threshold condition so as to stop the iteration, and the problem including lack of accuracy and over estimated caused by the fixed step size of the introduced SAMP is improved. The method provided by the invention greatly improves the reconstruction performance, estimated accuracy and application range of the reconstruction method based on the compressed sampling.
Description
Technical field
The present invention relates generally to compressed sensing (CompressedSensing, CS) field, particularly relates to the signal reconfiguring method field based on CS.
Background technology
Along with the develop rapidly of Internet technology, current era has entered the epoch of an information-based high speed development, and in daily life, needs and a large amount of information are come into contacts with, and comprise the identification to information, sampling, storage and transport etc.And simultaneously people to the demand of amount of information also in continuous increase, this has higher requirement just to the process of information and sampling rate etc., and traditional information processing manner is all based on nyquist sampling theorem, when acquisition of information, very high sample rate should be kept, complete the work such as the compression to a large amount of raw information, storage and transmission simultaneously again, thus cause resource to waste greatly; To hardware, higher requirement can be proposed simultaneously.So CS theory is arisen at the historic moment.The restriction of nyquist sampling theorem of CS theoretical breakthrough, can realize sampling to signal with lower sample rate, and the compression of complete pair signals while sampling, directly useless information is got rid of, then information stored and transmit, then being reconstructed accurately by being close to of the complete pair signals of reconstructing method in reconstruction end.
Can see, the reconstructing method of signal is a step important in CS theory, and its quality reconstruction directly has influence on the quality and reconstructed velocity etc. of reconstruction quality, can have influence on the application of whole CS method in the middle of reality.Up to now, Chinese scholars has done large quantifier elimination in reconstructing method, mainly contains several large classes such as greedy method, convex optimization method, combined method, statistic optimization.And greedy method for tracing is the more typical sparse signal reconfiguring method of a class, its advantage is that operand is little and be easy to realize, therefore more conventional.These class methods mainly comprise match tracing (MatchingPursuit, MP) method, orthogonal matching pursuit (OrthogonalMP, OMP) method, regularization match tracing (RegularizedOMP, ROMP) method, compression sampling match tracing (CompressedSamplingMP, CoSaMP) method and degree of rarefication Adaptive matching follow the trail of (SparseAdaptiveMP, SAMP) method etc.Wherein, because ROMP method reconstruction quality is good, its reconstruction accuracy close to convex optimization method, therefore is often used, and the time that ROMP method reconstruction signal needs is few, therefore is particularly applicable to the reconstruction of the larger signal of data volume.
ROMP method is pointed out, to obtain high reconstruction quality, iterations value should be equal with degree of rarefication K value.And degree of rarefication cannot be predicted usually in reality, if carry out certain computing at observation end to observation side to carry out the operand that compute sparse degree can increase again Sensor section.In this case, due to accurate estimation cannot be made to degree of rarefication K, reconstruction quality is thus caused to ensure.On the other hand, because ROMP adopts the method for Forward Trace to upgrade support set, atom, once be selected into support set and will forever exist, can not be deleted, lack backtracking thought, thus cause the waste of ample resources.
Based on this, the present invention is directed to ROMP Problems existing, the backtracking thought of CoSaMP and the self adaptation thought of SAMP being combined innovatively applies in ROMP, propose a kind of new variable step regularization self-adapting compressing sampling match tracing method, better applicability can be had and reach higher precision.
Summary of the invention
Goal of the invention: based on the reconstructing method of CS signal, for the two large problems that ROMP exists at present, proposes corresponding solution.
Problem one: ROMP needs the degree of rarefication K knowing signal in advance, and is often difficult to obtain degree of rarefication K in reality, therefore the present invention proposes the self adaptation thought of SAMP to be transplanted in ROMP.
Problem two: ROMP adopts the method for Forward Trace to upgrade support set, and atom is once be selected into support set and will forever exist, cannot delete, therefore the present invention proposes the backtracking thought of CoSaMP to apply in ROMP.
In addition, the present invention also adopts orthogonal matching pursuit (StageOMP, StOMP) thought stage by stage to arrange threshold condition stopping iteration, thus the inadequate and excessive estimation problem of precision that the fixed step size improving introduced SAMP brings.
Technical scheme of the present invention:
Symbol description is as follows:
Compression observation y=Φ x, wherein y is that the observation station that M × 1 is tieed up obtains vectorial, and x is the original signal that N × 1 (M<<N) is tieed up.X is not generally sparse, but can be expressed as sparse under certain transform domain Ψ, i.e. x=Ψ θ, and wherein θ is that K is sparse, is the rarefaction representation of signal x at certain transform domain.Now y=Φ Ψ θ, make A=Φ Ψ, then y=Α θ, wherein, Φ is called calculation matrix, and size is M × N; Ψ is called sparse matrix, and size is N × N; A is called sensing matrix, and size is M × N.
A kind of idiographic flow of variable step regularization self-adapting compressing sampling match tracing method is as follows:
Input:
(1) the sensing matrix A of M × N dimension;
(2) the observation vector y of M × 1 dimension;
(3) step-length S.
Export:
(1) the sparse estimation of M × N dimension
(2) the residual error r of M × 1 dimension
m.
In following flow process: r
trepresent residual error, t represents iterations,
represent empty set, J
0represent the index (row sequence number) that each iteration finds, Λ
trepresent the index (row sequence number) set (element number is that L, L and step-length S-phase are closed) of t iteration, a
jthe jth row of representing matrix A, A
t={ a
j(for all j ∈ J
0) represent and press indexed set Λ
tthe row set selected,
for value to be estimated, symbol ∪ represents set union, and <, > represent and ask inner product, and abs [] represents and asks modulus value, jth row and the residual error r of u representing matrix A
t-1the modulus value of inner product, i-th row of u (i) representing matrix A and residual error r
t-1the modulus value of inner product.
Flow process:
Step 1, initialization r
0=y,
l=S, t=1;
Step 2, calculating u=abs [A
tr
t-1] (namely calculate <r
t-1, a
j>, 1≤j≤N), select 2L maximum in u, the row sequence number j of these value corresponding A is formed set J (set of row sequence number);
Step 3, regularization: in set J, find subset J
0, meet: | u (i) |≤2|u (j) |, for all i, j ∈ J
0, select all subset J met the demands
0in there is ceiling capacity
j
0;
Step 4, make Λ
t=Λ
t-1∪ J
0, A
t=A
t-1∪ a
j(for all j ∈ J
0);
Step 5, ask y=A
tθ
tleast square solution:
Step 6, from
in select maximum absolute value L item be designated as
corresponding A
tin L row be designated as A
tL, the row sequence number of corresponding A is designated as Λ
tL, be designated as set Λ
t=Λ
tL;
Step 7, renewal residual error
Step 8, judge whether meet stop iterated conditional 1, if meet, enter step 9, if do not meet, enter step 10;
Step 9, judge whether to meet iterated conditional 2, if meet, then stop iteration, enter step 11, if do not meet, then change step-length S=S/2, L=L+S, t=t+1 and return step 2 and continue iteration;
Step 10, judge whether to meet || r
tnew||
2>=|| r
t-1||
2if meet, renewal L=L+S, t=t+1 return step 2 and continue iteration; If do not meet, then upgrade r
t=r
tnew, t=t+1, if t≤M, stops iteration entering step 11, otherwise returns step 2 and continue iteration;
Step 11, reconstruct gained
at Λ
tMthere is nonzero term at place, and its value is respectively last iteration gained successively
Above-mentioned stopping iterated conditional 1 is as follows respectively with stopping iterated conditional 2:
Stop iterated conditional 1: reconstruction signal energy difference in adjacent two stages
Stop iterated conditional 2: reconstruction signal energy difference in adjacent two stages
or
About two threshold value T in stopping iterated conditional
1and T
2value, the substantial connection of threshold value and compression goal itself and sample rate (M/N) should be considered, therefore should consider according to follow-up abundant experimental results.
As mentioned above, the backtracking thought of CoSaMP and the self adaptation thought of SAMP combine and apply in ROMP by the present invention innovatively, adopt StOMP thought that threshold condition is set and stop iteration, propose a kind of variable step regularization self-adapting compressing sampling match tracing method, greatly improve reconstruction property and the range of application in CS field.In addition, this reconstructing method goes for multiple field, such as: image procossing, and imaging of medical, channel estimating etc.
Accompanying drawing explanation
Below above-mentioned and/or additional aspect of the present invention and advantages, accompanying drawing will become obvious and easy understand in the description of embodiment, wherein:
The handling process of Fig. 1 variable step regularization self-adapting compressing sampling match tracing method.
Embodiment
Be described below in detail embodiments of the invention, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has element that is identical or similar functions from start to finish.Being exemplary below by the embodiment be described with reference to the drawings, only for explaining the present invention, and can not limitation of the present invention being interpreted as.
In describing the invention, it will be appreciated that, term " longitudinal direction ", " transverse direction ", " on ", D score, "front", "rear", "left", "right", " vertically ", " level ", " top ", " end ", " interior ", the orientation of the instruction such as " outward " or position relationship be based on orientation shown in the drawings or position relationship, only the present invention for convenience of description and simplified characterization, instead of indicate or imply that the device of indication or element must have specific orientation, with specific azimuth configuration and operation, therefore can not be interpreted as limitation of the present invention.
In describing the invention, unless otherwise prescribed and limit, it should be noted that, term " installation ", " being connected ", " connection " should be interpreted broadly, such as, can be mechanical connection or electrical connection, also can be the connection of two element internals, can be directly be connected, also indirectly can be connected by intermediary, for the ordinary skill in the art, the concrete meaning of above-mentioned term can be understood as the case may be.
Below in conjunction with accompanying drawing, 1 couple of the present invention is described further.
With reference to Fig. 1, a kind of variable step regularization self-adapting compressing sampling match tracing method, concrete implementation step is as follows:
Input:
1) the sensing matrix A of M × N dimension;
2) the observation vector y of M × 1 dimension;
3) step-length S.
Export:
1) the sparse estimation of M × N dimension
2) the residual error r of M × 1 dimension
m.
In following implementation step: r
trepresent residual error, t represents iterations,
represent empty set, J
0represent the index (row sequence number) that each iteration finds, Λ
trepresent the index (row sequence number) set (element number is that L, L and step-length S-phase are closed) of t iteration, a
jthe jth row of representing matrix A, A
t={ a
j(for all j ∈ J
0) represent and press indexed set Λ
tthe row set selected,
for value to be estimated, symbol ∪ represents set union, and <, > represent and ask inner product, and abs [] represents and asks modulus value, jth row and the residual error r of u representing matrix A
t-1the modulus value of inner product, i-th row of u (i) representing matrix A and residual error r
t-1the modulus value of inner product;
Flow process:
Implementation step:
Step 10, starts;
Step 20, initialization r
0=y,
l=S, t=1;
Step 30, calculates u=abs [A
tr
t-1] (namely calculate <r
t-1, a
j>, 1≤j≤N), select 2L maximum in u, the row sequence number j of these value corresponding A is formed set J (set of row sequence number);
Step 40, regularization: find subset J in set J
0, meet: | u (i) |≤2|u (j) |, for all i, j ∈ J
0, select all subset J met the demands
0in there is ceiling capacity
j
0;
Step 50, makes Λ
t=Λ
t-1∪ J
0, A
t=A
t-1∪ a
j(for all j ∈ J
0);
Step 60, asks y=A
tθ
tleast square solution:
Step 70, from
in select maximum absolute value L item be designated as
corresponding A
tin L row be designated as A
tL, the row sequence number of corresponding A is designated as Λ
tL, be designated as set Λ
t=Λ
tL;
Step 80, upgrades residual error
Step 90, judges whether to meet stopping iterated conditional 1, if meet, enters step 100, if do not meet, enter step 110;
Step 100, judges whether to meet iterated conditional 2, if meet, then stops iteration, enters step 160, if do not meet, then enter step 120;
Step 110, judges whether to meet || r
tnew||
2>=|| r
t-1||
2if meet, then enter step 130; If do not meet, then enter step 140;
Step 120, changes step-length S=S/2, L=L+S, t=t+1, returns step 30 and continue iteration;
Step 130, upgrades L=L+S, t=t+1, enters step 150;
Step 140, upgrades r
t=r
tnew, t=t+1;
Does step 150, judge whether t≤M? if meet, then stop iteration entering step 160, otherwise return step 30 and continue iteration;
Step 160, reconstruct gained
at Λ
tMthere is nonzero term at place, and its value is respectively last iteration gained successively
Step 170, terminates.
Wherein, iterated conditional 1 is stopped: reconstruction signal energy difference in adjacent two stages
stop iterated conditional 2: reconstruction signal energy difference in adjacent two stages
or
And about two threshold value T in stopping iterated conditional
1and T
2value, the substantial connection of threshold value and compression goal itself and sample rate (M/N) should be considered, therefore should consider according to follow-up abundant experimental results.
In the description of this specification, specific features, structure, material or feature that the description of reference term " embodiment ", " some embodiments ", " example ", " concrete example " or " some examples " etc. means to describe in conjunction with this embodiment or example are contained at least one embodiment of the present invention or example.In this manual, identical embodiment or example are not necessarily referred to the schematic representation of above-mentioned term.And the specific features of description, structure, material or feature can combine in an appropriate manner in any one or more embodiment or example.
Although illustrate and describe embodiments of the invention, those having ordinary skill in the art will appreciate that: can carry out multiple change, amendment, replacement and modification to these embodiments when not departing from principle of the present invention and aim, scope of the present invention is by claim and equivalents thereof.
Claims (7)
1. the present invention proposes a kind of variable step regularization self-adapting compressing sampling match tracing method, is specially:
The degree of rarefication K existed for regularization match tracing (ROMP) be difficult to obtain and atom once be selected into the two large problems that cannot delete, give a set of solution, and propose a kind of new reconstructing method;
The innovation that the method comprises has:
S1, ROMP need the degree of rarefication K knowing signal in advance, and are often difficult to obtain degree of rarefication K in reality, and the self adaptation thought proposing degree of rarefication Adaptive matching to follow the trail of (SAMP) applies in ROMP;
S2, ROMP adopt the method for Forward Trace to upgrade support set, and atom, once be selected into support set and will forever exist, cannot delete, proposes the backtracking thought of compression sampling match tracing (CoSaMP) to apply in ROMP;
S3, adopts orthogonal matching pursuit (StOMP) thought stage by stage to arrange threshold condition and stops iteration, the inadequate and excessive estimation problem of the precision that the fixed step size improving introduced SAMP brings.
2. a kind of variable step regularization self-adapting compressing sampling match tracing method according to claim 1, it is characterized in that, in described claim 1 for ROMP exist degree of rarefication K be difficult to obtain and atom once be selected into the two large problems that cannot delete, give a set of solution, and propose a kind of new reconstructing method and comprise:
Symbol description is as follows:
Compression observation y=Φ x, wherein y is that the observation station that M × 1 is tieed up obtains vectorial, x is the original signal that N × 1 (M < < N) is tieed up, x is not generally sparse, but can be expressed as sparse under certain transform domain Ψ, i.e. x=Ψ θ, wherein θ is that K is sparse, is the rarefaction representation of signal x at certain transform domain; Now y=Φ Ψ θ, make A=Φ Ψ, then y=Α θ, wherein, Φ is called calculation matrix, and size is M × N; Ψ is called sparse matrix, and size is N × N; A is called sensing matrix, and size is M × N;
A kind of idiographic flow of variable step regularization self-adapting compressing sampling match tracing method is as follows:
Input:
(1) the sensing matrix A of M × N dimension;
(2) the observation vector y of M × 1 dimension;
(3) step-length S;
Export:
(1) the sparse estimation of M × N dimension
(2) the residual error r of M × 1 dimension
m;
In following flow process: r
trepresent residual error, t represents iterations,
represent empty set, J
0represent the index (row sequence number) that each iteration finds, Λ
trepresent the index (row sequence number) set (element number is that L, L and step-length S-phase are closed) of t iteration, a
jthe jth row of representing matrix A, A
t={ a
j(for all j ∈ J
0) represent and press indexed set Λ
tthe row set selected,
for value to be estimated, symbol ∪ represents set union, and <, > represent and ask inner product, and abs [] represents and asks modulus value, jth row and the residual error r of u representing matrix A
t-1the modulus value of inner product, i-th row of u (i) representing matrix A and residual error r
t-1the modulus value of inner product;
Flow process:
Step 1, initialization r
0=y,
l=S, t=1;
Step 2, calculating u=abs [A
tr
t-1] (namely calculate <r
t-1, a
j>, 1≤j≤N), select 2L maximum in u, the row sequence number j of these value corresponding A is formed set J (set of row sequence number);
Step 3, regularization: in set J, find subset J
0, meet: | u (i) |≤2|u (j) |, for all i, j ∈ J
0, select all subset J met the demands
0in there is ceiling capacity
j
0;
Step 4, make Λ
t=Λ
t-1∪ J
0, A
t=A
t-1∪ a
j(for all j ∈ J
0);
Step 5, ask y=A
tθ
tleast square solution:
Step 6, from
in select maximum absolute value L item be designated as
corresponding A
tin L row be designated as A
tL, the row sequence number of corresponding A is designated as Λ
tL, be designated as set Λ
t=Λ
tL;
Step 7, renewal residual error
Step 8, judge whether meet stop iterated conditional 1, if meet, enter step 9, if do not meet, enter step 10;
Step 9, judge whether to meet iterated conditional 2, if meet, then stop iteration, enter step 11, if do not meet, then change step-length S=S/2, L=L+S, t=t+1 and return step 2 and continue iteration;
Step 10, judge whether to meet || r
tnew||
2>=|| r
t-1||
2if meet, renewal L=L+S, t=t+1 return step 2 and continue iteration; If do not meet, then upgrade r
t=r
tnew, t=t+1, if t≤M, stops iteration entering step 11, otherwise returns step 2 and continue iteration;
Step 11, reconstruct gained
at Λ
tMthere is nonzero term at place, and its value is respectively last iteration gained successively
Above-mentioned stopping iterated conditional 1 is as follows respectively with stopping iterated conditional 2:
Stop iterated conditional 1: reconstruction signal energy difference in adjacent two stages
Stop iterated conditional 2: reconstruction signal energy difference in adjacent two stages
or
About two threshold value T in stopping iterated conditional
1and T
2value, the substantial connection of threshold value and compression goal itself and sample rate (M/N) should be considered, therefore should consider according to follow-up abundant experimental results.
3., according to a kind of in claim 2 idiographic flow of variable step regularization self-adapting compressing sampling match tracing method, it is characterized in that, described step 2 and step 6 embody the backtracking thought of CoSaMP, are specially:
Step 2 and step 6 embody the backtracking thought of CoSaMP, namely first select multiple atom during each iteration, and the atom selected now in next iteration may be abandoned, therefore selected atom can be deleted in support set, are not permanent existence.
4., according to a kind of in claim 2 idiographic flow of variable step regularization self-adapting compressing sampling match tracing method, it is characterized in that, described step 3 embodies ROMP regularization thought, is specially:
Step 3 embodies ROMP regularization thought, namely 2L row (if in all inner products inadequate 2L nonzero value, all selected by the row of inner product value non-zero) of inner product maximum absolute value is first selected, and then one time is selected again by regularization standard from this 2L arranges, be the column vector that current iteration is selected; Wherein, regularization standard refers to selects the maximum of each column vector and residual error inner product absolute value can not exceed more than the twice of minimum value and maximum one group of energy.
5., according to a kind of in claim 2 idiographic flow of variable step regularization self-adapting compressing sampling match tracing method, it is characterized in that, described step 8, step 9 and step 10 embody the thought stage by stage of StOMP, are specially:
Step 8, step 9 and step 10 embody the thought stage by stage of StOMP, namely by arranging different threshold value T
1, T
2and enter the different stages, select corresponding Candidate Set, thus reach progressively close to the object of reconstruct target.
6. according to a kind of in claim 1 idiographic flow of variable step regularization self-adapting compressing sampling match tracing method, it is characterized in that, in described S1, ROMP needs the degree of rarefication K knowing signal in advance, and in reality, be often difficult to obtain degree of rarefication K, the self adaptation thought of SAMP is proposed to apply to, in ROMP, be specially:
Whole flow process embodies the self adaptation thought of SAMP, namely constantly approaches reconstruct target by newly-built step-length S, and without the need to knowing degree of rarefication K.
7. according to a kind of in claim 1 idiographic flow of variable step regularization self-adapting compressing sampling match tracing method, it is characterized in that, adopt StOMP thought that threshold condition is set in described S3 and stop iteration, inadequate and the excessive estimation problem of the precision that the fixed step size improving introduced SAMP brings, is specially:
By the stopping iterated conditional of SAMP is divided into two stages, the fixed step size of SAMP is made to be improved to variable step size, the inadequate and excessive estimation problem of the precision that the fixed step size that compensate for introduced SAMP brings; Namely stop iterated conditional 1 by differentiating successively and stop iterated conditional 2 whether to set up, thus select whether change step-length S; Can see from flow process: stop iterated conditional 1 if met simultaneously and stop iterated conditional 2, then stopping iteration; If do not meet and stop iterated conditional 1, then remaining step identical with original SAMP (namely entering " by the large step-length fast approaching reconstructed object " stage); Stop iterated conditional 1 if met and do not meet stopping iterated conditional 2, then continuing iteration (namely entering " by the little step-length Step wise approximation reconstruct target " stage) after step-length being reduced half.
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