CN105721868B - A kind of compressed sensing based image Asia nyquist sampling method - Google Patents

A kind of compressed sensing based image Asia nyquist sampling method Download PDF

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CN105721868B
CN105721868B CN201610049601.0A CN201610049601A CN105721868B CN 105721868 B CN105721868 B CN 105721868B CN 201610049601 A CN201610049601 A CN 201610049601A CN 105721868 B CN105721868 B CN 105721868B
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CN105721868A (en
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王汝言
杜阳
赵辉
罗华丰
李红兵
赵小梅
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/132—Sampling, masking or truncation of coding units, e.g. adaptive resampling, frame skipping, frame interpolation or high-frequency transform coefficient masking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/117—Filters, e.g. for pre-processing or post-processing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/134—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or criterion affecting or controlling the adaptive coding
    • H04N19/136—Incoming video signal characteristics or properties
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/134—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or criterion affecting or controlling the adaptive coding
    • H04N19/146—Data rate or code amount at the encoder output
    • H04N19/149—Data rate or code amount at the encoder output by estimating the code amount by means of a model, e.g. mathematical model or statistical model
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
    • H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock

Abstract

The present invention relates to a kind of compressed sensing based image Asia nyquist sampling methods, belong to technical field of image processing.Method includes the following steps: 1) being distributed in the feature on the limited or even a small amount of frequency sub-band in its bandwidth range mostly according to the energy in picture signal establishes two-dimentional multiband picture signal model；2) picture signal frequency spectrum is evenly dividing, and choose generating function to divide resulting each frequency spectrum sub-block, to obtain effectively indicating the translation invariant signal space of picture signal feature；3) spatial sampling scheme for being suitable for signal under the translation semigroups is established；4) spatial sampling scheme in step 3) is improved, establishes the sub- nyquist sampling scheme for being suitable for signal under the translation semigroups；5) corresponding reconfiguration scheme is established, original analog signal is reconstructed.The challenge that the sampling rate faced in current image capture device is high, sampled data output is big can be effectively relieved in the present invention.

Description

A kind of compressed sensing based image Asia nyquist sampling method
Technical field
The invention belongs to technical field of image processing, are related to a kind of compressed sensing based image Asia nyquist sampling side Method.
Background technique
Picture signal intuitive is strong, the information content is abundant, it has also become the mankind obtain and the important sources of exchange information.Number Image processing techniques is good because having many advantages, such as processing accuracy height, strong flexibility, stability, be widely used in remote sensing space flight, The fields such as biomedical, military public security, communication engineering.One prerequisite of Digital Image Processing is to obtain discrete digitized map Picture.Existing digital picture acquisition methods be all first according to nyquist sampling theorem to analog image carry out high-speed sampling, then Compressed encoding is carried out to remove redundancy to collected mass data, reduces the data volume for needing to transmit or store.This scheme is deposited The problems such as sampling rate pressure is big, serious waste of resources.These problems signal bandwidth is larger, data acquisition environment is severe, The occasions such as sampling and storage functions of the equipments are limited are particularly evident.Compressive sensing theory (Compressive sampling, CS) is prominent The limitation for having broken nyquist sampling theorem can be directly to acquire letter compared with low rate by means of the prior information that signal is sparse Useful information in number, and guarantee undistorted recovery, offer the possibility to solve the above problem.
The research about CS theory of current main-stream all concentrate on to the limited n dimensional vector n obtained after high-speed sampling into Row post-processing is not directed to the direct conversion of analog domain to information field.It really realizes and the low rate compression of analog signal is adopted Sample key is to excavate the structural information of signal to be sampled, and establishes the signal model that can describe this structural information, Jin Erjie It closes signal characteristic and designs rationally effective sampling plan.Currently, also there are some sub- nyquist samplings based on CS theory Method.Laska J N, Kirolos S, Duarte M F is waited in " Theory and implementation of an analog-to-information converter using random demodulation”【Circuits and Systems,2007.ISCAS 2007.IEEE International Symposium on.IEEE,2007:1959-1962】 Propose the random demodulation device that can be realized to the sampling of multitone signal compression.Mishali M, EldarY C are in " From theory to practice:Sub-Nyquist sampling of sparse wideband analog signals” [Selected Topics in Signal Processing, IEEE Journal of, 2010,4 (2): 375-391] propose Modulation bandwidth converter using successively to input signal mixing, filtering and low rate sampling method, realize to sparse width The sub- nyquist sampling of band signal.The program is with compression sampling effect is good, stability is good, is easy to the advantages such as hardware realization. Eldar YC is at " Compressed sensing of analog signals in shift-invariant spaces " [Signal Processing, IEEE Transactions on, 2009,57 (8): 2986-2997] combine spatial sampling and CS Theory establishes a kind of sub- nyquist sampling Framework suitable for signal under sparse translation semigroups.
In above-mentioned typical sub- nyquist sampling method, random demodulation device and modulation bandwidth converter are both for spy What different one-dimensional signal proposed, the sampling to two dimensional image signal can not be used for.And translation semigroups are a kind of comprising rich The signal space of rich signal type, and corresponding sub- nyquist sampling frame structure is simple, has stronger universality.So And the sub- nyquist sampling scheme established really suitable for signal under sparse translation semigroups is also needed according to practical application Occasion embodies the links of signal model therein, translation invariant signal space and system.Therefore, there is presently no A kind of specific method that can effectively realize to two dimensional image signal Asia nyquist sampling.
Summary of the invention
In view of this, the purpose of the present invention is to provide a kind of compressed sensing based image Asia nyquist sampling sides Method, this method initially set up a kind of most of energy that can effectively describe picture signal be often distributed it is limited in its frequency spectrum Then the two-dimentional multi-band signal model of this feature on frequency sub-band chooses the reasonable constant letter of two-dimension translational for the signal model Number space is finally applicable in by means of the sub- nyquist sampling Framework design of signal under sparse translation semigroups is specific In the sub- nyquist sampling method of two dimensional image signal.
In order to achieve the above objectives, the invention provides the following technical scheme:
A kind of compressed sensing based image Asia nyquist sampling method, it is characterised in that: the following steps are included:
1) it is distributed on the limited or even a small amount of frequency sub-band in its bandwidth range mostly according to the energy in picture signal Feature establishes two-dimentional multiband picture signal model；
2) picture signal frequency spectrum is evenly dividing, and choose generating function to divide resulting each frequency spectrum sub-block, To obtain effectively indicating the translation invariant signal space of picture signal feature；
3) spatial sampling scheme for being suitable for signal under the translation semigroups is established；
4) spatial sampling scheme in step 3) is improved, establishes the Asia for being suitable for signal under the translation semigroups Nyquist sampling scheme；
5) corresponding reconfiguration scheme is established, original analog signal is reconstructed；
In step 1), in the two-dimentional multiband picture signal model, the frequency spectrum of signal is by several positions and band It is wide can Arbitrary distribution frequency sub-band composition, which can not only effectively describe the spy of the above structure in picture signal frequency spectrum Point, and have and the comparable universality of band-limited signal model；
In step 2), if two dimension multi-band signal x (t1,t2) frequency spectrum X (f1,f2) in have N number of non-zero sub-blocks, and The bandwidth of each non-zero sub-blocks is no more than B=[B1,B2] (" [a, b] " representing matrix, similarly hereinafter), signal highest frequency are as follows:
fmax=[f1max,f2max]；
Take fp=[fp1,fp2] (wherein, fp1≥B1,fp2≥B2) it is that interval is evenly dividing its frequency spectrum, after note divides Obtained sub-block (spectrum unit) number is M, thenRemember the number of non-zero sub-blocks in M sub-block Mesh is k, then has k≤4N；
Following SPACE V is chosen as the translation invariant signal space for indicating two-dimentional multi-band signal:
Wherein, generating functioni∈{1, 2 ..., M },WithI-th of sub-block is respectively indicated along centre frequency both horizontally and vertically, T1And T2(T1≤1/2fp1,T2 ≤1/2fp2) it is respectively shift factor both horizontally and vertically,Indicate signal f (t1,t2) in i-th of sub-block Basic functionOn weight coefficient sequence；f(t1,t2) it is only intended to elemental characteristic in description collections, Without actual physical meaning；
In step 3), by multi-band signal x (t1,t2) it is respectively f by cutoff frequencyp=[fp1,fp2] low pass filtered Wave device h1(-t1,-t2) and centre frequency be respectivelyBandwidth is all fp=[fp1,fp2] bandpass filtering Device group { hi(-t1,-t2)}I=2 .., M, then to the output of corresponding M path filter with T=[T1,T2],(T1≤1/2fp1,T2≤1/ 2fp2) it is to carry out uniform sampling respectively in the period, it can establish for multi-band signal x (t1,t2) spatial sampling scheme, obtain x (t1,t2) in M group basic functionOn weight coefficient sequenceWherein, Wherein, set of basis functionIt is with { αi(t1,t2)}I=1,2 ..., MFor generating function, sampling period T1 And T2For obtained by shift factor, in the spatial sampling scheme, each sample circuit is along sampling rate both horizontally and vertically To be respectively 1/T1And 1/T2, therefore, the global sample rate of whole system in both directions is respectively M/T1And M/T2；
In step 4), in order to improve the spatial sampling scheme in step 3), obtain being suitable for translation invariant sky Between lower signal sub- nyquist sampling scheme, consider that its samples resulting M group sequence firstBase Description in claim 3, signal x (t1,t2) it is divided after non-zero sub-blocks number k≤4N, and general picture signal is equal Meet feature of most of Energy distribution on a small number of frequency sub-band, i.e. N < < M, thus, for arbitrary m and M dimensional vector d [m] [n]=[d1[m][n],d2[m][n],...,dM[m][n]]TIt is k- sparse, therefore, according to compressed sensing Theory, can be to vector d [m] [n] and a compression observing matrix Φp×MIt is multiplied, the vector compression of M dimension to p is tieed up, wherein Φp×M For the observing matrix for meeting related request in compressed sensing, p >=2k, corresponding result is denoted as:
Y [m] [n]=Φp×MD [m] [n], in which:
Y [m] [n]=[y1[m][n],...,yp[m][n]]T, d [m] [n]=[d1[m][n],...,dM[m][n]]T；
By above-mentioned processing, although can be by sample sequenceP group is compressed to by M group, but Whole system is still M/T along global sampling rate both horizontally and vertically1And M/T2, in order to really realize the Ya Nai to signal Qwest's sampling, directly to obtain compressed sequence compared with low rateCompression can be observed link Φp×MAnalog end (before sampling) is moved forward to, with analog filter group { hi(-t1,-t2)}I=1,2 .., MMerge, obtains p group and add Filter after power combination, is denoted as { si(-t1,-t2)}I=1,2 .., p, which is to use Φp×MTo analog filter group {hi(-t1,-t2)}I=1,2 .., MIt is weighted combination, physical relationship is as follows:
s(-t1,-t2)p×1=Φp×Mh(-t1,-t2)M×1, wherein
h(-t1,-t2)=[h1(-t1,-t2),h2(-t1,-t2),...,hM(-t1,-t2)]T, s (- t1,-t2)=[s1(- t1,-t2),...,sp(-t1,-t2)]T；
By the program, sample sequence can be directly obtainedAnd per sampling rate all the way not Under the premise of change, sample circuit number is compressed to the road p by the road M, thus, the global sample rate of the system in both directions also drops For p/T1And p/T2, to realize real low rate compression sampling；
In step 5), it is contemplated that in actual samples often collected sequence be all it is time-limited, i.e., space is adopted The resulting M group sample sequence of sample prescription caseWith the resulting p group sample sequence of compression sampling schemeIn any one group be it is time-limited, therefore, which meets survey more Vector (MMV) model is measured, d [m] [n], Jin Erchong can be solved by y [m] [n] by means of the restructing algorithm in MMV model Structure original analog signal, wherein y [m] [n]=Φp×MD [m] [n], y [m] [n]=[y1[m][n],...,yp[m][n]]T, d [m] [n]=[d1[m][n],...,dM[m][n]]T。
The beneficial effects of the present invention are: the frequency spectrum characteristic of present invention combination compressive sensing theory and picture signal is established A kind of sub- nyquist sampling scheme suitable for picture signal.When the broader bandwidth of signal, when spectrum occupancy is lower, this Scheme can in the case where the Location-Unknown of specific non-zero frequency range with far below Nyquist rate sample rate to signal into The sampling of row Lossless Compression.For alleviating, sampling rate present in existing image capturing and transmitting equipment is high, stores and presses for this The problems such as power is big, serious waste of resources is of great significance.Further, since every in this programme all the way all can be by means of existing filter Involve sample circuit to realize, therefore also has and be easy to hard-wired advantage.
Detailed description of the invention
In order to keep the purpose of the present invention, technical scheme and beneficial effects clearer, the present invention provides following attached drawing and carries out Illustrate:
Fig. 1 is the frequency spectrum of two-dimentional multi-band signal；
Fig. 2 is that the frequency spectrum of two-dimentional multi-band signal divides；
Fig. 3 is the spatial sampling and reconstruct of picture signal；
Fig. 4 is that the spatial sampling of picture signal and compression are observed；
Fig. 5 is the sub- nyquist sampling of picture signal；
Fig. 6 is system schematic；
Fig. 7 is system design flow figure.
Specific embodiment
Below in conjunction with attached drawing, a preferred embodiment of the present invention will be described in detail.
Fig. 7 is system design flow figure, and Fig. 6 is system schematic, as shown, the method for the invention includes following step It is rapid:
One, signal model is established
In practice, the energy of most of signals is not to have on the optional frequency component within the scope of its whole bandwidth point Cloth, but be focusing only on limited or even a small amount of frequency sub-band.In order to effectively describe this structural information, while in view of closing at present On the basis of the realization of the more mature theoretical result and hardware device of sampling is built upon to signal spectral analysis, the present invention will Picture signal is modeled as two-dimentional multi-band signal model.It is described in detail below:
If signal x (t1,t2) be real value time domain continuous signal, maximum bandwidth both horizontally and vertically is respectively f1max And f2max.If frequency spectrum X (f1,f2) supported collection is disjoint by several, position can the frequency sub-band of Arbitrary distribution constitute, and The bandwidth of each frequency sub-band is no more than [B1,B2], then claim signal x (t1,t2) it is two-dimentional multi-band signal.
In the multi-band signal model, the number of non-zero frequency range, width and position are all arbitrary in signal spectrum, because This, which can not only effectively describe energy in signal and often be distributed in this structural information on limited frequency, and have with The comparable universality of band-limited signal model.The spectrum diagram of this two-dimentional multi-band signal model is as shown in Figure 1.Wherein f1maxWith f2maxHighest frequency both horizontally and vertically is respectively indicated, dash area indicates the non-zero sub-blocks with Energy distribution, corresponding Effective frequency range in image.In the signal model, number, the size and location of non-zero sub-blocks are all arbitrary, therefore, the mould Type has stronger universality.
Two, sub- nyquist sampling scheme is established
1. choosing translation invariant signal space for signal
Effectively to represent the structural information of this two-dimentional multi-band signal, and then designs effective sub- Nyquist and adopt Sample prescription case, it is necessary first to choose suitable translation invariant signal space for it.And in order to choose translation invariant signal space, it is first First consider to carry out classifying rationally to its frequency spectrum.For having N number of non-zero sub-blocks, highest frequency f in frequency spectrummax=[f1max, f2max] two-dimentional multi-band signal x (t1,t2), it is assumed that its frequency spectrum X (f1,f2) in the bandwidth of each non-zero sub-blocks be no more than B= [B1,B2].It takesThe frequency spectrum is evenly dividing for interval, then is obtainedIt is non-zero that k=4N are up in a sub-block.Spectrum diagram after division is shown in figure 2。
One group of basic function is chosen respectively to divide M obtained sub-block, then a signal space V, the signal space can be obtained It can accurately indicate that arbitrary highest frequency is no more than fmax=[f1max,f2max] Two Dimensional Band-limited Signal.If with SPACE V come table Show the above-mentioned two-dimentional multi-band signal with N number of non-zero sub-blocks, is then up to k=4N group right and wrong in corresponding M group projection sequence Zero.It therefore, then can be by means of believing under sparse translation semigroups if signal space V is translation invariant, and k < < M Number sub- Nyquist scheme realize the sub- nyquist sampling to this two-dimentional multi-band signal.And most of images in practice Energy is all concentrated on a small amount of frequency sub-band in its frequency spectrum in signal, that is, meets k < < M, therefore, establishes sub- nyquist sampling One of critical issue of scheme is exactly to find suitable translation invariant signal space V.
Two-dimensional nyquist sampling theorem is pointed out, is no more than B=[B for bandwidth1,B2] band-limited signal fL(t1,t2), It can be by with T=[T1,T2](1/T1≥2B1,1/T2≥2B2) it is that interval carries out the obtained sample sequence f of uniform samplingL(mT1, nT2) Perfect Reconstruction, corresponding reconstruction formula are as follows:
By the reconstruction formula it is found that with sin c (t1/T1)sin c(t2/T2)(1/T1≥2B1,1/T2≥2B2) nucleation of making a living The translation semigroups that function generates can indicate that arbitrary frequency is no more than B=[B1,B2] band-limited signal.
Similarly, B=[B is no more than for arbitrary bandwidth1,B2], centre frequency isTwo dimension band communication Number fB(t1,t2), can by with(1/T1≥2B1,1/T2≥ 2B2) kernel function translation semigroups generated are made a living into indicate:
Due to multi-band signal x (t1,t2) frequency spectrum X (f1,f2) it is divided after resulting M sub-block be all band limit or band logical , therefore, take fp=[fp1,fp2](fp1≥B1,fp2≥B2), T=[T1,T2]=[1/2fp1,1/2fp2], and set the center frequency of M sub-block Rate is respectively f=[f1,f2,...,fM], wherein Then following generation kernel function is chosen respectively for M sub-block:
Can be obtained can indicate that arbitrary highest frequency is no more than fmax=[f1max,f2max], the band of each non-zero sub-blocks Width is no more than B=[B1,B2] two-dimentional multi-band signal M weight translation semigroups V:
Wherein,Table Show the generating function of base band sub-block,WithI-th of sub-block is respectively indicated along centre frequency both horizontally and vertically, T1And T2 (T1≤1/2fp1,T2≤1/2fp2) it is respectively shift factor both horizontally and vertically,Indicate signal f (t1, t2) in the basic function of i-th of sub-blockOn weight coefficient sequence；f(t1,t2) it is only intended to description collection Elemental characteristic in conjunction, no actual physical meaning.
2. establishing spatial sampling scheme
In order to establish the sub- nyquist sampling scheme for being suitable for signal under translation invariant signal space V, it is necessary first to set Meter is suitable for the spatial sampling scheme of such signal, and designs such spatial sampling scheme, it is necessary first to which one kind can obtain Signal x (t to be sampled1,t2) in the set of basis function { α of SPACE Vi(t1-mT1,t2-nT2)}m,n∈, i=1,2 ..., the power system on M Number Sequence { di[m][n]}m,n∈, i=1,2 ..M method.
Bandwidth is no more than B=[B it can be seen from the reconstruction formula of the band-limited signal shown in formula (1)1,B2] band-limited signal fL(t1,t2) with βL(t1,t2)=sin c (t1/T1)sin c(t2/T2),(1/T1≥2B1,1/T2≥2B2) for generating function institute Basic function { the β of the translation semigroups of generationL(t1-mT1,t2-nT2)}m,n∈On weight coefficient sequence be that the band-limited signal exists The value f at corresponding momentL(mT1,nT2)。
Similarly, bandwidth is no more than B=[B it can be seen from (2)1,B2], centre frequency isBand communication Number fB(t1,t2) with(1/T1≥2B1,1/ T2≥2B2) be generating function translation semigroups generated basic function { βB(t1-mT1,t2-nT2)}m,n∈On weight coefficient Sequence is value f of the bandpass signal at the corresponding momentB(mT1,nT2)。
Therefore, by multi-band signal x (t1,t2) it is respectively f by cutoff frequencyp=[fp1,fp2] low-pass filter and Centre frequency is respectivelyBandwidth is fp=[fp1,fp2] bandpass filter group, then to the corresponding road M The output of filter is with T=[T1,T2]=[1/2fp1,1/2fp2] it is that interval carries out uniform sampling respectively, x (t can be obtained1,t2) In M group basic function { αi(t1-mT1,t2-nT2)}m,n∈, i=1,2 ..., the weight coefficient sequence { d on Mi[m][n]}m,n∈, i=1, 2,..M。
According to the above analysis, for multi-band signal x (t1,t2), it takes Spatial sampling scheme as shown in Figure 3 can be established.In Fig. 3,h1(-t1,-t2) and { hi(-t1,- t2)}I=2 ..., MRespectively indicating cutoff frequency isLow-pass filter and centre frequency be respectivelyBandwidth isBandpass filter group.Due to passing through { hi(-t1,-t2)}I=1,2 .., MFiltering is simultaneously After sampling, weight coefficient sequence of the original signal on corresponding M group basic function can be directly obtained In the spatial sampling scheme, each sample circuit is respectively 1/T along sampling rate both horizontally and vertically1And 1/T2, because This, the global sample rate of whole system in both directions is respectively M/T1And M/T2。
3. establishing sub- nyquist sampling scheme
For the two-dimentional multi-band signal x (t with N number of non-zero sub-blocks1,t2), frequency spectrum X (f1,f2) by withIt is non-zero that be up to k=4N is a in resulting M sub-block after dividing for interval, on corresponding M group basic function Weight coefficient sequenceIn be up to k group be non-zero, i.e., for arbitrary m and n, M dimensional vector d [m] [n]=[d1[m][n],d2[m][n],...,dM[m][n]]TIt is k- sparse.Therefore, spatial sampling that can be shown in Fig. 3 On the basis of, to the resulting sparse sequence of samplingIncrease by a compression observation link Φp×M, with reality Now to sequenceCompression.Concrete structure schematic diagram is as shown in Figure 4.However, knot shown in Fig. 4 In structure, compression observation link Φp×MIt is to by with M/T1And M/T2It is obtained after high-speed sampling for whole-sample rate What sample sequence carried out, it can not really realize the useful information directly acquired in analog end with low sampling rate in signal.Therefore, Structure shown in Fig. 4 need to be further improved.Compression observation link in Fig. 4 is moved into analog end, and and analog filter Group { hi(-t1,-t2)}I=1,2 .., MMerge, the Ya Nai for being really suitable for simulating two-dimensional multi-band signal as shown in Figure 5 can be obtained Qwest's sampling plan.In Fig. 5, s (- t1,-t2)p×1=Φp×Mh(-t1,-t2)M×1, 2k≤p < M, Φp×MIndicate compression sense Observing matrix in knowing, h (- t1,-t2)=[h1(-t1,-t2),h2(-t1,-t2),...,hM(-t1,-t2)]T.According to this structure, It only need to be by signal x (t1,t2) pass through p filter { si(-t1,-t2)}I=1,2 .., p, then withFor sampling Interval carries out uniform sampling to the output of each filter respectively, can be realized with lower global sampling rate to original signal into The sampling of row Lossless Compression.The p group sample sequence of output is expressed asAnd enable y [m] [n] =[y1[m][n],y2[m][n],...,yp[m][n]]T, then the projection sequence of sample sequence and signal on M group basic function is full The following relationship of foot:
The function that structure shown in Fig. 5 is realized can be regarded as first will be more after division by the filter of special designing with p Band signal x (t1,t2) M sub-block carry out p time combination, obtain p combined result, then only to p combine after signal into The sampling of row low rate.It is reduced by the road M to p since the structure will sample number under conditions of guaranteeing that often sampling rate is constant all the way Road, therefore, global sampling rate is by original M/T1And M/T2It is down to p/T1And p/T2.According to compressive sensing theory, to guarantee Enough by sample sequenceAccurate Reconstruction goes out original input signal, need to there is p >=2k.Therefore, image spectrum The number of middle non-zero sub-blocks is fewer, and required sampling number p is fewer, and corresponding overall situation sample rate is lower.In addition, in this configuration, most Whole global sample rate is determined by the number and bandwidth of non-zero sub-blocks in original image signal spectrum, and depends no longer on original signal most High-frequency, and to can be priori unknown for the position of non-zero sub-blocks.
Three, design reconfiguration scheme
For the two-dimentional multi-band signal x (t with N number of non-zero sub-blocks1,t2), due to according to the scheme in the present invention Only being no more than k=4N in M sub-block of gained after dividing to its frequency spectrum is non-zero, and therefore, the signal is in set of basis functionOn M group projection sequenceIn be up to K group is non-zero, i.e., the M n dimensional vector n d [m] [n] being made of the M group projection sequence meets the joint sparse that joint sparse degree is k Structure.Since sequence collected in actual samples is all time-limited, i.e. sequence di[m][n]|i∈{1,...,M}And sequences yi[m] [n]|i∈{1,...,p}Be it is time-limited, therefore, measurement model described in formula (5) meets measures vector (Multiple more MeasurementVectors, MMV) model, d [m] can be solved by y [m] [n] by means of the restructing algorithm in MMV model [n]。
The reconstruction of MMV model can be expressed as how from measurement value matrix Y ∈M×rIn solve with joint sparse knot The signal value matrix X ∈ of structureN×r:
Y=ΦM×NX (6)
Wherein, ΦM×NFor observing matrix in compressed sensing.Specific solve can be converted into following optimization problem:
Min | I (X) |, s.t.Y=ΦM×NX (7)
Wherein, | I (X) | indicate the joint sparse degree of X.Therefore, it can be realized by means of common optimization algorithm and MMV asked The solution of topic.
Fig. 6 gives the entire structural schematic diagram sampled with reconstruct of the invention, and Fig. 7 gives the stream of entire design process Cheng Tu.
Finally, it is stated that preferred embodiment above is only used to illustrate the technical scheme of the present invention and not to limit it, although logical It crosses above preferred embodiment the present invention is described in detail, however, those skilled in the art should understand that, can be Various changes are made to it in form and in details, without departing from claims of the present invention limited range.

Claims (1)

1. a kind of compressed sensing based image Asia nyquist sampling method, it is characterised in that: the following steps are included:
1) feature being distributed in mostly according to the energy in picture signal on the limited or even a small amount of frequency sub-band in its bandwidth range Establish two-dimentional multiband picture signal model；
2) picture signal frequency spectrum is evenly dividing, and choose generating function to divide resulting each frequency spectrum sub-block, thus Obtain effectively indicating the translation invariant signal space of picture signal feature；
3) spatial sampling scheme for being suitable for signal under the translation semigroups is established；
4) spatial sampling scheme in step 3) is improved, establishes the Ya Naikui for being suitable for signal under the translation semigroups This special sampling plan；
5) corresponding reconfiguration scheme is established, original analog signal is reconstructed；
In step 1), in the two-dimentional multiband picture signal model, the frequency spectrum of signal is equal by several positions and bandwidth Can Arbitrary distribution frequency sub-band composition, which can not only effectively describe the above structure feature in picture signal frequency spectrum, and And have and the comparable universality of band-limited signal model；
In step 2), if two dimension multi-band signal x (t1,t2) frequency spectrum X (f1,f2) in there are N number of non-zero sub-blocks, and it is each non- The bandwidth of zero sub-block is no more than B=[B1,B2] (" [a, b] " representing matrix, similarly hereinafter), signal highest frequency are as follows:
fmax=[f1max,f2max]；
Take fp=[fp1,fp2] (wherein, fp1≥B1,fp2≥B2) it is that interval is evenly dividing its frequency spectrum, note obtains after dividing Sub-block (spectrum unit) number be M, thenThe number of non-zero sub-blocks is in M sub-block of note K then has k≤4N；
Choose such as down spaceAs the translation invariant signal space for indicating two-dimentional multi-band signal:
Wherein, generating function WithI-th of sub-block is respectively indicated along centre frequency both horizontally and vertically, T1And T2(T1≤1/2fp1,T2≤1/2fp2) Shift factor respectively both horizontally and vertically,Indicate signal f (t1,t2) in the basic function of i-th of sub-blockOn weight coefficient sequence, l2Indicate square can and sequence space, that is, belong to the sequence in the space Be square can sum, correspondence then indicates hereinf(t1,t2) it is only intended to elemental characteristic in description collections, Without actual physical meaning；
In step 3), by multi-band signal x (t1,t2) it is respectively f by cutoff frequencyp=[fp1,fp2] low-pass filter h1(- t1,-t2) and centre frequency be respectivelyBandwidth is all fp=[fp1,fp2] bandpass filter group { hi(- t1,-t2)}I=2 .., M, then to the output of corresponding M path filter with T=[T1,T2],(T1≤1/2fp1,T2≤1/2fp2) it is the period Uniform sampling is carried out respectively, can be established for multi-band signal x (t1,t2) spatial sampling scheme, obtain x (t1,t2) in M group Basic functionOn weight coefficient sequenceIts In, wherein set of basis functionIt is with { αi(t1,t2)}I=1,2 ..., MFor female letter Number, sampling period T1And T2For obtained by shift factor, in the spatial sampling scheme, each sample circuit is along horizontal and vertical side To sampling rate be respectively 1/T1And 1/T2, therefore, the global sample rate of whole system in both directions is respectively M/T1With M/T2；
In step 4), in order to improve the spatial sampling scheme in step 3), obtain being suitable under translation semigroups The sub- nyquist sampling scheme of signal considers that it samples resulting M group sequence firstLetter Number x (t1,t2) it is divided after non-zero sub-blocks number k≤4N, and general picture signal is all satisfied most of Energy distribution few Feature on number frequency sub-band, i.e. N < < M, thus, for arbitrary m andM dimensional vector d [m] [n]=[d1[m] [n],d2[m][n],...,dM[m][n]]TIt is k- sparse, it therefore, can be to vector d [m] [n] according to compressive sensing theory With a compression observing matrix Φp×MIt is multiplied, the vector compression of M dimension to p is tieed up, wherein Φp×MIt is wanted to meet correlation in compressed sensing The observing matrix asked, p >=2k, corresponding result are denoted as:
Y [m] [n]=Φp×MD [m] [n], in which:
Y [m] [n]=[y1[m][n],...,yp[m][n]]T, d [m] [n]=[d1[m][n],...,dM[m][n]]T；
By above-mentioned processing, although can be by sample sequenceP group, but entire system are compressed to by M group System is still M/T along global sampling rate both horizontally and vertically1And M/T2, in order to really realize the sub- Nyquist to signal Sampling, directly to obtain compressed sequence compared with low rateLink Φ is observed into compressionp×MIt moves forward to Analog end, that is, before sampling, with analog filter group { hi(-t1,-t2)}I=1,2 .., MMerge, the filter after obtaining p group weighted array Wave device, is denoted as { si(-t1,-t2)}I=1,2 .., p, which is to use Φp×MTo analog filter group { hi(-t1,- t2)}I=1,2 .., MIt is weighted combination, physical relationship is as follows:
s(-t1,-t2)p×1=Φp×Mh(-t1,-t2)M×1, wherein
h(-t1,-t2)=[h1(-t1,-t2),h2(-t1,-t2),...,hM(-t1,-t2)]T, s (- t1,-t2)=[s1(-t1,- t2),...,sp(-t1,-t2)]T；
By the program, sample sequence can be directly obtainedAnd constant per sampling rate all the way Under the premise of, sample circuit number is compressed to the road p by the road M, thus, the global sample rate of the system in both directions is also reduced to p/T1And p/T2, to realize real low rate compression sampling；
In step 5), it is contemplated that often collected sequence is all time-limited, the i.e. resulting M of spatial sampling scheme in actual samples Group sample sequenceWith the resulting p group sample sequence of compression sampling scheme In any one group be it is time-limited, therefore, which meets measures vector (MMV) models, energy more It is enough to be solved d [m] [n] by means of the restructing algorithm in MMV model by y [m] [n], and then reconstruct original analog signal, wherein y [m] [n]=Φp×MD [m] [n], y [m] [n]=[y1[m][n],...,yp[m][n]]T, d [m] [n]=[d1[m][n],..., dM[m][n]]T。
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