CN103886625A - Point cloud data sparse representation method based on compressed sensing - Google Patents

Abstract

The invention provides a point cloud data sparse representation method based on compressed sensing. Under the premise of ensuring certain precision, massive point cloud data is compressed, thus the sparsity of the point cloud data is greatly raised, and a good foundation is laid for point cloud data compression and reconstruction based on compressed sensing. The method comprises the steps of (1) point cloud data normalization, (2) over-complete dictionary sparse representation based on a K-SVD algorithm, (3) normalized point cloud data observation, transmission and storage, (4) point cloud data reconstruction based on l1 norm minimization, and (5) normalized point cloud data recovery.

Description

A kind of cloud data rarefaction representation method based on compressed sensing

Technical field

The invention belongs to the technical field of three dimensional point cloud compressed encoding, relate to particularly a kind of cloud data rarefaction representation method based on compressed sensing.

Background technology

Along with 3-D scanning technology develops rapidly, cloud data becomes very important class data in multi-medium data gradually.Scanning device of today can efficiently obtain mass cloud data discrete, distribution at random and represent object, and therefore cloud data Efficient Compression, coding become one of study hotspot gradually.The main goal in research of cloud data compression is in the situation that retaining as far as possible original model geometric feature, reduces the size of data file, makes cloud data can store more fast and propagate under finite bandwidth.Although many scholars are devoted to compression and the reconstruction of complicated cloud data, how in the situation that not reducing point cloud model geometric properties, cloud data are compressed and is one and has more challenging work.

Scattered point cloud data compression method mainly contains two kinds at present: the compression method based on grid and the compression method based on point.The former will first set up the triangle gridding of cloud data, then the maximum method of the tri patch of same vertices is vowed and counts after angle, compression and maximum boundary error etc., with corresponding self-defined threshold, accepts or rejects, and grid is simplified.Compression method compression effectiveness based on grid is relatively good, but builds grid, especially builds the work that mass data grid is a complicated and time consumption, and efficiency is low, and there is no fixing threshold value Criterion of Selecting, and compression effectiveness has certain randomness.Compression method based on point is to calculate corresponding Discrete geometry information according to the spatial topotaxy of a cloud, as equalization point apart from value, bounding box count, uniform grid center, curvature etc., according to quantity of information, a cloud is simplified to processing.Compression method based on point is directly simplified a cloud, and efficiency is higher, but the loss of packed data in details and feature is difficult to avoid be even difficult to control.

The people such as Donoho, Candes has proposed a kind of new acquisition of information guiding theory in recent years, be compressed sensing (Compressive Sensing, CS), this theory is pointed out: for signal sparse under transform domain, can utilize optimization method to carry out Exact Reconstruction by generating a small amount of data with the observing matrix of the non-uniform relation of transform-based.This theory utilizes the sparse characteristic of signal the sampling process based on Shannon/Nyquist theorem to be converted into the observation process of observing matrix, thereby the sampling rate of data does not depend on signal bandwidth, but the structure of signal and content, and the quality of the sparse property of signal is to utilize compressed sensing signal to be carried out to one of key factor of compression reconfiguration quality good or not.Therefore the compression that, this theory is cloud data provides a kind of brand-new thinking and direction.

Consider the characteristic of the discrete distribution of cloud data, can make the scattered point cloud data to a certain extent can rarefaction based on crossing the rarefaction representation method of complete dictionary.Sparse signal representation theory based on crossing complete dictionary can be thought under the condition of reconstruct original signal as far as possible, utilizes complete redundancy base to replace traditional orthogonal basis, and this is crossed complete redundancy functions set and conventionally chooses by the method for study.Therefore, the rarefaction representation of signal is mainly contained two aspects, and one is the sparse coding of signal, and another was the training of complete dictionary.

How finding a suitable dictionary D is to study a question in the hot topic of carrying out rarefaction representation based on the complete dictionary of mistake in recent years.Also there is kinds of schemes about crossing choosing of complete dictionary: a kind of is the dictionary that direct utilization has been constructed, such as steerable small echo, curvelets small echo etc.Another kind method is to select by the dictionary of parameter adjustment, under restriction on the parameters, to generate dictionary.

Dictionary training method occurs more late as a kind of method of dictionary design, the main benefit brought of study dictionary be trained dictionary can be in training process the signal of the many reality of self-adaptation, and Chinese scholars has also proposed many more effective dictionary training algorithms.The earliest for rarefaction representation, the main contributions of MOD algorithm is its simple dictionary updating strategy to the optimal direction method (MOD, Method of Optimal Directions) that the people such as Engan proposed in 2000.Generally, MOD only needs the iteration of a small amount of number of times just can restrain, more effective generally, but this method needs the contrary of compute matrix in solution procedure, its complexity is higher, therefore, scholar's afterwards research fundamental purpose is to have introduced some more practical methods in order to reduce time complexity.

On the basis of K-Means algorithm, the people such as Michal Aharon have proposed again K-SVD and have crossed complete dictionary training algorithm, K-SVD algorithm is very flexible, can with the optimum atom searching algorithm of common Its Sparse Decomposition, as MP, OMP, BP, FOCUSS, is combined with, and it is as a dictionary training algorithm, convergence is that it obtains the newly guarantee of the good dictionary of energy.K-SVD algorithm upgrades the redundant dictionary that obtains being best suited for sample set by continuous training, obtain owing to upgrading self-adaptation by training, signal can decompose according to own special excellent architectural feature in redundant dictionary, i.e. the sparse property that the redundant dictionary that training renewal obtains can better be excavated signal.Therefore this method takes K-SVD algorithm to carry out cloud data to carry out rarefaction representation, thereby reaches the priori conditions of compressed sensing.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of cloud data rarefaction representation method based on compressed sensing is provided, and it compresses, makes the degree of rarefication of cloud data significantly to improve, is the good basis that cloud data compresses and reconstruction is established based on compressed sensing mass cloud data under the prerequisite that ensures certain precision.

Technical solution of the present invention is: this cloud data rarefaction representation method based on compressed sensing, comprises the following steps:

(1) cloud data normalization;

(2) the complete dictionary rarefaction representation of the mistake based on K-SVD algorithm;

(3) observation of normalization cloud data, transmits and stores;

(4) cloud data based on l1 Norm minimum is rebuild;

(5) normalization cloud data recovers.

Because this method is before doing sparse solving to cloud data, first cloud data is done to pretreatment operation, it is the normalization of cloud data, and the complete dictionary training method of mistake based on rarefaction representation, with traditional complete dictionary (as FFT, DCT, small echo, Gabor dictionary) to compare be to extract its feature according to training signal adaptively, thereby there is stronger rarefaction representation ability, thereby under the prerequisite that ensures certain precision, mass cloud data is compressed, the degree of rarefication of cloud data is significantly improved, for the cloud data based on compressed sensing compresses and rebuilds the good basis of establishing.

Embodiment

This cloud data rarefaction representation method based on compressed sensing, comprises the following steps:

(1) cloud data normalization;

(2) the complete dictionary rarefaction representation of the mistake based on K-SVD algorithm;

(3) observation of normalization cloud data, transmits and stores;

(4) cloud data based on l1 Norm minimum is rebuild;

(5) normalization cloud data recovers.

Because this method is before doing sparse solving to cloud data, first cloud data is done to pretreatment operation, it is the normalization of cloud data, and the complete dictionary training method of mistake based on rarefaction representation, with traditional complete dictionary (as FFT, DCT, small echo, Gabor dictionary) to compare be to extract its feature according to training signal adaptively, thereby there is stronger rarefaction representation ability, thereby under the prerequisite that ensures certain precision, mass cloud data is compressed, the degree of rarefication of cloud data is significantly improved, for the cloud data based on compressed sensing compresses and rebuilds the good basis of establishing.

Adopt in step (1) least-squares algorithm to carry out plane equation matching to sheet unit, by planar process to sheet unit normal direction is estimated, so that follow-up cloud data is standardized; Point cloud in sheet unit is carried out to geometric transformation, make the sheet unit with similar geometry characteristic numerically there is equally certain similarity.

Calculate the sheet unit of cloud data by formula (1), (2):

Point converges and is combined into

sheet unit barycenter is

point p _jk nearest neighbor burst S _jfor:

$S_j=\left\{p_{j_k}\right|{p_j}_k\∈P,{\left|\right|p_{j_k}-{\stackrel{\‾}{P}}_j\left|\right|}_2^2\≤\mathrm{\δ}\}---\left(1\right)$

By barycenter

the direction vector that points to the central point of k nearest neighbor sheet unit is

with the angle of fit Plane be β,

with the normal direction simulating

angle is α,

with

inner product be:

in the time of ρ > 0, the normal direction n direction model outside that expression simulates, does not adjust the normal direction simulating, in the time of < 0, and the normal direction n direction model inside that expression simulates, to normal direction, n adjusts, to normal direction

carry out inversion operation;

The regularization transformation matrix of cloud data sheet unit is:

normMat _j=T _j*R _j (2)

Wherein T _jfor building translation transformation matrix, R according to center-of-mass coordinate _jfor rotation matrix.

Preferably, step (4) comprises step by step following:

(1) establish D ∈ R ^{n × K}, y ∈ R ⁿ, x ∈ R ^k,

wherein, D is former over-complete dictionary of atoms, and y represents training signal, the rarefaction representation coefficient vector that x is training signal, and Y is M training signal set, the solution vector set that X is Y, R ⁿrepresent n dimensional signal collection, calculate by formula (3):

$\min \left\{{\left|\right|y_i-{\mathrm{Dx}}_i\left|\right|}_2^2\right\}s.t.\&ForAll;i,{\left|\right|x_i\left|\right|}_0\&le;T_0,i=\mathrm{1,2},...,M---\left(3\right)$

Wherein, T ₀for the upper limit of nonzero component number in rarefaction representation coefficient;

(2) D is carried out to iteration training, establish d _kfor the k column vector of the former word bank D that will upgrade, now the decomposed form of set of signals is formula (4):

$\begin{array}{c}{\left|\right|Y-\mathrm{DX}\left|\right|}_F^2=\left|\right|(Y-{\mathrm{\&Sigma;}}_{j\&NotEqual;k}{d}_j{x}_T^j)-d_k{x}_T^k{\left|\right|}_F^2\\ ={\left|\right|E_k-d_k{x}_T^k\left|\right|}_F^2\end{array}---\left(4\right)$

By svd, upgrade by column dictionary, produce new dictionary

then according to new dictionary

the sparse coefficient that must make new advances, and iteration renewal, until convergence.

Preferably, step (5) is rebuild cloud data by formula (9), (10):

$\hat{x}=\arg {\min \left|\right|x\left|\right|}_{1}s.t.{\left|\right|\widetilde{\mathrm{\&Phi;}}x-y\left|\right|}_2\&le;\&Element;---\left(9\right)$

$\widehat{p^{\&prime;}}=D\hat{x}---\left(10\right)$

Wherein

for the sparse coefficient reconstruction result of normalization cloud data under dictionary D,

Then to the normalization cloud data of rebuilding

do contravariant and bring the cloud data that obtains reconstruction

Describe embodiment of the present invention below in detail.

1) cloud data standardized method

Cloud data due to its space be scattered distribute characteristic, do not have obvious sparse property, can not directly utilize compressed sensing correlation theory to compress, rebuild.Therefore the method that, the present invention utilizes K-SVD to cross complete dictionary is carried out rarefaction representation to cloud data.But original scattered point cloud data does not have good similarity, directly utilize K-SVD to cross complete dictionary training algorithm and can not obtain good rarefaction representation result.Therefore, in order to make cloud data excessively can have better degree of rarefication under complete dictionary, the present invention is first to the scattered point cloud data processing of standardizing, make different parts, but the cloud data with similar geometry character can numerically have higher similarity, thereby reach the object that improves cloud data internal similarity, and then improve the rarefaction representation effect of cloud data.

By k nearest neighbor cluster, make the quantity of the point of every can be consistent, but can not ensure that the sheet unit with geometric similarity numerically also has similarity.

In order to address the above problem, consider that k nearest neighbor clustering algorithm is that the dispersion point cloud with similar geometry characteristic is carried out to cluster, according to a character of cloud k nearest neighbor cluster result, the normal direction of sheet unit internal point has high similarity, therefore the present invention adopts least-squares algorithm to carry out plane equation matching to sheet unit, by planar process to sheet unit normal direction is estimated, so that the normalization of follow-up cloud data.

If scattered point set

scattered point set after cutting apart can be expressed as

s _jbe j subset, the element in set is all the distance ordered categorization according to element and cluster centre.For subset S _jin normal direction n, the normal direction of trying to achieve by least square can because concrete numerical value difference cause towards difference.For same model, the inconsistent meeting of the normal direction of adjacent sheet unit causes surface gradient to change inconsistent in normal orientation projection, therefore, need to carry out consistance adjustment to a direction for cloud normal direction, makes normal direction between adjacent sheet unit towards can be identical.

Conventionally do not have mathematical method can solve the positive negative sense problem of normal, calculate normal orientation by principal component analysis (PCA) and there is ambiguity yet, cannot carry out consistance adjustment to the normal direction of whole cloud data collection.The present invention adopt a kind of for barycenter the point cloud normal direction method of adjustment in cloud data inside.

Set up an office to converge and be combined into

, sheet unit barycenter is

point p _jk nearest neighbor burst S _jfor:

$S_j=\left\{p_{j_k}\right|{p_j}_k\&Element;P,{\left|\right|p_{j_k}-{\stackrel{\&OverBar;}{P}}_j\left|\right|}_2^2\&le;\mathrm{\&delta;}\}---\left(1\right)$

If by barycenter

the direction vector that points to the central point of k nearest neighbor sheet unit is

if

with the angle of fit Plane be β,

with the normal direction simulating angle is α, note

with

inner product be:

due to barycenter at point cloud model inside, direction vector

all the time direction model outside, and barycenter with the angle β scope of fit Plane 180 ° of 0 < β <, therefore, in the time of ρ > 0, represent the normal direction n direction model outside simulating, without the normal direction simulating is adjusted, in the time of ρ < 0, represent the normal direction n direction model inside simulating, need normal direction n to adjust, to normal direction

carry out inversion operation.

After sheet unit is carried out to normal estimation, the present invention carries out geometric transformation to the some cloud in sheet unit, makes the sheet unit with similar geometry characteristic numerically have equally certain similarity, for follow-up cloud data rarefaction representation is prepared.

First build translation transformation matrix T according to center-of-mass coordinate _j, by translation transformation matrix by the S of sheet unit _jpoint move near true origin.Pass through aforesaid operations, in cloud data, the data similarity of adjacent some units can increase, for uniform point cloud model, the situation that even there will be all data points to overlap completely, this can make to improve greatly the similarity between data in the time carrying out rarefaction representation.In fact, only can not maximize the similarity of numerical value between sheet unit by translation, due to the sheet unit normal direction of apart from each other towards difference, although cause thering is similar geometrical property, but there is larger difference on concrete data value, therefore in order to eliminate the difference of this respect, passing through after translation transformation the S of k nearest neighbor sheet unit _jbarycenter

be positioned at true origin, the normal direction n of its approximate evaluation, for make each k nearest neighbor sheet unit towards identical, to sheet unit do rotational transform make all units towards all with z axle in the same way, establish rotation matrix and be respectively R _j, the regularization transformation matrix of cloud data sheet unit is:

normMat _j=T _j*R _j (2)

Can make all units of k nearest neighbor burst result be distributed near true origin by above-mentioned transformation matrix, and the normal direction of each burst is all towards z axle, this will make the sheet unit on geometric properties with similarity in a cloud coordinate values, also to have certain similarity, and this has represented to provide good basis for follow-up cloud data rarefaction.

2) the rarefaction representation method of cloud data

2006, the people such as Michal Aharon proposed K-SVD algorithm on the basis of summing up K means clustering algorithm.It is by realizing the training of the complete dictionary of original mistake under sample in iterative process, constantly adjusts the atom in former word bank by Its Sparse Decomposition coefficient, the over-complete dictionary of atoms that final acquisition more can effecting reaction signal characteristic.K-SVD algorithm upgrades the redundant dictionary that obtains being best suited for sample set by continuous training, obtain owing to upgrading self-adaptation by training, signal can decompose the sparse property that can better excavate signal according to own special excellent architectural feature in redundant dictionary.Signal can decompose according to own special excellent architectural feature in redundant dictionary, i.e. the sparse property that the redundant dictionary that training renewal obtains can better be excavated signal.

Be normalized cloud data to be tried to achieve to it cross complete dictionary for problem solved by the invention, thereby obtain its rarefaction representation.By 1) described in cloud data standardized algorithm, made cloud data burst even, and the dimension of every a slice is all identical, and there is similar geometrical property.

If scattered point set

normalization cloud data is P ', and the scattered point set after cutting apart can be expressed as s _jbe j subset, element in set is all the distance ordered categorization according to element and cluster centre, after normalization, make can numerically there is high similarity in the sheet unit geometrically with similarity, therefore train to upgrade using the cloud data S set after normalization as the training set of crossing complete dictionary and obtain redundant dictionary, thereby better excavate the sparse property of cloud data, also for the cloud data compression based on compressed sensing is laid a good foundation.

Cloud data based on K-SVD is crossed complete dictionary training algorithm and can be realized in two steps.First, establish D ∈ R ^{n × K}, y ∈ R ⁿ, x ∈ R ^k,

wherein, D is former over-complete dictionary of atoms, and y represents training signal, the rarefaction representation coefficient vector that x is training signal, and Y is M training signal set, the solution vector set that X is Y, R ⁿrepresent n dimensional signal collection.The target that the first step of K-SVD algorithm will reach is:

$\min \left\{{\left|\right|y_i-{\mathrm{Dx}}_i\left|\right|}_2^2\right\}s.t.\&ForAll;i,{\left|\right|x_i\left|\right|}_0\&le;T_0,i=\mathrm{1,2},...,M---\left(3\right)$

Wherein, T ₀for the upper limit of nonzero component number in rarefaction representation coefficient, next former word bank D is carried out to iteration training.If d _kfor the k column vector of the former word bank D that will upgrade, now the decomposed form of set of signals can be expressed as:

$\begin{array}{c}{\left|\right|Y-\mathrm{DX}\left|\right|}_F^2=\left|\right|(Y-{\mathrm{\&Sigma;}}_{j\&NotEqual;k}{d}_j{x}_T^j)-d_k{x}_T^k{\left|\right|}_F^2\\ ={\left|\right|E_k-d_k{x}_T^k\left|\right|}_F^2\end{array}---\left(4\right)$

By svd, upgrade by column dictionary, finally produce new dictionary

then according to new dictionary

the sparse coefficient that must make new advances, and iteration renewal, until convergence.

3) application of cloud data rarefaction representation

Consider that original scattered point cloud data P numerically possesses any sparse property hardly, adopt the method for the invention, original point cloud P is standardized and obtains the result P ' after its normalization, for cloud data, the present invention has obtained the complete dictionary of mistake of cloud data, the theory of sparse signal representation is pointed out, natural sign can convert to carry out rarefaction representation by certain, therefore, cloud data can carry out rarefaction representation under complete transform-based excessively, be P '=Dx, x is that this signal is at the rarefaction representation of crossing under complete dictionary transform domain, consider measure equation y=Φ P ', and P ' can rarefaction representation, be P '=Dx, have

$y={\mathrm{\&Phi;P}}^{\&prime;}=\mathrm{\&Phi;Dx}=\widetilde{\mathrm{\&Phi;}}x---\left(5\right)$

Wherein

for the matrix of M × N, be called as sensing matrix, y can be regarded as sparse signal x about measuring matrix

measured value.If at this moment

meet the equidistant condition of constraint, can carry out reconstruct sparse signal x by solving minimum l0 norm problem (5-4).Compression for cloud data is rebuild, and is actually solving following problem:

$\hat{x}=\arg \min {\left|\right|x\left|\right|}_{0}s.t.\widetilde{\mathrm{\&Phi;}}x=y---\left(7\right)$

Wherein,

measure matrix Φ and utilize gaussian random matrix to observe, by the rarefaction representation that can obtain cloud data P ' that solves to (7) problem

can be further by crossing complete dictionary D by following formula Accurate Reconstruction original point cloud

But, be a NP-hard problem in essence for the problem solving of (7), in the exhaustive x of needs, nonzero value is all

plant and arrange possibility, thereby cannot solve [9].Given this, researchist has proposed to try to achieve the algorithm of suboptimum solution for solving of this problem, mainly refer to l ₁norm minimum, common solution is to utilize l ₁norm substitutes l ₀norm.Therefore the present invention transfers solving of following problem to for solving of (7) problem:

$\hat{x}=\arg \min {\left|\right|x\left|\right|}_{1}s.t.\widetilde{\mathrm{\&Phi;}}x=y---\left(8\right)$

Consider reconstructed error, the problems referred to above are converted to following minimum l the most at last ₁solving of norm problem:

$\hat{x}=\arg {\min \left|\right|x\left|\right|}_{1}s.t.{\left|\right|\widetilde{\mathrm{\&Phi;}}x-y\left|\right|}_2\&le;\&Element;---\left(9\right)$

By to the solving of problem (9), can obtain the sparse coefficient reconstruction result of normalization cloud data under dictionary D

therefore the normalization cloud data of rebuilding

can be obtained by following formula:

$\widehat{p^{\&prime;}}=D\hat{x}---\left(10\right)$

Because standardized method of the present invention has been introduced geometric transformation, therefore for the normalization cloud data of rebuilding

need to do contravariant and bring the cloud data that obtains reconstruction

Consider k nearest neighbor clustering algorithm based on Euclidean distance the cluster later stage can because around cluster point quantity rareness not, cause producing the excessive sheet unit of some radiuses, therefore, we ignore the excessive sheet unit of part radius in the coalescent fruit of k nearest neighbor, to avoid this type of impact of sheet unit on result.In follow-up work, we can do relevant optimization to the clustering algorithm of cloud data, avoid producing similar unit.

Method of the present invention can be applied in the middle of the compression and process of reconstruction of cloud data compressive sensing theory, and has good reconstructed results.

The above; it is only preferred embodiment of the present invention; not the present invention is done to any pro forma restriction, any simple modification, equivalent variations and modification that every foundation technical spirit of the present invention is done above embodiment, all still belong to the protection domain of technical solution of the present invention.

Claims (5)

1. the cloud data rarefaction representation method based on compressed sensing, is characterized in that: comprise the following steps:

(1) cloud data normalization;

(2) the complete dictionary rarefaction representation of the mistake based on K-SVD algorithm;

(3) observation of normalization cloud data, transmits and stores;

(4) cloud data based on l1 Norm minimum is rebuild;

(5) normalization cloud data recovers.

2. the cloud data rarefaction representation method based on compressed sensing according to claim 1, it is characterized in that: in step (1), adopt least-squares algorithm to carry out plane equation matching to sheet unit, by planar process to sheet unit normal direction is estimated, so that the normalization of follow-up cloud data; Point cloud in sheet unit is carried out to geometric transformation, make the sheet unit with similar geometry characteristic numerically there is equally certain similarity.

3. the cloud data rarefaction representation method based on compressed sensing according to claim 2, is characterized in that: the sheet unit of calculating cloud data by formula (1), (2):

Point converges and is combined into

sheet unit barycenter is

point p _jk nearest neighbor burst S _jfor:

$S_j=\left\{p_{j_k}\right|{p_j}_k\&Element;P,{\left|\right|p_{j_k}-{\stackrel{\&OverBar;}{P}}_j\left|\right|}_2^2\&le;\mathrm{\&delta;}\}---\left(1\right)$

By barycenter

the direction vector that points to the central point of k nearest neighbor sheet unit is

with the angle of fit Plane be β,

with the normal direction simulating

angle is α,

with

inner product be:

in the time of ρ > 0, the normal direction n direction model outside that expression simulates, does not adjust the normal direction simulating, in the time of < 0, and the normal direction n direction model inside that expression simulates, to normal direction, n adjusts, to normal direction

carry out inversion operation;

The regularization transformation matrix of cloud data sheet unit is:

normMat _j=T _j*R _j (2)

Wherein T _jfor building translation transformation matrix, R according to center-of-mass coordinate _jfor rotation matrix.

4. the cloud data rarefaction representation method based on compressed sensing according to claim 3, is characterized in that: step (2) comprises step by step following:

(1) establish D ∈ R ^{n × K}, y ∈ R ⁿ, x ∈ R ^k,

wherein, D is former over-complete dictionary of atoms, and y represents training signal, the rarefaction representation coefficient vector that x is training signal, and Y is M training signal set, the solution vector set that X is Y, R ⁿrepresent n dimensional signal collection, calculate by formula (3):

$\min \left\{{\left|\right|y_i-{\mathrm{Dx}}_i\left|\right|}_2^2\right\}s.t.\&ForAll;i,{\left|\right|x_i\left|\right|}_0\&le;T_0,i=\mathrm{1,2},...,M---\left(3\right)$

Wherein, T ₀for the upper limit of nonzero component number in rarefaction representation coefficient;

(2) D is carried out to iteration training, establish d _kfor the k column vector of the former word bank D that will upgrade, now the decomposed form of set of signals is formula (4):

$\begin{array}{c}{\left|\right|Y-\mathrm{DX}\left|\right|}_F^2=\left|\right|(Y-{\mathrm{\&Sigma;}}_{j\&NotEqual;k}{d}_j{x}_T^j)-d_k{x}_T^k{\left|\right|}_F^2\\ ={\left|\right|E_k-d_k{x}_T^k\left|\right|}_F^2\end{array}---\left(4\right)$

By svd, upgrade by column dictionary, produce new dictionary

then according to new dictionary the sparse coefficient that must make new advances, and iteration renewal, until convergence.

5. the cloud data rarefaction representation method based on compressed sensing according to claim 4, is characterized in that: step (5) is rebuild cloud data by formula (9), (10):

$\hat{x}=\arg {\min \left|\right|x\left|\right|}_{1}s.t.{\left|\right|\widetilde{\mathrm{\&Phi;}}x-y\left|\right|}_2\&le;\&Element;---\left(9\right)$

$\widehat{p^{\&prime;}}=D\hat{x}---\left(10\right)$

Wherein

for the sparse coefficient reconstruction result of normalization cloud data under dictionary D,

Then to the normalization cloud data of rebuilding

do contravariant and bring the cloud data that obtains reconstruction