CN102968781B - Image fusion method based on NSCT (Non Subsampled Contourlet Transform) and sparse representation - Google Patents

Abstract

The invention provides an image fusion method based on NSCT (Non Subsampled Contourlet Transform) and sparse representation. According to the image fusion method, a learning dictionary is provided for the coefficients of a low-frequency sub-band lower in sparseness, and the common and special coefficients of a source image are extracted by virtue of spare representation, so that the purpose of improving the sparseness of the low-frequency sub-band can be realized; the weight fusion are horizontally adjusted in a self-adoption manner according to the movement of the special coefficient; and the coefficient of a high-frequency directional sub-band higher in sparseness is fused through absolute value of the directional sub-band with the same dimension by a maximizing method, thus the marked features of the source image can be captured, and as a result, the fusion effect is finally improved.

Description

Based on the image interfusion method of NSCT and rarefaction representation

Technical field

The present invention relates to a kind of image interfusion method.

Background technology

In recent years, based on non-downsampling Contourlet conversion (Non-Subsampled Contourlet Transform, NSCT) with it, there is translation invariant, multiresolution, multi-direction and anisotropic image represent ability, and effectively can overcome the problem that traditional wavelet can not process 2D or more higher-dimension singularity, be used successfully to image co-registration domain variability and obtain preferably syncretizing effect.But in image co-registration problem, we wish that the image representation coefficients extracted has outstanding openness and feature retentivity, thus only need a small amount of coefficient of fusion just can obtain preferably fusion results.But, through NSCT conversion obtain image low frequency sub-band coefficient be approximately zero very limited, the low frequency sub-band information of expression image that namely can not be sparse, if directly merge to it feature being unfavorable for our extraction source image.Consider that low frequency sub-band contains the main energetic of image, determine the quality of fusion results to a great extent, so we wish the degree of rarefication by improving low frequency sub-band coefficient, to obtain more excellent fusion results.

Summary of the invention

Poor in order to overcome the low frequency sub-band coefficient degree of rarefication comprising image main energetic after prior art NSCT changes, be unfavorable for that extraction useful information carries out the deficiency merged, the invention provides a kind of image interfusion method based on NSCT and rarefaction representation, the low frequency sub-band coefficient study dictionary poor to degree of rarefication, rarefaction representation extraction source image is utilized to have and peculiar coefficient, to reach the object improving low frequency sub-band degree of rarefication, then according to the activity level self-adaptative adjustment weight fusion of peculiar coefficient; The high frequency direction sub-band coefficients higher to degree of rarefication to adopt under same yardstick directional subband absolute value and gets maximum method and merge, and to catch the notable feature in source images, finally improves syncretizing effect.

The technical solution adopted for the present invention to solve the technical problems comprises the following steps:

1 training dictionary portion:

Suppose source images through registration, have K width size to be the source images of M × N, and be denoted as I respectively ₁..., I _k.

(1.1) decompose each width training image with NSCT, through J level NSCT decompose after (J is generally 3 ~ 5 grades of decomposition), obtain 1 low frequency sub-band coefficient with individual high frequency direction sub-band coefficients, wherein l _jfor the Directional Decomposition progression under yardstick j.Wherein, training image can be source images itself, also can be the image identical with source images acquisition mode;

(1.2) initialization dictionary D ∈ R ^{n × m}, wherein, n is the size of dictionary atom, and m is the atomicity of every sub-dictionary.In order to the complexity of the mistake completeness and calculating that ensure dictionary, usually get n=64, m=256;

(1.3) to low frequency sub-band coefficient with step-length for 1, size is moving window according to extracting block from top left to bottom right, then block is stretching and be arranged in order composition matrix;

(1.4) to above-mentioned matrix K-SVD Algorithm for Training dictionary D, and this dictionary is preserved;

2 image co-registration parts:

(2.1) source images is decomposed according to the method NSCT of step (1.1);

(2.2) according to following 6 steps, source images low frequency sub-band coefficient is merged:

1. according to method in step (1.3), source images low frequency sub-band is arranged in matrix V _k, k=1 ..., K;

2. by the matrix V of institute's active image _kbe expressed as:

Wherein, α ^crepresent total rarefaction representation coefficient, it is contained in institute's active image; represent the peculiar rarefaction representation coefficient of kth width image, it is only contained in kth width source images, and 0 represents that size is the full null matrix of n × m, and D is the dictionary that step (1.4) trains.

Order,

Then (1) formula can be reduced to

V＝D′α (2)

3. in order to make α in (2) formula the most sparse, orthogonal matching pursuit (OMP) Algorithm for Solving following formula is adopted:

$\widehat{\mathrm{\α}}=\arg \underset{\mathrm{\α}}{\min }{\left|\right|\mathrm{\α}\left|\right|}_0,s.t.{\left|\right|D^{\′}\mathrm{\α}-V\left|\right|}_2^2\≤\mathrm{\ϵ}---\left(3\right)$

That is, α is obtained ^cwith

4. according to the contribution of institute's active image to fusion, low frequency sub-band coefficient is merged according to the following formula:

${\mathrm{\α}}_f={\mathrm{\α}}^C+\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\ω}}_k{\mathrm{\α}}_k^U,{\mathrm{\ω}}_k=\frac{n_k}{\underset{1\≤i\≤K}{\max }\left(n_k\right)}---\left(4\right)$

Wherein, n _irepresent the activity factor of coefficient, it has reacted the energy size of feature, i.e. significance level:

$n_i={\left|\right|{\mathrm{\α}}_i^U\left|\right|}_1---\left(5\right)$

5. fused images low frequency sub-band coefficient can be reconstructed into:

V _f＝Dα _f (6)

6. Ergodic Matrices V _f, each row in matrix are arranged in the block of size, then these blocks are put into according to the order extracted correspondence position, and to be averaged, namely the sub-band coefficients of same position to be carried out cumulative and divided by cumulative number of times, thus obtain source images low-frequency subband fusion coefficient

(2.3) according to following 2 steps, high-frequency sub-band coefficient is merged:

1. calculating source images is 2 at yardstick ^-lon directional subband information, l is 2 at yardstick ^-lthe direction number of decomposing, rule of thumb, 2≤l≤4:

$V_l(n,m)=\underset{l\≤i\≤l_j}{\mathrm{\Σ}}\left|V_{l,i}(n,m)\right|---\left(7\right)$

Wherein, V _l,i(n, m) represents at yardstick 2 ^-l, i direction, directional subband coefficient value on (n, m) location of pixels.

2. to choose under same yardstick directional subband absolute value and get maximum method and merge:

$V_{l,i}^F(n,m)=V_{l,i}^{k^{*}}(n,m),k^{*}=\underset{l\≤k\≤K}{\arg \max }{V}_l^k(n,m)---\left(8\right)$

Wherein, 1≤l≤J, 1≤i≤l _j; with represent fused images or kth respectively ^*width source images is at yardstick 2 ^-l, i direction, directional subband coefficient value on (n, m) location of pixels; k ^*represent in K width source images, at the label of the source images of l directional subband information maximization; represent the sub-band information of kth width source images on l direction, can obtain according to the definition of (7) formula.

(2.4) to the low frequency sub-band coefficient after fusion and the high-frequency sub-band coefficient after merging carry out NSCT inverse transformation, obtain final fused images F.

The invention has the beneficial effects as follows:

The present invention effectively can improve the rear image low frequency sub-band degree of rarefication of NSCT conversion: by handwriting practicing allusion quotation of going to school in NSCT territory, rarefaction representation is utilized to solve the rarefaction representation coefficient of low frequency sub-band, significantly improve the rear image low frequency sub-band degree of rarefication of NSCT conversion, be more conducive to the essential characteristic extracting image, to improve image syncretizing effect.

The more single fusion method based on NSCT and rarefaction representation of the present invention all has advantage: the degree of rarefication of more single NSCT fusion method is higher, more effectively extract characteristics of image, the fusion method of more single rarefaction representation has multiple dimensioned, multi-direction analysis ability, more meets eye-observation image mode.So the inventive method all has more excellent syncretizing effect compared with these two large class methods.

Accompanying drawing explanation

Fig. 1 extracts total and characteristic feature legend, wherein, a () is infrared radiation source image, b () is visible light source image, c () is infrared image low frequency sub-band, (d) is visible images low frequency sub-band, and (e) is infrared image low frequency sub-band characteristic feature, f () is visible images low frequency sub-band characteristic feature, (g) is infrared with visible ray low frequency sub-band common characteristic.

Fig. 2 is the fusion results of several method, and wherein, (a) is DWT method, and (b) is NSCT method, and (c) is SOMP method, and (d) is JSR method, and (e) is context of methods.

Fig. 3 is image interfusion method process flow diagram of the present invention.

Embodiment

Based on an image interfusion method for NSCT and rarefaction representation, the method mainly comprises training dictionary and image co-registration two large divisions, is described below:

1 training dictionary portion:

Suppose source images through registration, have K width size to be the source images of M × N, and be denoted as I respectively ₁..., I _k.

(1.1) decompose each width training image with NSCT, through J level NSCT decompose after, obtain 1 low frequency sub-band coefficient and individual high frequency direction sub-band coefficients, wherein l _jfor the Directional Decomposition progression under yardstick j.Wherein, training image can be source images itself, also can be the image identical with source images acquisition mode;

(1.2) initialization dictionary D ∈ R ^{n × m}, wherein, n is the size of dictionary atom, and m is the atomicity of every sub-dictionary;

(1.3) to low frequency sub-band coefficient with step-length for 1, size is moving window according to extracting block from top left to bottom right, then block is stretching and be arranged in order composition matrix;

(1.4) to above-mentioned matrix K-SVD Algorithm for Training dictionary D, and this dictionary is preserved;

2 image co-registration parts:

(2.1) source images is decomposed with NSCT in same step (1);

(2.2) according to following 5 steps, source images low frequency sub-band coefficient is merged:

1. according to method in step (3), source images low frequency sub-band is arranged in matrix V _k, k=1 ..., K;

2. by the matrix V of institute's active image _kbe expressed as:

Wherein, α ^crepresent total rarefaction representation coefficient, it is contained in institute's active image; it is only contained in a corresponding width source images to represent peculiar rarefaction representation coefficient, and 0 represents that size is the full null matrix of n × m.

Order,

Then (1) formula can be reduced to

V＝D′α (2)

3. in order to make α in (2) formula the most sparse, orthogonal matching pursuit (OMP) Algorithm for Solving following formula is adopted:

$\widehat{\mathrm{\α}}=\arg \underset{\mathrm{\α}}{\min }{\left|\right|\mathrm{\α}\left|\right|}_0,s.t.{\left|\right|D^{\′}\mathrm{\α}-V\left|\right|}_2^2\≤\mathrm{\ϵ}---\left(3\right)$

That is, α is obtained ^cwith

4. according to the contribution of institute's active image to fusion, low frequency sub-band coefficient is merged according to the following formula:

${\mathrm{\α}}_f={\mathrm{\α}}^C+\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\ω}}_k{\mathrm{\α}}_k^U,{\mathrm{\ω}}_k=\frac{n_k}{\underset{1\≤i\≤K}{\max }\left(n_k\right)}---\left(4\right)$

Wherein, n _irepresent that coefficient represents the activity factor of coefficient, it has reacted the energy size of feature, i.e. significance level:

$n_i={\left|\right|{\mathrm{\α}}_i^U\left|\right|}_1---\left(5\right)$

5. fused images low frequency sub-band coefficient can be reconstructed into:

V _f＝Dα _f (6)

6. Ergodic Matrices V _f, each row in matrix are arranged in the block of size, then these blocks are put into according to the order extracted correspondence position, and to be averaged, namely the sub-band coefficients of same position to be carried out cumulative and divided by cumulative number of times, thus obtain source images low-frequency subband fusion coefficient

(2.3) because the base of NSCT has abundant direction and shape, the notable feature in image can be caught on high frequency direction subband, as edge, linear feature and zone boundary.And these notable features all show larger modulus value on all directional subbands of same yardstick, and other non-significant characteristic coefficient modulus value are almost nil.So, according to following 2 steps, merge high-frequency sub-band coefficient:

1. calculating source images is 2 at yardstick ^-lon directional subband information:

$V_l(n,m)=\underset{l\≤i\≤l_j}{\mathrm{\Σ}}\left|V_{l,i}(n,m)\right|---\left(7\right)$

Wherein, V _l,i(n, m) represents at yardstick 2 ^-l, i direction, the directional subband coefficient value on (n, m) location of pixels.

2. to choose under same yardstick directional subband absolute value and get maximum method and merge:

$V_{l,i}^F(n,m)=V_{l,i}^{k^{*}}(n,m),k^{*}=\underset{l\≤k\≤K}{\arg \max }{V}_l^k(n,m)---\left(8\right)$

Wherein, 1≤l≤J, 1≤i≤l _j.

(2.4) to the low frequency sub-band coefficient after fusion and the high-frequency sub-band coefficient after merging carry out NSCT inverse transformation, obtain final fused images F.

Below in conjunction with drawings and Examples, the present invention is further described.

Example 1. utilizes rarefaction representation to improve NSCT low frequency sub-band degree of rarefication and extraction source image is peculiar and common characteristic example

in 1 example, dictionary learning step is as follows:

(1.1) decompose infrared with visible light source image respectively with NSCT, adopt " 9-7 " Pyramid transform and " c-d " directional filter banks, the direction number that high frequency layer is got is followed successively by 2 ⁴, 2 ³, 2 ², 2 ²;

(1.2) initialization dictionary D ∈ R ^{64 × 256};

(1.3) to low frequency sub-band coefficient with step-length for 1, size be the moving window of 8 × 8 according to extracting block from top left to bottom right, then block is stretching and be arranged in order composition matrix, infrared low frequency sub-band matrix is designated as V ₁; Visible ray low frequency sub-band matrix is designated as V ₂;

(1.4) to above-mentioned matrix K-SVD Algorithm for Training dictionary D, K-SVD algorithm permissible error ε gets conventional numerical value 0.01, and preserves this dictionary;

to low frequency sub-band rarefaction representation and extraction source image is peculiar and common characteristic step is as follows in 2 examples:

(2.1) by infrared with the low frequency sub-band matrix representation of visible light source image be:

$\left[\begin{array}{c}{V}_1\\ V_2\end{array}\right]=\left[\begin{array}{ccc}D& D& 0\\ D& 0& D\end{array}\right]\left[\begin{array}{c}{\mathrm{\α}}^C\\ {\mathrm{\α}}_1^U\\ {\mathrm{\α}}_2^U\end{array}\right]---\left(9\right)$

Wherein, α ^crepresent total rarefaction representation coefficient, it is contained in institute's active image; with represent peculiar rarefaction representation coefficient, be only contained in infrared radiation source image and visible light source image respectively, 0 represents that size is the full null matrix of 64 × 256.

Order, $V=\left[\begin{array}{c}{V}_1\\ V_2\end{array}\right],\mathrm{\α}=\left[\begin{array}{c}{\mathrm{\α}}^C\\ {\mathrm{\α}}_1^U\\ {\mathrm{\α}}_2^U\end{array}\right],D^{\′}\left[\begin{array}{ccc}D& D& 0\\ D& 0& D\end{array}\right],$

Then (4) formula can be reduced to

V＝D′α (10)

(2.2) OMP Algorithm for Solving following formula is adopted:

$\widehat{\mathrm{\α}}=\arg \underset{\mathrm{\α}}{\min }{\left|\right|\mathrm{\α}\left|\right|}_0,s.t.{\left|\right|D^{\′}\mathrm{\α}-V\left|\right|}_2^2\≤\mathrm{\ϵ}---\left(11\right)$

That is, α is obtained ^c, and

(2.3) source images common characteristic matrix V IC and the infrared image characteristic feature matrix of extraction is tried to achieve respectively with visible images characteristic feature matrix

${\mathrm{VI}}^C=D\×{\mathrm{\α}}^C,{\mathrm{VI}}_1^U=D\×{\mathrm{\α}}_1^U,{\mathrm{VI}}_2^U=D\×{\mathrm{\α}}_2^U---\left(12\right)$

(2.4) difference Ergodic Matrices with each row in matrix are arranged in the block of 8 × 8 sizes, then these blocks are put into I respectively according to the order extracted ^c, correspondence position, and to be averaged, namely the sub-band coefficients of same position to be carried out cumulative and divided by cumulative number of times, thus obtain infraredly having low frequency sub-band coefficient image I with visible images ^c, infrared image and visible images be peculiar low frequency sub-band coefficient image separately with

Fig. 1 (e)-(g) is the image reconstructed again after the peculiar and common characteristic of extraction source image low frequency sub-band coefficient respectively.The more black partial pixel value of image is more close to 0, and null value is more sparse.Can find out, original infrared image and visible images degree of rarefication poor, there is no the essential characteristic of extraction source image.And degree of rarefication of the present invention significantly improves, and to extract in infrared low frequency sub-band the feature such as distinctive roof road in distinctive personage and trees profile and visible ray low frequency sub-band, and their feature such as building wall and road of having, be more beneficial to the subsequent treatment such as fusion.

Example 2. image co-registration example of the present invention

The method that invention is proposed and tradition based on the image interfusion method of DWT and current performance comparatively superior based on NSCT image interfusion method and based on the image interfusion method SOMP of rarefaction representation and JSR Measures compare.First two method is the method based on transform domain, and latter two is the fusion method based on image area rarefaction representation.Adopt 240 × 320 sizes in experiment and pass through the infrared and visible images aimed at, the wavelet type that wherein DWT decomposes is 3 grades of db4 small echos, NSCT optimum configurations is identical with document, i.e. " 9-7 " Pyramid transform and " c-d " directional filter banks, and the direction number that high frequency layer is got is followed successively by 2 ⁴, 2 ³, 2 ², 2 ².The dictionary size of rarefaction representation is 64 × 256, ε=0.01.

image interfusion method performing step based on NSCT and rarefaction representation in this example is as follows:

dictionary learning step is identical with step in example 1, and image co-registration part steps is:

(1) decompose infrared with visible light source image respectively with NSCT, it is consistent with study part that NSCT converts parameter, i.e. employing " 9-7 " Pyramid transform and " c-d " directional filter banks, and the direction number that high frequency layer is got is followed successively by 2 ⁴, 2 ³, 2 ², 2 ²;

(2) source images low frequency sub-band coefficient is merged:

1. source is obtained by 2.1 and 2.2 steps in same example 1 infrared with visible ray common characteristic factor alpha ^c, source infrared image characteristic feature coefficient and visible images characteristic feature coefficient

2. low frequency sub-band coefficient is merged according to the following formula:

${\mathrm{\α}}_f={\mathrm{\α}}^C+\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\ω}}_k{\mathrm{\α}}_k^U,{\mathrm{\ω}}_k=\frac{n_k}{\underset{1\≤i\≤2}{\max }\left(n_k\right)}---\left(13\right)$

Wherein, n _irepresent that coefficient represents the activity factor of coefficient, it has reacted the energy size of feature, i.e. significance level:

$n_i={\left|\right|{\mathrm{\α}}_i^U\left|\right|}_1---\left(14\right)$

5. fused images low frequency sub-band coefficient can be reconstructed into:

V _f＝Dα _f (15)

6. Ergodic Matrices V _f, each row in matrix are arranged in the block of 8 × 8 sizes, then these blocks are put into according to the order extracted correspondence position, and to be averaged, namely the sub-band coefficients of same position to be carried out cumulative and divided by cumulative number of times, thus obtain source images low-frequency subband fusion coefficient

(3) high-frequency sub-band coefficient is merged:

1. solving source images at yardstick is 2 ^-lon directional subband information:

$V_l(n,m)=\underset{l\≤i\≤l_j}{\mathrm{\Σ}}\left|V_{l,i}(n,m)\right|---\left(16\right)$

Wherein, 1≤l≤4,1≤i≤l _j(l ₁=2 ⁴, l ₂=2 ³, l ₃=2 ², l ₄=2 ²).

2. to choose under same yardstick directional subband absolute value and get maximum method and merge:

$V_{l,i}^F(n,m)=V_{l,i}^{k^{*}}(n,m),k^{*}=\underset{l\≤k\≤2}{\arg \max }{V}_l^k(n,m)---\left(17\right)$

(4) to the low frequency sub-band coefficient after fusion and the high-frequency sub-band coefficient after merging carry out NSCT inverse transformation, obtain final fused images F.

Fusion results as shown in Figure 2, as seen from Figure 2, the house of DWT fusion results and surrounding scenes contrast reduction; In NSCT fusion results, still texture is unintelligible comparatively by force for trees road stereovision, and personage and house are also outstanding not; SOMP and JSR personage is comparatively outstanding, but obtains too level and smooth to the obvious area merges of the textural characteristics such as leaf; The atural objects such as railing, house, leaf and road then merge more clear by context of methods, and personage is also comparatively obvious, and continuity is good, and visual effect is best.

In order to the different fusion method of quantitative evaluation is used for performance that is infrared and visual image fusion, adopt index root mean square cross entropy RCE (Rooted Cross Entropy), Q in comparative approach herein _w, Q _eand Q _abfevaluate.Wherein, index RCE is used for evaluating the comprehensive differences between fused images and source images, the smaller the better; Q _wthe fusion mass evaluation of source images and fused images window weight, Q _eand Q _abfrespectively from local and the overall situation reflecting fused images fusion source images edge, Q ₀, Q _w, Q _abfvalue all between [0,1], more show that fusion mass is better close to 1.

The performance index of several fusion method of table 1

Table 1 is the performance index (wherein runic represents optimum desired value) of several fusion method, the data of observation table 1 can be found out, relative to the method directly merged at domain of variation (DWT and NSCT) and in the method (SOMP and JSR) of image area single scale based on rarefaction representation, not only method in this paper can be carried out multiscale analysis to source images but also can be improved the degree of rarefication of image representation coefficients further, enhance the details expressive ability of fused images, extract more useful information from source images and merged, so have more excellent syncretizing effect.

Claims (5)

1., based on an image interfusion method for NSCT and rarefaction representation, it is characterized in that comprising the steps:

Suppose source images through registration, have K width size to be the source images of M × N, and be denoted as I respectively ₁..., I _k;

(1.1) decompose each width training image with NSCT, through J level NSCT decompose after, obtain 1 low frequency sub-band coefficient and individual high frequency direction sub-band coefficients, wherein l _jfor the Directional Decomposition progression under yardstick j;

(1.2) initialization dictionary D ∈ R ^{n × m}, wherein, n is the size of dictionary atom, and m is the atomicity of every sub-dictionary;

(1.3) to low frequency sub-band coefficient with step-length for 1, size is moving window according to extracting block from top left to bottom right, then block is stretching and be arranged in order composition matrix;

(1.4) to above-mentioned matrix K-SVD Algorithm for Training dictionary D, and this dictionary is preserved;

(2.1) source images is decomposed according to the method NSCT of step (1.1);

(2.2) according to following 6 steps, source images low frequency sub-band coefficient is merged:

1. according to method in step (1.3), source images low frequency sub-band is arranged in matrix V _k, k=1 ..., K;

2. by the matrix V of institute's active image _kbe expressed as:

Wherein, α ^crepresent total rarefaction representation coefficient, it is contained in institute's active image; represent the peculiar rarefaction representation coefficient of kth width image, it is only contained in kth width source images, and 0 represents that size is the full null matrix of n × m;

Order, $V=\left[\begin{array}{c}{V}_1\\ \·\\ \·\\ \·\\ V_K\end{array}\right],$ $\mathrm{\α}=\left[\begin{array}{c}{\mathrm{\α}}^C\\ {\mathrm{\α}}_1^U\\ \·\\ \·\\ \·\\ {\mathrm{\α}}_K^U\end{array}\right],$

Then (1) formula can be reduced to

V＝D′α (2)

3. in order to make α in (2) formula the most sparse, orthogonal matching pursuit algorithm is adopted to solve following formula:

$\widehat{\mathrm{\α}}=\arg \underset{\mathrm{\α}}{\min }{\left|\right|\mathrm{\α}\left|\right|}_0,s.t.{\left|\right|D^{\′}\mathrm{\α}-V\left|\right|}_2^2\≤\mathrm{\ϵ}---\left(3\right)$

That is, α is obtained ^cwith

4. according to the contribution of institute's active image to fusion, low frequency sub-band coefficient is merged according to the following formula:

${\mathrm{\α}}_f={\mathrm{\α}}^C+\underset{i=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\ω}}_k{\mathrm{\α}}_k^U,{\mathrm{\ω}}_k=\frac{n_k}{\underset{1\≤i\≤K}{\max }\left(n_k\right)}---\left(4\right)$

Wherein, n _irepresent the activity factor of coefficient, it has reacted the energy size of feature, i.e. significance level:

$n_i={\left|\right|{\mathrm{\α}}_i^U\left|\right|}_1---\left(5\right)$

5. fused images low frequency sub-band coefficient can be reconstructed into:

V _f＝Dα _f (6)

6. Ergodic Matrices V _f, each row in matrix are arranged in the block of size, then these blocks are put into according to the order extracted correspondence position, and to be averaged, namely the sub-band coefficients of same position to be carried out cumulative and divided by cumulative number of times, thus obtain source images low-frequency subband fusion coefficient

(2.3) according to following 2 steps, high-frequency sub-band coefficient is merged:

1. calculating source images is 2 at yardstick ^-lon directional subband information, l is 2 at yardstick ^-lthe direction number of decomposing:

$V_l(n,m)=\underset{1\≤i\≤l_j}{\mathrm{\Σ}}\left|V_{l,i}(n,m)\right|---\left(7\right)$

Wherein, V _l,i(n, m) represents at yardstick 2 ^-l, i direction, directional subband coefficient value on (n, m) location of pixels;

2. to choose under same yardstick directional subband absolute value and get maximum method and merge:

$V_{1,i}^F(n,m)=V_{1,i}^{k^{*}}(n,m),k^{*}=\underset{1\≤k\≤K}{\arg \max }{V}_1^k(n,m)---\left(8\right)$

Wherein, 1≤l≤J, 1≤i≤l _j; with represent fused images or kth respectively ^*width source images is at yardstick 2 ^-l, i direction, directional subband coefficient value on (n, m) location of pixels; k ^*represent in K width source images, at the label of the source images of l directional subband information maximization; represent the sub-band information of kth width source images on l direction;

(2.4) to the low frequency sub-band coefficient after fusion and the high-frequency sub-band coefficient after merging carry out NSCT inverse transformation, obtain final fused images F.

2. the image interfusion method based on NSCT and rarefaction representation according to claim 1, is characterized in that: described J is taken as 3 ~ 5.

3. the image interfusion method based on NSCT and rarefaction representation according to claim 1, is characterized in that: described training image is source images itself or the image identical with source images acquisition mode.

4. the image interfusion method based on NSCT and rarefaction representation according to claim 1, is characterized in that: described n=64, m=256.

5. the image interfusion method based on NSCT and rarefaction representation according to claim 1, is characterized in that: described l span is 2≤l≤4.