CN104915937A - Quick single-lens calculating imaging method based on frequency domain matrix decomposition - Google Patents

Abstract

The invention provides a quick single-lens calculating imaging method based on frequency domain matrix decomposition. In a frequency domain, a frequency domain matrix of a to-be-solved blurred image is disassembled into linear combination of a series of bases. Image restoration calculation is performed on each base and bases corresponding to obtained clear images are saved. Then a new blurred image is also disassembled into linear combination of a series of bases and a final image restoration effect can be obtained through the bases of the obtained clear images. According to the invention, multiple iterative optimization processes in a prior image restoration algorithm are saved and the method is a novel breakthrough of the image restoration field. Required calculation time is reduced substantially and requirement for real time performance of single-lens calculation imaging can be met generally.

Description

Quick simple lens based on frequency domain matrix decomposition calculates formation method

Technical field

The present invention is mainly concerned with digital image processing field, refers in particular to a kind of quick simple lens based on frequency domain matrix decomposition and calculates formation method.

Background technology

At present, slr camera plays more and more important effect with advantages such as the image quality of its high definition, the selection of abundant camera lens, fast response speed, remarkable manual abilities in daily life.But for making up geometric distortion and the aberration of eyeglass in single anti-camera lens, improve image quality further, the design of single anti-camera lens is day by day complicated, even comprises dozens of independently optical device.Complicated camera lens, while raising image quality, also can increase the volume and weight of camera lens undoubtedly, also cause the cost of camera lens greatly to improve.The increase of camera lens volume and weight brings inconvenience to the routine use of user, and the raising of the cost also single oppositely large area user of inconvenience is promoted the use of.Therefore, eliminate eyeglass aberration as far as possible, while increasing image quality, how to reduce camera lens cost, make it more light, also become one of important need of current slr camera design.In recent years, along with the fast development of image restoration technology, the methods such as image deblurring are more and more ripe, the eyeglass of some elimination aberration and Modified geometrical distortion in camera lens can calculate camera work by deblurring etc. and replace, therefore, the research direction that the combination of simple lens imaging (as shown in Figure 2) and image restoration technology one of also becoming that slr camera designs gradually is new.

Current simple lens is calculated to be and as existing problem is, even if estimated fuzzy core corresponding to simple lens, the process of trying to achieve picture rich in detail still needs successive ignition, and that expends is chronic.Become the form of matrix multiple under the convolution algorithm of image restoration can be transformed into frequency domain, can calculated amount be reduced to a certain extent, but still be difficult to meet the real-time demand that simple lens is calculated to be picture.Therefore, proposing one simple lens calculating more fast formation method, reach real time imagery, is that simple lens is calculated to be picture urgent problem.

Summary of the invention

Calculate imaging algorithm for existing simple lens and need successive ignition optimizing process, expend time in length, is difficult to meet the problem that simple lens is calculated to be the real-time demand of picture, and the present invention proposes a kind of quick simple lens based on frequency domain matrix decomposition and calculates formation method.Under frequency domain, the frequency domain matrix-split of blurred picture to be solved is become the linear combination of a series of base, image restoration calculating is carried out to each base, and preserve the base of the corresponding picture rich in detail obtained, then for new blurred picture, it is split into equally the linear combination of a series of base, directly can obtain final image restoration effect by the base of obtained picture rich in detail.Image Restoration Algorithm based on matrix decomposition eliminates the successive ignition optimizing process in conventional images restoration algorithm, and be the full new breakthrough in image restoration field, required computing time greatly reduces, and substantially can meet the real-time demand that simple lens is calculated to be picture.

Technical scheme of the present invention is,

Quick simple lens based on frequency domain matrix decomposition calculates a formation method, comprises the following steps:

S1: blurred picture y under time domain and corresponding fuzzy core k is transformed into frequency domain, obtains the corresponding spectral matrix Y of blurred picture and the spectral matrix K of fuzzy core;

S2: by a series of basis representation Y=α of spectral matrix Y ₁h ₁₊α ₂h ₂+ ... + α _nh _n; Wherein: the base of spectral matrix choose mode: with the central point of spectral matrix for initial point, spectral matrix is divided into the identical straight-flanked ring of the multiple width equal with the number of base by number according to base from the inside to the outside successively, size and the spectral matrix of each base are in the same size, innermost matrix ring is set to the first matrix ring successively to the matrix ring of outermost, second matrix ring ... n-th matrix ring, first each for innermost matrix ring pixel is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₁; Then each pixel of the second matrix ring is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₂; According to the method the like, finally obtain all bases; The factor alpha of linear combination _inamely be with frequency domain matrix Y in base H _ithat corresponding a part of numerical value.

S3: for each base H of Y _i, in conjunction with fuzzy core K, adopt the non-blind convolution algorithm under frequency domain to carry out deblurring, obtain corresponding picture rich in detail base X _i; The method applied in the present invention is the non-blind convolved image restoration algorithm based on L2 norm, and algorithm main flow is as follows:

Blurred picture y can be expressed as the convolution y=x*k of picture rich in detail x and fuzzy core k, if based on the thought of Maximize, image restoration problem can be expressed as:

x＝arg max _xP(x|y)∝P(y|x)P(x) (1)

Wherein, x represents the picture rich in detail of finally trying to achieve; Y represents known blurred picture; P (x|y) represents known blurred picture, obtains the probability that picture rich in detail is x; If represent known picture rich in detail, obtain the probability that corresponding blurred picture is y; P (x) represents the known prior probability of original picture rich in detail.

Suppose noise Gaussian distributed, and variance is η, then can be expressed as:

$P\left(y\right|x)\∝e^{-\frac{1}{2{\mathrm{\η}}^2}{||x-C_{f}y||}^2}---\left(2\right)$

Wherein, P (y|x), if represent known picture rich in detail, obtains the probability that corresponding blurred picture is y, and the process obtaining blurred picture by picture rich in detail is interpreted as and with the addition of noise, so this probability is approximately the Gaussian distribution that variance is η c _ffor the convolution matrix of N × N.

Suppose a series of filtering g of image prior _krepresent, and image is little as much as possible to the reaction of priori filtering, then image prior is expressed as:

$P\left(x\right)=e^{-{\mathrm{\α\Σ}}_{i,k}\mathrm{\ρ}(g_{i,k}*x)}---\left(3\right)$

Wherein, P (x) represents the known prior imformation of picture rich in detail, also can represent by similar probability distribution; Horizontal direction be filtered into g _x=[1-1]; Vertical direction be filtered into g _y=[1-1] ^t; ρ represents priori function; g _i,krepresent the kth filtering for i-th pixel.

Go the logarithmic form of formula (1), (2), (3), then obtain the objective function of image restoration:

${||y-C_{f}x||}^2+\mathrm{\ω}\underset{i,k}{\Σ}\mathrm{\ρ}(g_{i,k}*x)---\left(4\right)$

Wherein ω=α η ².Get Gaussian image priori, and establish ρ (z)=| z| ².To formula (4) differentiate, and make derivative be zero, then can obtain Ax=b, wherein solve under Ax=b being transformed into frequency domain, can obtain:

$X(v,\mathrm{\ω})=\frac{K(v,\mathrm{\ω})*Y(v,\mathrm{\ω})}{|K(v,\mathrm{\ω}){|}^2+{\mathrm{\ω\Σ}}_k|G_k(v,\mathrm{\ω}){|}^2}---\left(5\right)$

Formula (5) is the non-blind convolved image restoration algorithm net result based on L2 norm under frequency domain, and wherein v and ω represents the coordinate under frequency domain,

S4: because the base X corresponding with picture rich in detail _iby base H corresponding to blurred picture _iobtained by deblurring algorithm, obtain X _iprocess carried out deblurring.So for blurred picture y new under time domain ₁with the fuzzy core k of correspondence ₁, be transformed into frequency domain, obtain corresponding spectral matrix Y ₁and K ₁.For the spectral matrix Y of new blurred picture ₁, be split into the linear combination Y of base equally ₁=α ₁' H ₁+ α ₂' H ₂+ ... + α _n' H _n, then corresponding picture rich in detail energy direct representation is

X=α ₁' X ₁+ α ₂' X ₂+ ... + α _n' X _n, obtained picture rich in detail is transformed into time domain again.The mode of choosing of the base of new blurred picture is the same with the mode of choosing of the base of blurred picture in step 2, and what the image under frequency domain is forwarded to time domain adopts is ifft2 function in Matlab.

Advantageous Effects of the present invention:

The present invention is based on simple lens and calculate imaging system, the matrix multiple of frequency domain hypograph restoration algorithm is split, propose a kind of simple lens based on frequency domain matrix decomposition and calculate formation method, fundamentally eliminate conventional images restoration algorithm successive ignition optimizing process, directly by tried to achieve base X _iwith corresponding linear combination coefficient α _ibe added by being multiplied and obtain final picture rich in detail, required computing time greatly reduces, and can meet the real-time demand that simple lens is calculated to be picture, this method all has very important significance at image procossing and camera design field.

Accompanying drawing explanation

Fig. 1 be the corresponding base of frequency domain matrix choose mode;

Fig. 2 is simple lens imaging schematic diagram;

Fig. 3 is the quick simple lens calculating formation method process flow diagram based on frequency domain matrix decomposition;

Fig. 4 is test set data;

Fig. 5 is the spectral matrix of blurred picture and fuzzy core;

Fig. 6 is the schematic diagram of blurred picture spectral matrix base;

Fig. 7 is experimental result comparison diagram;

Embodiment

Below, by the invention will be further described with specific embodiment by reference to the accompanying drawings.

As shown in Figure 3, a kind of simple lens based on frequency domain matrix decomposition that the present embodiment provides calculates formation method, comprises the steps:

Step one: the blurred picture getting picture rich in detail as shown in Figure 4, fuzzy core and correspondence.And blurred picture and fuzzy core are transformed into frequency domain by the ifft2 function in Matlab, the spectral matrix obtained is as shown in Figure 5.

Step 2: by a series of basis representation Y=α of spectral matrix Y ₁h ₁+ α ₂h ₂+ ... + α _nh _nthe mode of choosing of the base of spectral matrix as shown in Figure 1, Fig. 1 is to be decomposed into the linear combination of three bases, with the central point of spectral matrix for initial point, spectral matrix is divided into the identical straight-flanked ring of three width by number according to base from the inside to the outside successively, and size and the spectral matrix of each base are in the same size, first each for innermost matrix ring pixel is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₁, then each for the matrix ring of centre pixel is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₂, finally each for the matrix ring of outermost pixel is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₃.In other case study on implementation, for the base of different number, also according to the method, finally obtain all bases.In concrete enforcement, the number of the base of spectral matrix elects n=3 as, and as shown in Figure 1, the schematic diagram of the base obtained as shown in Figure 6 for selection mode.

Step 3: for each base H of Y _i, in conjunction with fuzzy core K, adopt the non-blind convolved image restoration algorithm based on L2 norm to carry out deblurring computing, and the restoration result X that will finally obtain _ipreserve.Algorithm main flow is as follows:

Blurred picture y can be expressed as the convolution y=x*k of picture rich in detail x and fuzzy core k, if based on the thought of Maximize, image restoration problem can be expressed as:

x＝arg max _xP(x|y)∝P(y|x)P(x) (1)

Wherein, x represents the picture rich in detail of finally trying to achieve; Y represents known blurred picture; P (x|y) represents known blurred picture, obtains the probability that picture rich in detail is x; If represent known picture rich in detail, obtain the probability that corresponding blurred picture is y; P (x) represents the known prior probability of original picture rich in detail.

Suppose noise Gaussian distributed, and variance is η, then can be expressed as:

$P\left(y\right|x)\∝e^{-\frac{1}{2{\mathrm{\η}}^2}{||x-C_{f}y||}^2}---\left(2\right)$

Wherein, P (y|x), if represent known picture rich in detail, obtains the probability that corresponding blurred picture is y, and the process obtaining blurred picture by picture rich in detail can be understood as and with the addition of noise, so this probability can be approximated to be the Gaussian distribution that variance is η c _ffor the convolution matrix of N × N.

Suppose that image prior can with a series of filtering g _krepresent, and image is little as much as possible to the reaction of priori filtering, then image prior can be expressed as:

$P\left(x\right)=e^{-{\mathrm{\α\Σ}}_{i,k}\mathrm{\ρ}(g_{i,k}*x)}---\left(3\right)$

Wherein, P (x) represents the known prior imformation of picture rich in detail, also can represent by similar probability distribution; Horizontal direction be filtered into g _x=[1-1]; Vertical direction be filtered into g _y=[1-1] ^t; ρ represents priori function; g _i,krepresent the kth filtering for i-th pixel.

Go the logarithmic form of formula (1), (2), (3), then can obtain the objective function of image restoration:

${||y-C_{f}x||}^2+\mathrm{\ω}\underset{i,k}{\Σ}\mathrm{\ρ}(g_{i,k}*x)---\left(4\right)$

Wherein ω=α η ².Get Gaussian image priori, and establish ρ (z)=| z| ².To formula (4) differentiate, and make derivative be zero, then can obtain Ax=b, wherein solve under Ax=b being transformed into frequency domain, can obtain:

$X(v,\mathrm{\ω})=\frac{K(v,\mathrm{\ω})*Y(v,\mathrm{\ω})}{|K(v,\mathrm{\ω}){|}^2+{\mathrm{\ω\Σ}}_k|G_k(v,\mathrm{\ω}){|}^2}---\left(5\right)$

Formula (5) is the non-blind convolved image restoration algorithm net result based on L2 norm under frequency domain, and wherein v and ω represents the coordinate under frequency domain.

Step 4: for new blurred picture Y ₁, as shown in Figure 7, obtain blurred picture Y and blurred picture Y respectively by picture rich in detail ₁the fuzzy core used is identical.Be split into the linear combination Y of base equally ₁=α ₁' H ₁+ α ₂' H ₂+ ... + α _n' H _n, base H _ithe same with the base in Fig. 6, according to the X preserved in step 3 _i, then corresponding picture rich in detail can direct representation be X=α ₁' X ₁+ α ₂' X ₂+ ... + α _n' X _n, then the frequency domain picture rich in detail obtained is transformed into time domain by ifft2.Under direct use frequency domain L2 norm image restoration effect with based on matrix decomposition under frequency domain image restoration effect as shown in Figure 7.For the gray level image of 255 × 255 sizes, when image restoration effect close to, time needed for matrix decomposition of use is 0.0253s, and does not directly adopt the time needed for Image Restoration Algorithm of L2 norm under frequency domain to be 0.0588s.If image size increases to 1024 × 1024, then the computing time needed for two kinds of algorithms is respectively 0.2334s and 2.2806s.Be calculated to be the real-time demand of picture in conjunction with simple lens, the image recovery method based on matrix decomposition can meet this demand substantially.

As mentioned above, the present invention is directed to the real-time demand that simple lens is calculated to be picture, under blurred picture and fuzzy core are transformed into frequency domain, and spectral matrix is split, the base of blurred picture spectral matrix is carried out image restoration process as input blurred picture, preserves the base of the corresponding picture rich in detail obtained.Then for new blurred picture to be processed, the base of having tried to achieve only need be utilized to carry out the computing be added that is multiplied, completely avoid the process that in Image Restoration Algorithm in the past, successive ignition is optimized, the required overall calculation time greatly reduces, and substantially can meet the real-time demand that simple lens is calculated to be picture.This method all has very important significance at image procossing and camera design field.

More than contain the explanation of the preferred embodiment of the present invention; this is to describe technical characteristic of the present invention in detail; be not want summary of the invention to be limited in the concrete form described by embodiment, other amendments carried out according to content purport of the present invention and modification are also protected by this patent.The purport of content of the present invention defined by claims, but not defined by the specific descriptions of embodiment.

Claims (3)

1. the quick simple lens based on frequency domain matrix decomposition calculates a formation method, it is characterized in that, comprises the following steps:

S1: blurred picture y under time domain and corresponding fuzzy core k is transformed into frequency domain, obtains the corresponding spectral matrix Y of blurred picture and the spectral matrix K of fuzzy core;

S2: by a series of basis representation Y=α of spectral matrix Y ₁h ₁+ α ₂h ₂+ ... + α _nh _n; The factor alpha of linear combination _inamely be with frequency domain matrix Y in base H _ithat corresponding a part of numerical value;

S3: for each base H of Y _i, in conjunction with fuzzy core K, adopt the non-blind convolution algorithm under frequency domain to carry out deblurring, obtain corresponding picture rich in detail base X _i;

S4: because the base X corresponding with picture rich in detail _iby base H corresponding to blurred picture _iobtained by deblurring algorithm, obtain X _iprocess carried out deblurring; So for blurred picture y new under time domain ₁with the fuzzy core k of correspondence ₁, be transformed into frequency domain, obtain corresponding spectral matrix Y ₁and K ₁; For the spectral matrix Y of new blurred picture ₁, be split into the linear combination of base equally then corresponding picture rich in detail can direct representation be X=α ₁' X ₁+ α ₂' X ₂+ ... + α _n' X _n, obtained picture rich in detail is transformed into time domain again.

2. the quick simple lens based on frequency domain matrix decomposition according to claim 1 calculates formation method, it is characterized in that, in step S2, the base of spectral matrix choose mode: with the central point of spectral matrix for initial point, spectral matrix is divided into the identical straight-flanked ring of the multiple width equal with the number of base by number according to base from the inside to the outside successively, size and the spectral matrix of each base are in the same size, innermost matrix ring is set to the first matrix ring successively to the matrix ring of outermost, second matrix ring ... n-th matrix ring, first each for innermost matrix ring pixel is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtain base H ₁, then each pixel of the second matrix ring is set to 1, the pixel of all the other two straight-flanked rings is set to 0, obtains base H ₂, according to the method the like, finally obtain all bases.

3. the quick simple lens based on frequency domain matrix decomposition according to claim 1 calculates formation method, and it is characterized in that, the method that step S3 adopts is the non-blind convolved image restoration algorithm based on L2 norm, and algorithm main flow is as follows:

Blurred picture y is expressed as the convolution y=x*k of picture rich in detail x and fuzzy core k, if based on the thought of Maximize, image restoration problem representation is:

x＝argmax _xP(x|y)∝P(y|x)P(x) (1)

Wherein, x represents the picture rich in detail of finally trying to achieve; Y represents known blurred picture; P (x|y) represents known blurred picture, obtains the probability that picture rich in detail is x; If represent known picture rich in detail, obtain the probability that corresponding blurred picture is y; P (x) represents the known prior probability of original picture rich in detail;

Suppose noise Gaussian distributed, and variance is η, be then expressed as:

$P\left(y\right|x)\∝e^{-\frac{1}{2{\mathrm{\η}}^2}{||x-C_{f}y||}^2}---\left(2\right)$

Wherein, P (y|x), if represent known picture rich in detail, obtains the probability that corresponding blurred picture is y, and the process obtaining blurred picture by picture rich in detail is interpreted as and with the addition of noise, so this probability is approximately the Gaussian distribution that variance is η c _ffor the convolution matrix of N × N;

Suppose that image prior can with a series of filtering g _krepresent, and image is little as much as possible to the reaction of priori filtering, then image prior is expressed as:

$P\left(x\right)=e^{-{\mathrm{\α\Σ}}_{i,k}\mathrm{\ρ}(g_{i,k}*x)}---\left(3\right)$

Wherein, P (x) represents the known prior imformation of picture rich in detail; Horizontal direction be filtered into g _x=[1-1]; Vertical direction be filtered into g _y=[1-1] ^t; ρ represents priori function; g _i,krepresent the kth filtering for i-th pixel;

Go the logarithmic form of formula (1), (2), (3), then can obtain the objective function of image restoration:

${||y-C_{f}x||}^2+\mathrm{\ω}\underset{i,k}{\Σ}\mathrm{\ρ}(g_{i,k}*x)---\left(4\right)$

Wherein ω=α η ²; Get Gaussian image priori, and establish ρ (z)=| z| ²; To formula (4) differentiate, and make derivative be zero, then can obtain Ax=b, wherein solve under Ax=b being transformed into frequency domain, obtain:

$X(v,\mathrm{\ω})=\frac{K(v,\mathrm{\ω})*Y(v,\mathrm{\ω})}{{\left|K(v,\mathrm{\ω})\right|}^2+{\mathrm{\ω\Σ}}_k{\left|G_k(v,\mathrm{\ω})\right|}^2}---\left(5\right)$

Formula (5) is the non-blind convolved image restoration algorithm net result based on L2 norm under frequency domain, and wherein v and ω represents the coordinate under frequency domain.