CN109683343B - Design method of super-resolution imaging system - Google Patents
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Abstract
The invention discloses a design method of a super-resolution imaging system, which comprises the steps of firstly carrying out model selection on a detector in the super-resolution imaging system, determining the size p of a pixel and obtainingThe focal length f of the optical lens; determining resolution improvement factor of super-resolution imaging system according to requirement
Performance factor eta, and obtaining F of optical lens in super-resolution imaging system#Counting; calculating to obtain the SNR of the super-resolution imaging system, and checking F#Whether the number meets the requirements of the imaging signal-to-noise ratio index; if the requirement of the index is met, obtaining the caliber D of the optical lens in the super-resolution imaging system, and further obtaining the design parameters of the optical lens; then, the super-resolution imaging system is used for observing the target to be detected for multiple times, and an image sequence y of the target to be detected is formedk(ii) a And then image sequence ykAnd substituting the obtained data into a super-resolution reconstruction equation, and solving the super-resolution reconstruction equation according to the minimum relative entropy to obtain a super-resolution imaging result. The method can enable the system to fully exert the advantages of super-resolution imaging and realize the system-level optimization design.
Description
Technical Field
The invention relates to the technical field of photoelectric imaging systems, in particular to a design method of a super-resolution imaging system.
Background
The geometric resolution is an important performance index of a photoelectric imaging system, in the traditional imaging system, the imaging geometric resolution is directly related to the focal length of an optical lens of the system and the pixel size of an imaging detector, and the longer the focal length is, the higher the resolution is, and the smaller the pixel size is, the higher the resolution is. However, with the continuous pursuit of imaging quality, the development of high-geometric resolution imaging systems is limited by the optical lens and the detector, and mainly occurs in that: firstly, the increase of the focal length increases the volume and the weight of the system while improving the resolution, thereby not only limiting the application of the system, but also improving the manufacturing period and the development cost of the system; secondly, due to the limitations of electronic technology and semiconductor technology, reducing the size of the detector pixels can greatly reduce the luminous flux of each pixel of the detector, and the imaging quality is seriously affected.
With the rapid development of the signal processing technology, the super-resolution imaging technology provides a more direct solution for solving the above contradictions, and the spectrum reconstruction high-resolution image of the detector is expanded by utilizing sub-pixel non-redundant information among multi-frame images, so that the limitation of an imaging device on the resolution of the system is broken through. The design of the super-resolution imaging system comprises two parts, namely algorithm design, wherein a super-resolution reconstruction algorithm belongs to the inverse problem of mathematics, has strong ill-conditioned property, and is used for inhibiting the propagation of registration errors and calculation noise in order to obtain a high-precision reconstruction result; secondly, camera parameter optimization design, wherein a super-resolution algorithm is closely related to optical system parameters and detector parameters, if the algorithm is only optimized by design of a camera, local optimization of a super-resolution enhancement effect can be obtained from the aspect of a super-resolution imaging system, and only by constraining the design parameters of the optical system and the detector around the essence and the requirement of a super-resolution algorithm, a system-level optimal solution can be obtained. In the design of a traditional super-resolution imaging system, the propagation and amplification of calculation noise are caused by insufficient optimization of a reconstruction algorithm for inverse problems, and in addition, the coupling relation among detector parameters, optical lens parameters and reconstruction algorithm parameters is not considered in the traditional design method, so that the reconstruction algorithm is difficult to exert ideal efficiency.
Disclosure of Invention
The invention aims to provide a design method of a super-resolution imaging system, which fully considers the restraint of solving the ill-conditioned problem, gives consideration to the reconstruction and noise suppression of image edge texture information, and simultaneously unifies the main parameters of a detector, the main parameters of an optical lens and algorithm efficiency into the same design model, so that the system fully exerts the advantages of super-resolution imaging and realizes the system-level optimization design.
The purpose of the invention is realized by the following technical scheme:
a method of designing a super-resolution imaging system, the method comprising:
and 6, observing the target to be detected for multiple times by using the super-resolution imaging system, so that different sub-pixel displacements exist between every two observed images, and the result of the multiple observation forms an image sequence y of the target to be detectedk；
According to the technical scheme provided by the invention, the method fully considers the constraint of solving the ill-conditioned problem and gives consideration to the reconstruction and noise suppression of the image edge texture information; meanwhile, the main parameters of the detector, the main parameters of the optical lens and the algorithm efficiency are unified into the same design model, so that the decoupling between the hardware parameters of the camera and the algorithm parameters is realized, the advantage of super-resolution imaging is fully exerted by the system, and further the system-level optimization design is realized.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a design method of a super-resolution imaging system according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of sub-pixel displacement provided by an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the present invention will be further described in detail with reference to the accompanying drawings, and as shown in fig. 1, a flow chart of a design method of a super-resolution imaging system provided by the embodiment of the present invention is shown, where the method includes:
where L represents the imaging distance and GSD represents the pixel resolution.
in this step, the resolution is increased by a factor of
In the range of
Wherein,
the maximum value of the resolution improvement factor which can be realized by the super-resolution reconstruction algorithm is shown;
the performance factor eta of the super-resolution imaging system is expressed as
Wherein, ω isSRepresenting the detector cut-off frequency, omegaORepresents the optical cut-off frequency;
and satisfy the relationship
Wherein λ represents the wavelength of the incident light; p is the determined pixel size; f#For optical lenses in super-resolution imaging systemsAnd (4) counting.
For example, an optical lens can be generally optimized as a diffraction limited system, where the modulation transfer function of the optical lens is approximated as:
wherein, ω isOFor the optical cut-off frequency, the limit capability of the optical lens is represented, ωOThe relationship with the optical system aperture D can be expressed as:
in the above formula, D represents the diameter of the aperture of the optical system, and λ represents the wavelength of incident light.
The modulation transfer function of the detector is:
wherein,
is the relative width of the detector pixel and is related to the filling factor; σ represents the angular separation of the detector, and the cutoff frequency ω of the detectorSAre in reciprocal relation, ωSAnd also represents the ultimate capability of the detector.
In a super-resolution imaging system, the maximum resolution improvement factor that can be achieved by a reconstruction algorithm is
The cut-off frequency omega of the super-resolution imaging systemSCan be expressed by the following inequality:
expressing the performance of the imaging system as the detector cut-off frequency ωSAnd optical cut-off frequency omegaOThe ratio of:
in the above formula, η is a performance factor of the super-resolution imaging system, and further includes:
the main parameters of the optical lens of the imaging system, the main parameters of the detector and the parameters of the reconstruction algorithm are connected together by the formula, so that the overall optimization design of the parameters of the super-resolution imaging system is realized.
in this step, the imaging signal-to-noise ratio SNR is first calculated according to the following formula:
wherein E isimg(lambda) is the radiation energy of the lens on any position on the target surface of the detector, h upsilon is the single photon energy, QE is the quantum efficiency of the detector, VNSHFor shot noise, VfloorRepresenting detector noise floor including charge transfer noise, dark current noise, readout noise and quantization noise, VPRNURepresenting the response inhomogeneity noise, SNR, of the detectortargetThe signal-to-noise ratio index required to be achieved by the super-resolution imaging system is represented;
above Eimg(lambda) and F#The relationship of numbers is expressed as:
wherein, ToptIs the optical system transmittance, Lλ(λ) represents the optical lens entrance pupil radiance, θtiltIs the optical axis inclination angle;
checking the F obtained in step 2 according to the relational expression#Whether the number meets the requirements of the imaging signal-to-noise ratio index.
and 6, observing the target to be detected for multiple times by using the super-resolution imaging system, so that different sub-pixel displacements exist between every two observed images, and the result of the multiple observation forms an image sequence y of the target to be detectedk；
In this step, as shown in fig. 2, a schematic diagram of sub-pixel displacement provided by the embodiment of the present invention is shown, where the sub-pixel displacement refers to: in the image coordinate system OXY, a point on the ground object target corresponds to a pixel O in a graph B represented by a solid line1Corresponding to the picture element O in the diagram A indicated by the dotted line2，O1And O2The number of pixels that differ in the OX and OY directions, respectively, is not an integer. If the affine transformation of the graph A and the graph B has rotation besides translation, the two graphs need to be converted to the same plane through rotation transformation.
The specific implementation process of the step is as follows:
in this step, ykRepresenting K times of observation of image data of the same target scene, the super-resolution reconstruction equation can be expressed as:
yk＝AHC(sk)x+nk,k＝1,2,...,K
where x denotes the target scene, ykThe image sequence obtained by observing the target K times is shown, H represents the optical point spread function, and if the imaging result of the 1 st observation is taken as the reference image, the rotational displacement theta of the K-th observation image relative to the reference imagekHorizontal displacement ckVertical displacement dkIs denoted by sk＝(θk,ck,dk)T；
C(sk) Is a sum motion vector skA matrix of related displacements; a is a down-sampling function of the detector and is related to the pixel number amplification rate of super-resolution reconstruction; n iskRepresenting additive noise.
Further, the image data y is observed for each framekMatrix C(s)k) And noise nkEach varying, matrix A, H, C(s)k) And x are convolution relations, and for the super-resolution reconstruction of global optimization, s is decoupled from the convolution relations of the four at the same timekAnd x, ykThe probabilistic form solution of (c) is:
in the above formula, the symbol {. denotes a set, and the probability p (x, { s) } is requiredk}|{yk}), the posterior probability distributions p ({ y) are first aligned separatelyk}|x,{skAnd (4) respectively carrying out modeling design on the prior probability distribution p (x), wherein the posterior probability is also called a least square term, and the prior probability is also called a regularization term.
Subject the noise to a zero-mean Gaussian distribution, then
Variance σkObeys a Gamma distribution:
to improve the accuracy of super-resolution reconstruction, let registration parameter skObey a priori mean
Prior covariance
Gaussian distribution of (a):
the posterior probability or least square term p ({ y) is obtained by combining the formulak}|x,{sk}):
the second factor affecting the super-resolution reconstruction accuracy is a regularization term introduced in image restoration, namely prior probability distribution p (x), which has the function of constraining the solving space of an equation and reflects that edge information reconstruction and noise filtering are performed on the result of the reconstructed image, however, edge reconstruction and noise filtering are contradictory to each other and need to be balanced to enhance the robustness of the algorithm, so that modeling of the regularization term is particularly important for designing the super-resolution reconstruction algorithm, and in the example, modeling of the regularization term can be designed into the following two forms of a or B:
1) regularization term design form a:
in the above formula, p (x | α) is described belowwB) And p (alpha)wB) Meaning and expression of (1).
pwB(x|αwB)＝(αwB)P2exp[-αwBUwB(x)]
In the above formula, UwB(x) The expression of (a) is:
wherein, DeltahiAnd ΔviThe differential operators representing the horizontal and vertical directions, respectively, the "arrow" symbol representing the distance along this direction to the pixel point xiThe nearest pixel points take first-order difference to embody the gradient distribution, lambda, of the imagewB(x) The expression of (a) is:
λSrepresenting the constraint strength factor and the notation norm representing the normalization operator.
In the above formula, alphawBObeying a Gamma distribution:
2) design form B of the regularization term:
the meanings and expressions of the terms on the right side of the middle number in the formula are respectively explained as follows:
order to
Representing parameters
Set of (1), then
Can be recorded as
The expression is as follows:
wherein,
expression (c):
λwh(x) And λwv(x) Comprises the following steps:
wherein λ ishAnd λvIs a constant parameter, and the relationship between them is:
to this end, the process is completedEquation of pairs
The medium prior probability distribution p (x), the design of the regularization term.
Further, the advantages of the above regularization term form a and form B designs are reflected in: through UwB(x) Or
The regularization item can adaptively constrain the edge region and the flat region in the image according to the image gradient information, reconstruct the edge texture information in the edge region, and suppress noise in the flat region, thereby ensuring to obtain a better super-resolution reconstruction result.
Finally, distribution q (theta) and distribution p (theta | { y) are utilizedk}) relative entropy minimization to solve the equation
Namely:
Θ denotes the set of all unknowns, Θ ═ x, { sk},α,{βkThe specific solving process of the formula can be understood by combining the prior art.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (3)
1. A method of designing a super-resolution imaging system, the method comprising:
step 1, carrying out model selection on a detector in a super-resolution imaging system, determining a pixel size p, and obtaining a focal length f of an optical lens according to the following formula:
wherein L represents an imaging distance, and GSD represents a pixel resolution;
step 2, determining the resolution improvement multiple of the super-resolution imaging system according to the requirement
And determining a performance factor eta of the super-resolution imaging system by combining specific application scenes, installation sizes and manufacturing cost to obtain F of an optical lens in the super-resolution imaging system#Counting;
step 3, calculating to obtain the SNR of the imaging signal to noise ratio of the super-resolution imaging system, and checking the F obtained in the step 2#Whether the number meets the requirement of the imaging signal-to-noise ratio index or not is determined by the following specific process:
first, the imaging signal-to-noise ratio SNR is calculated according to the following formula:
wherein E isimg(lambda) is the radiation energy of the lens on any position on the target surface of the detector, h upsilon is the single photon energy, QE is the quantum efficiency of the detector, VNSHFor shot noise, VfloorRepresenting the detector noise floor, VPRNURepresenting the response inhomogeneity noise, SNR, of the detectortargetThe signal-to-noise ratio index required to be achieved by the super-resolution imaging system is represented;
above Eimg(lambda) and F#The relationship of numbers is expressed as:
wherein, ToptIs the optical system transmittance, Lλ(λ) represents the optical lens entrance pupil radiance, θtiltIs the optical axis inclination angle;
checking F obtained in step 2 according to the relation#Whether the number meets the requirements of the imaging signal-to-noise ratio index;
step 4, if the obtained signal-to-noise ratio meets the index requirement, according to a formula F#Obtaining the caliber D of an optical lens in the super-resolution imaging system and further obtaining the design parameters of the optical lens;
step 5, if the obtained signal-to-noise ratio does not meet the index requirement, repeating the operations of the steps 2 and 3 until the signal-to-noise ratio meets the index requirement, and determining F#Number, and further according to formula F#Determining the caliber D of an optical lens in the super-resolution imaging system as f/D;
and 6, observing the target to be detected for multiple times by using the super-resolution imaging system, so that different sub-pixel displacements exist between every two observed images, and the result of the multiple observation forms an image sequence y of the target to be detectedk；
Step 7, the image sequence y is re-processedkSubstituting the image gradient information into a super-resolution reconstruction equation, establishing a regularization model which changes adaptively according to the image gradient information, constraining the marginal area and the flat area of the observed image of the target to be detected, and solving the super-resolution reconstruction equation according to the minimum relative entropy to obtain a super-resolution imaging result.
2. The design method of the super-resolution imaging system according to claim 1, wherein, in step 2,
resolution improvement factor
In the range of
Wherein,
the maximum value of the resolution improvement factor which can be realized by the super-resolution reconstruction algorithm is shown;
the performance factor eta of the super-resolution imaging system is expressed as
Wherein, ω isSRepresenting the detector cut-off frequency, omegaORepresents the optical cut-off frequency;
and satisfy the relationship
Wherein λ represents the wavelength of the incident light; p is the determined pixel size; f#The parameters of the optical lens in the super-resolution imaging system.
3. The method for designing a super-resolution imaging system according to claim 1, wherein, in step 7,
ykrepresenting K times of observation image data of the same target scene, the super-resolution reconstruction equation is expressed as:
yk＝AHC(sk)x+nk,k＝1,2,...,K
where x denotes the target scene, ykRepresenting that K times of target observation are carried out to obtain an image sequence; a is a down-sampling function of the detector and is related to the pixel number amplification rate of super-resolution reconstruction; c(s)k) Is a sum motion vector skA matrix of related displacements; h represents an optical point spread function; n iskRepresenting additive noise.
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