CN112488919B - Lorentz fitting fuzzy kernel image super-resolution reconstruction method - Google Patents
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Abstract
A Lorentz fitting fuzzy kernel image super-resolution reconstruction method aims at solving the problem that an existing point spread function form in an image super-resolution process cannot effectively approximate an actual degradation process, namely, the existing point spread function form has larger approximation error with an actual degradation function model, and the final effect of super-resolution reconstruction is directly affected. The method fully considers the fuzzy effect formed by the actual degradation, models the fuzzy effect caused by the actual degradation by adopting the linear combination of the Lorentz function, and carries out super-resolution reconstruction on the image by taking the minimum mean square error as a criterion. According to the invention, four parameters are adopted to specifically describe the objective blurring process, so that the objective blurring process is more approximate to the actual blurring situation, and the objective blurring process is obtained through theoretical analysis and experimental results.
Description
Technical Field
The invention relates to the field of vision processing, in particular to an image super-resolution reconstruction method of Lorentz fitting fuzzy kernels.
Background
With the continuous progress of technology and the wide application of visual processing technology, the demand for high quality images is greatly increased. Image resolution is a key to measuring image accuracy and sharpness, and has a direct relationship with image sharpness. Therefore, how to improve the resolution of an image has become a research hotspot in the field of image processing. A high resolution image may provide more detailed information, and the higher the resolution of the acquired image, the more information contained in the image, which is also the basis for various studies of related images. The hardware condition of the imaging device is the most direct and effective method for obtaining the high-resolution image, but at present, if the imaging device such as CCD, CMOS and the like is simply started from the hardware device to improve the image resolution, the imaging device is expensive, and the improvement effect of the imaging device cannot be broken through more. Therefore, new software means must be implemented to overcome the limitations of optical manufacturing technology.
Since the degradation function of the device for acquiring the image is mostly a low-pass filter, which limits the related information above the cut-off frequency of the acquired image, early super-resolution techniques were defined as methods for estimating the spectral information of the image above the diffraction limit, and their specific theory support is derived from analytic extension theory, information superposition theory, and the like, which are mainly means of linear deconvolution and blind deconvolution. Today, "super resolution" expands its traditional meaning, which is broadly defined as a technique to restore one or more low resolution images to a high resolution image. The aim is to reconstruct high resolution images by fusing a priori knowledge in a single image or a series of consecutive images with sub-pixel offset using a correlation algorithm without increasing the hardware level of the image acquisition device. Due to the adoption of the data soft processing mode, the implementation cost is far lower than that of the hardware level.
For low resolution images, the degradation model describes the overall degradation process of the single or multiple low resolution images collected from the actual scene, so the correct construction of the degradation model in the super resolution reconstruction algorithm is very important. One general simplified image degradation model is:
y＝Hx+N (1)
where N is noise introduced during imaging and H is a point spread function (Point Spread Function, PSF) operator of the imaging system. Since most acquisition systems are not ideal, the image will experience some degradation during acquisition. For example, the obtained point light source cannot be the same point as the original scene, and a blurred diffusion caused by the point diffusion function is generated. The point spread function is used to represent the degradation process of the acquisition system to the original high resolution scene and image, which is determined by the image acquisition system. And H is often a pathological matrix. Common point spread functions are: gaussian form, sinc form, etc.
Assuming that the original high resolution image is subject to some image degradation (degradation) process to obtain one or more low resolution images, the degradation model of a single frame image can be expressed as:
Y k ＝D k B k F k X+N (2)
wherein Y is k Is the kth low resolution image, X is the original high resolution image, D k Is a downsampling factor, B k Is the blurring factor of the system, including the point spread function operators H, F in equation (1) k Is a motion factor, which can be obtained by a motion estimation method, and N is noise. The degradation process of the plurality of low resolution images is generally the same, so equation (2) can be abbreviated as:
Y k ＝DBF k X+N (3)
insufficient numbers of low resolution images and various degradation factors can lead to pathological features of the image reconstruction problem. In general, unconstrained optimization methods are effective in solving such problems. However, the solution of this method is not unique and is not stable. To solve the drawbacks of the optimization problem, constraint conditions may be added to the optimization method to limit the desirable range of the solution, and this optimization method with constraint properties for solving the pathological problem is called regularization method.
For the linear equation ax=b, when the solution does not exist or is not unique, it can be said to be a pathological problem (ill posed problem). The super-resolution reconstruction problem is basically a pathological problem, and if some constraint constraints are applied to the problem, the solution of the problem is more stable and unique. When the solution does not exist, an approximate solution is obtained by adding some limiting conditions; when the solution is not unique, the desirable range of the solution is limited by adding some constraints (such as sparsity, a priori knowledge of energy constraints, etc.). This approach to solving the problem of morbidity by imposing conditions or constraints is called regularization.
A common method of solving the linear equation is the least squares method, i.e., solving min Ax-b 2 2 For the sick linear equation, tikhonov proposes that a Tikhonov canonical constraint term can be added to solve:
where Γ is called Tikhonov matrix is commonly regarded as a form of the product of unit matrices (Γ=αi) or a differential operator, laplace operator, etc. Therefore, the pathological problem becomes to find x which can make the formula (4) take the minimum value, and the regularization method limits the solving condition to directly obtain the corresponding minimum solution:
the traditional regularization method can improve the resolution of the single-frame image, but the original scene contained in the single-frame image is insufficient in information, and the reconstruction effect is poor. It is therefore a critical issue how to effectively reconstruct high resolution images from multiple sets of low resolution images. Meanwhile, the point spread function form is more similar to the actual degradation process and is an important part of the super-resolution process, so that the super-resolution result of the effective integral image is ensured.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the image super-resolution reconstruction method of the Lorentz fitting fuzzy core, which aims at the problem that the existing point spread function form in the image super-resolution process cannot effectively approximate the actual degradation process, namely has larger approximation error with the actual degradation function model, and directly influences the final effect of super-resolution reconstruction. The method fully considers the fuzzy effect formed by the actual degradation, models the fuzzy effect caused by the actual degradation by adopting the linear combination of the Lorentz function, and carries out super-resolution reconstruction on the image by taking the minimum mean square error as a criterion.
The technical scheme adopted for solving the technical problems is as follows:
a Lorentz fitting fuzzy kernel image super-resolution reconstruction method comprises the following steps:
step one: denoising pre-processing of a low-resolution image sequence g degraded due to the inadaptability of the optical system itself k ∈R M×N Denoising pretreatment is carried out, wherein k is the number of image sequences;
step two: selecting a frame g from a sequence of low resolution images 0 As a reference frame, diamond search or optical flow method is used for other low-resolution images g in the sequence l Registering to obtain sub-pixel registration parameter F k ，l＝1…k-1；
Step three: estimation model of degraded PSF: establishing an approximate PSF fuzzy core model based on a variable pulse width VPW (variable pulse width) function according to a construction formula, wherein the formula of the VPW function is as follows:
f(t)＝f s (t)+f a (t),t∈[0,T) (6)
wherein the method comprises the steps of
Where f s (t) and f a (t) represents a symmetric part and an asymmetric part of a VPW function f (t), respectively, the VPW function determining a degradation process by four parameters a, d, t', r, and the gaussian model and the Sinc model determining the degree of smoothness of the image blur by only one parameter σ; the VPW function model has higher flexibility and wider application range, and can more consider the approximation error with the actual blurring process;
and (3) parameter selection: selecting proper pulse width r and pulse time delay t' according to the characteristic that the pixel value of an imaging center point carried by an optical system is high and the pixel value of surrounding imaging points is reduced in diffusion; selecting proper amplitude values a and b according to the characteristic that an image degradation model is to be similar to the imaging of an actual point in morphology;
step four: establishing a VPW estimation model: constructing a formula (6) by utilizing the VPW function in the third step, and selecting values of four parameters a, d, t and r according to the physical characteristics of the optical system, thereby establishing an approximate PSF fuzzy core model based on the VPW function, wherein the formula is as follows:
f(x,y)＝f(x)·f(y) (9)
wherein x and x are integers, which respectively represent index values of rows and columns in the image matrix, and the value range is determined by the size of the fuzzy matrix in the next step five;
step five: the approximate PSF fuzzy core model based on the VPW function established by the steps is utilized to further construct a corresponding PSF convolution core h of 3 multiplied by 3, and the construction method is as follows: after generating a 3×3 matrix, taking the coordinate value of each grid as the coordinate value of a VPW function model f (x, y), calculating the weight of each point, carrying out normalization processing on element values, generating a final 3×3 PSF convolution kernel h, and generating a fuzzy matrix according to a convolution theorem;
step six: bicubic interpolation of selected images to form an initial estimate X of high resolution 0 For the super-resolution image reconstruction problem, a gradient descent method iteration mode is selected to solve, iteration times, iteration step lambda, regularization parameters alpha, regularization operators Γ and downsampling factors S are set according to actual conditions, wherein lambda is the iteration step, and the lambda can be determined according to factors such as the iteration times, reconstruction effects and the like in an actual experiment; a larger alpha value can weaken high-frequency parts in the image, so that the image is too smooth; a smaller alpha value will preserve the detail information of the image more completely, but the noise will also be preserved, Γ is typically set as an operator with high-pass filtering characteristics;
step seven: from the sequential low-resolution images LR, registration parameters F k The iterative error generation formula for generating the high-resolution image by the VPW fuzzy matrix B and the downsampling factor S is as follows:
step eight: estimation X of high-resolution image of last iteration according to regularization parameter alpha, regularization operator gamma n Generating a regularization constraint term U, which is used for constraining the final estimated value to meet the prior probability characteristic, and generating the following formula:
U＝αΓ T ΓX n (11)
wherein the regularization parameter α is set to a constant or to an adaptive coefficient that changes with the number of iterations;
step nine: substituting the calculation results of the step seven and the step eight into formulas (12) and (13) to start iterative reconstruction, and outputting a final high-resolution image X n+1 ：
X n+1 ＝X n -λ{W+U} (13)。
Further, the range of VPW model parameter settings using morphological approximation and optical imaging features is T.epsilon.1, 10, a.epsilon.10, 10, b.epsilon.10, 10, t.epsilon.0, 10.
Still further, the regularization parameter α has a value range of [0,5], and the iteration step λ has a value range of [0,10].
The beneficial effects of the invention are mainly shown in the following steps: in the image super-resolution reconstruction process, a VPW model is used for approximating the point spread function of image degradation, and the point spread function is used in the super-resolution reconstruction algorithm of the image. Because the Gaussian PSF is a fuzzy process which cannot be very similar to the actual fuzzy process, and the VPW model is selected to have wider adaptability from the morphological approximate consideration of the diffraction of the optical system, compared with the Gaussian model, the Gaussian model adopts four parameters to specifically describe the objective fuzzy process, the Gaussian PSF is more similar to the actual fuzzy situation, and the Gaussian model is obtained through theoretical analysis and experimental results and is used in a deblurring algorithm, so that the image reconstruction effect is improved.
Drawings
Fig. 1 is a schematic diagram of the PSF model of VPW.
FIG. 2 is a process diagram of a construction method of a blur kernel.
Fig. 3 is an original image and a low resolution image.
Fig. 4 is 4Sinc model restoration.
Fig. 5 is gaussian model restoration.
Fig. 6 is an image restoration of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 6, an image super-resolution reconstruction method of lorentz fitting blur kernels comprises the following steps:
step one: denoising pre-processing of a low-resolution image sequence g degraded due to the inadaptability of the optical system itself k ∈R M×N Denoising pretreatment is carried out, wherein k is the number of image sequences, and the best denoising effect of the notch filter is selected for the degraded image of the actual optical system;
step two: selecting a frame g from a sequence of low resolution images 0 As a reference frame, diamond search or optical flow method is used for other low-resolution images g in the sequence l Registering to obtain sub-pixel registration parameter F k ，l＝1…k-1；
Step three: estimation model of degraded PSF: establishing an approximate PSF fuzzy core model based on a variable pulse width VPW (variable pulse width) function according to a construction formula, wherein the formula of the VPW function is as follows:
f(t)＝f s (t)+f a (t),t∈[0,T) (6)
wherein the method comprises the steps of
Where f s (t) and f a (T) represents the symmetric and asymmetric parts of the VPW function f (T), respectively, obviously, the VPW function can determine the degradation process by four parameters of a, d, T', r, and the parameters of the VPW model are set to be in the range of T epsilon [1,10] by using the characteristics of morphological approximation and optical imaging]，a∈[-10,10]，b∈[-10,10]，t′∈[0,10]The method comprises the steps of carrying out a first treatment on the surface of the The Gaussian model and the Sinc model only determine the smoothness degree of the image blurring by one parameter sigma, and compared with the prior art, the VPW function model has higher flexibility, wider application range and better consideration of approximation errors with the actual blurring process;
and (3) parameter selection: selecting proper pulse width r and pulse time delay t' according to the characteristic that the pixel value of an imaging center point carried by an optical system is high and the pixel value of surrounding imaging points is reduced in diffusion; selecting proper amplitude values a and b according to the characteristic that an image degradation model is to be similar to the imaging of an actual point in morphology;
step four: establishing a VPW estimation model: constructing a formula (6) by utilizing the VPW function in the third step, and selecting values of four parameters a, d, t and r according to the physical characteristics of the optical system, thereby establishing an approximate PSF fuzzy core model based on the VPW function, wherein the formula is as follows:
f(x,y)＝f(x)·f(y) (9)
wherein x and y are integers and represent index values of rows and columns in the image matrix respectively, and the value range is determined by the size of the fuzzy matrix in the next step five; fig. 1 is a two-dimensional representation of a VPW model built with parameters a=2, d=0.3, t+=0, r=0.4. .
Step five: the approximate PSF fuzzy core model based on the VPW function established by the steps is utilized to further construct a corresponding PSF convolution core h of 3 multiplied by 3, and the construction method is as follows: after generating a 3×3 matrix, taking the coordinate value of each grid as the coordinate value of a VPW function model f (x, y), calculating the weight of each point, carrying out normalization processing on element values, generating a final 3×3 PSF convolution kernel h, and generating a fuzzy matrix according to a convolution theorem;
step six: bicubic interpolation of selected images to form an initial estimate X of high resolution 0 For the super-resolution image reconstruction problem, a gradient descent method iteration mode is selected to solve, iteration times, iteration step lambda, regularization parameters alpha, regularization operators Γ and downsampling factors S are set according to actual conditions, wherein lambda is the iteration step, and the lambda can be determined according to factors such as the iteration times, reconstruction effects and the like in an actual experiment; a larger alpha value can weaken high-frequency parts in the image, so that the image is too smooth; a smaller alpha value will preserve the detail information of the image more completely, but the noise will also be preserved, Γ is typically set as an operator with high-pass filtering characteristics;
the value range of the regularization parameter alpha is [0,5], and the value range of the iteration step lambda is [0,10];
step seven: from the sequential low-resolution images LR, registration parameters F k The iterative error generation formula for generating the high-resolution image by the VPW fuzzy matrix B and the downsampling factor S is as follows:
step eight: estimation X of high-resolution image of last iteration according to regularization parameter alpha, regularization operator gamma n Generating a regularization constraint term U, which is used for constraining the final estimated value to meet the prior probability characteristic, and generating the following formula:
U＝αΓ T ΓX n (11)
the regularization parameter alpha can be set as a constant or as an adaptive coefficient which changes with the number of iterations.
Step nine: substituting the calculation results of the step seven and the step eight into formulas (12) and (13) to start iterative reconstruction, and outputting a final high-resolution image X n+1 ；
X n+1 ＝X n -λ{W+U} (13)。
Aiming at the problem that the existing point spread function form in the image super-resolution process cannot effectively approximate the actual degradation process, namely, the actual degradation function model has larger approximation error, the final effect of super-resolution reconstruction is directly affected. An image super-resolution reconstruction algorithm of Lorentz fitting fuzzy kernels is provided. The method fully considers the fuzzy effect formed by the actual degradation, models the fuzzy effect caused by the actual degradation by adopting the linear combination of the Lorentz function, and carries out super-resolution reconstruction on the image by taking the minimum mean square error as a criterion.
In order to verify the performance of the method of the invention, computer simulation experiments were performed. The experiment adopts two shooting images with actual optical defocus blur under a blur data set HA, and the size is 256 multiplied by 256. In the experiment, a Gaussian model, a Sinc model and a VPW model are selected for regularized image super-resolution algorithm to reconstruct an image, and the images are compared according to the reconstruction effect. Peak signal-to-noise ratio (PSNR) and Structural Similarity of Images (SSIM) were introduced in the experiments as evaluation indexes for image reconstruction.
Fig. 3-6 are graphs of the results of the original image, the low resolution image, and the reconstruction simulation using different PSF models, respectively, from which it can be seen that the quality and visual effect of the restored image based on the VPW model is better than those of the Sinc model and the gaussian model. For quantitative objective comparison, table 1 shows the results of the numerical comparison of PSNR and SSIM for each model recovery.
| Restoration method | PSNR | SSIM |
| Sinc model restoration | 24.4536 | 0.9497 |
| Gaussian model restoration | 34.1596 | 0.9832 |
| The method of the invention | 35.6947 | 0.9912 |
Table 1.
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.
Claims (3)
1. An image super-resolution reconstruction method of Lorentz fitting fuzzy kernels is characterized by comprising the following steps:
step one: denoising pre-processing of a low-resolution image sequence g degraded due to the inadaptability of the optical system itself k ∈R M×N Denoising pretreatment is carried out, wherein k is the number of image sequences;
step two: selecting a frame g from a sequence of low resolution images 0 As a reference frame, diamond search or optical flow method is used for other low-resolution images g in the sequence l Registering to obtain sub-pixel registration parameter F k ，l＝1…k-1；
Step three: estimation model of degraded PSF: establishing an approximate PSF fuzzy core model based on a variable pulse width VPW function according to a construction formula, wherein the formula of the VPW function is as follows:
f(t)＝f s (t)+f a (t)，t∈[0，T) (6)
wherein the method comprises the steps of
Where f s (t) and f a (t) represents a symmetric part and an asymmetric part of a VPW function f (t), respectively, which determines a degradation process from four parameters a, d, t', r;
and (3) parameter selection: selecting pulse width r and pulse time delay t' according to the characteristic that the pixel value of an imaging center point carried by an optical system is high and the pixel value of surrounding imaging points is reduced in diffusion; selecting amplitude values a and b according to the characteristic that an image degradation model is to be similar to the imaging of an actual point in morphology;
step four: establishing a VPW estimation model: constructing a formula (6) by utilizing the VPW function in the third step, and selecting values of four parameters a, d, t and r according to the physical characteristics of the optical system, thereby establishing an approximate PSF fuzzy core model based on the VPW function, wherein the formula is as follows:
f(x，y)＝f(x)·f(y) (9)
wherein x and y are integers and represent index values of rows and columns in the image matrix respectively, and the value range is determined by the size of the fuzzy matrix in the next step five;
step five: and (3) constructing a corresponding 3 multiplied by 3 PSF convolution kernel h by utilizing the approximate PSF fuzzy kernel model based on the VPW function and established in the step (V), wherein the construction method is as follows: after generating a 3×3 matrix, taking the coordinate value of each grid as the coordinate value of a VPW function model f (x, y), calculating the weight of each point, carrying out normalization processing on element values, generating a final 3×3 PSF convolution kernel h, and generating a fuzzy matrix according to a convolution theorem;
step six: bicubic interpolation of selected images to form an initial estimate X of high resolution 0 For the super-resolution image reconstruction problem, a gradient descent method iteration mode is selected to solve, and iteration times, iteration step lambda, regularization parameter alpha, regularization operator gamma and downsampling factor S are set;
step seven: from the sequential low-resolution images LR, registration parameters F k The iterative error generation formula for generating the high-resolution image by the VPW fuzzy matrix B and the downsampling factor S is as follows:
step eight: estimation of high resolution image from regularization parameter alpha, regularization operator Γ, last iterationMeter X n Generating a regularization constraint term U, which is used for constraining the final estimated value to meet the prior probability characteristic, and generating the following formula:
U＝αΓ T ΓX n (11)
wherein the regularization parameter α is set to a constant or to an adaptive coefficient that changes with the number of iterations;
step nine: substituting the calculation results of the step seven and the step eight into formulas (12) and (13) to start iterative reconstruction, and outputting a final high-resolution image X n+1 ：
X n+1 ＝X n -λ{W+U} (13)。
2. The method of claim 1, wherein the parameters of the VPW model using morphological approximation and optical imaging features are set to be T e [1,10], a e [ -10,10], b e [ -10,10], T' e [0,10].
3. The method for image super-resolution reconstruction of a lorentz fit blur kernel according to claim 1 or 2, characterized in that the regularization parameter α has a value range of [0,5], and the iteration step λ has a value range of [0,10].
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| CN102800071A (en) * | 2012-06-20 | 2012-11-28 | 南京航空航天大学 | Method for reconstructing super resolution of sequence image POCS |
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| CN102360498A (en) * | 2011-10-27 | 2012-02-22 | 江苏省邮电规划设计院有限责任公司 | Reconstruction method for image super-resolution |
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