CN110335197B - Demosaicing method based on non-local statistical eigen - Google Patents
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Abstract
The invention discloses a demosaicing method based on non-local statistical eigen, which comprises the following steps: after separating the measured values according to the spectral channels, respectively carrying out initialization estimation to obtain a preset image of each channel; setting sample image sub-blocks, searching image sub-blocks with similar structures to the sample image sub-blocks in a preset image for matching, and combining the image sub-blocks with similar structures into a data matrix; performing low-rank regularization constraint on the data matrix, and combining the minimization constraint of the simulated measurement value and the real measurement value to obtain an optimized and reconstructed target function; solving the objective function to obtain an estimated value of the objective image; and taking the estimated value as a new preset image, and circularly iterating the steps until the specified times or the algorithm is converged to obtain the target demosaiced image. On the basis of a compressed sensing theory, the method fully utilizes the non-local structural information of the natural image, improves the reconstruction precision of the demosaicing of the image, and can achieve a better demosaicing effect.
Description
Technical Field
The invention relates to the technical field of computational reconstruction in computer vision and computational photography, in particular to a demosaicing method based on non-local statistical eigen.
Background
In order to be able to acquire color images or multispectral images with a small-sized, low-cost digital camera, cameras with a single sensor structure have been invented. The structure of the camera is characterized in that the camera only has one detector, and a layer of color/multi-channel filter array is arranged in front of the detector, so that each pixel point only receives light of one wave band. Images acquired by such a single-sensor structure camera are called mosaic images, and the process of estimating missing pixel components of each band by an algorithm is called a demosaicing process. The demosaicing problem has been attracting much attention since its birth, and it is important to reconstruct a high-precision image by a demosaicing algorithm.
The traditional demosaicing technology mainly uses interpolation method. Simple interpolation methods include nearest neighbor interpolation and bilinear interpolation, but they are extremely inefficient for reconstructing edge regions of an image. To solve this problem, J.F Hamilton and j.adams of kodak corporation in 1997 propose an adaptive interpolation method that interpolates along edge gradients and further utilizes the correlation between pixels of an image, and Li et al of the university of west virginia in 2005 proposed a successive approximation demosaic method on the basis of the adaptive interpolation method. In addition to the above interpolation method using correlation, Zhang et al, 2011 at hong kong physic university, also proposes a demosaicing method based on local directional interpolation and non-local mean filtering and a demosaicing method based on local directional interpolation and adaptive threshold, which utilize non-local redundancy of images to improve the reconstruction effect of images.
Meanwhile, with the development of a compressed sensing technology, A.A Moghadam et al of michigan state university in 2010 proposes a compressed demosaicing method, combines the compressed sensing and the demosaicing problem, and designs a new color filter array with random arrangement. The success of this study has opened a new direction to the demosaic problem. Inspired by this, Aggarwal et al tried to extend the demosaicing problem from a red-green-blue (RGB) three-channel model to a multi-channel (multi-spectral) model in 2014, and tried to solve the multi-spectral demosaicing problem using a compressive sensing theory. The color filter array used by the method has stronger expansibility and better demosaicing effect. Therefore, how to increase the spectrum channels and ensure the demosaicing reconstruction accuracy is urgently needed to be solved.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, the invention aims to provide a demosaicing method based on non-local statistical eigen, which fully utilizes non-local structure information of a natural image and can achieve a better demosaicing effect.
In order to achieve the above purpose, the invention provides a demosaicing method based on non-local statistical eigen, comprising the following steps: a scene is filtered by a filter matrix to obtain a total measurement value, and the total measurement value is separated according to a spectrum channel to obtain a plurality of sub-measurement values; respectively carrying out initialization estimation on the plurality of sub-measurement values to obtain a preset image of each channel; setting sample image sub-blocks, searching image sub-blocks with similar structures to the sample image sub-blocks in the preset image for matching, and combining the sample image sub-blocks and the image sub-blocks with similar structures into a data matrix; performing low-rank regularization constraint on the data matrix, and combining minimization constraint of a simulated measurement value and a real measurement value to obtain an optimized and reconstructed target function; solving the objective function to obtain an estimated value of the objective image; and taking the estimated value of the target image as a new preset image, and circularly iterating the steps until the specified times or the algorithm is converged to obtain the target demosaiced image.
According to the demosaicing method based on the non-local statistical eigen, the demosaicing problem is modeled into the compression sensing problem of the non-local statistical eigen, the non-local statistical feature and the structural sparsity of a natural image are fully utilized, the demosaicing method with the advantages of easily controlled reconstructed spectral channel number, high reconstructed image precision and strong reconstruction algorithm robustness is obtained, high-quality demosaicing image reconstruction is achieved, the reconstruction precision is improved, and the calculation process is simple, convenient and fast.
In addition, the demosaicing method based on non-local statistical eigen according to the above embodiment of the present invention may also have the following additional technical features:
optionally, in an embodiment of the present invention, the initialization estimation method of the preset image includes, but is not limited to, interpolation demosaicing or compressive sensing demosaicing.
Further, in one embodiment of the present invention, the interpolation demosaicing includes, but is not limited to, nearest neighbor interpolation, bilinear interpolation, and adaptive interpolation.
Further, in an embodiment of the present invention, the compressed sensing demosaicing method includes, but is not limited to, a compressed sensing method under discrete cosine transform, a compressed sensing method under total variation minimization, and a compressed sensing method under total variation minimization based on generalized alternative projection.
Further, in an embodiment of the present invention, before performing the matching process, the sample image sub-blocks need to be extracted according to a specified step length and an initial value T is preset as a similarity threshold for measuring the image sub-blocks, where when the similarity between the image sub-blocks in the search range and the sample image sub-blocks satisfies T, the image sub-blocks are selected as image sub-blocks with a structure similar to that of the sample image sub-blocks.
Optionally, in an embodiment of the present invention, the similarity measure includes, but is not limited to, manhattan distance, euclidean distance, and normalized euclidean distance.
Further, in an embodiment of the present invention, a search range in the process of searching for image sub-blocks in the preset image, which have similar structures to the sample image sub-blocks, for matching is a non-local range within a global range, and whether to select image sub-blocks having similar structures to the sample image sub-blocks depends only on whether the similarity satisfies a threshold requirement.
Further, in an embodiment of the present invention, the low-rank regularization constraint of the data matrix uses a weighted kernel norm instead of a kernel norm to transform an original convex optimization problem into a non-convex optimization problem, so that the low-rank regularization constraint is more precise.
Further, in one embodiment of the present invention, the weighted kernel norm is of the form:
wherein σjJ-th singular value representing an internal matrix X；ωjRepresenting the weight corresponding to the jth singular value.
Further, in an embodiment of the present invention, when the objective function is solved, an auxiliary variable is introduced, so that after the objective function is decomposed, the low rank estimation of the data matrix and the demosaic reconstruction of the target image are performed alternately, and finally, an estimation value of the target image is obtained.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a demosaicing method based on non-local statistical eigen according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a demosaiced imaging model based on non-local statistical eigen, where 1 is a scene, 2 is a camera lens, 3 is a filter array, and 4 is a detector;
fig. 3 is a structural schematic of a filter array Mask;
FIG. 4 is a flow chart of demosaicing for each channel based on non-local statistical eigen;
fig. 5 is a schematic diagram of demosaicing input and output based on non-local statistical eigen.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The demosaicing method based on non-local statistical eigen proposed according to the embodiment of the present invention is described below with reference to the accompanying drawings.
Fig. 1 is a flow chart of a demosaicing method based on non-local statistical eigen according to an embodiment of the present invention.
As shown in fig. 1, the demosaicing method based on non-local statistical eigen includes the following steps:
in step S101, a scene is filtered through a filter matrix to obtain a total measurement value, and the total measurement value is separated according to a spectrum channel to obtain a plurality of sub-measurement values.
That is, the measured values need to be decomposed, and the image of each channel needs to be individually initialized and estimated to obtain the preset image of each channel.
In step S102, the plurality of sub-measurement values are initialized and estimated respectively to obtain a preset image of each channel.
Further, in an embodiment of the present invention, the initialized estimated value of the preset image may be obtained by using interpolation or compressive sensing. The compressed sensing demosaicing method comprises a compressed sensing method DCT under the condition of not being limited to discrete cosine transform, a compressed sensing method TV under the condition of minimizing total variation and a compressed sensing GAP-TV method under the condition of minimizing total variation based on generalized alternative projection. The method provides a good iteration initial value for the demosaicing method based on the non-local statistical eigen, so that the reconstruction precision is improved.
In step S103, sample image sub-blocks are set, image sub-blocks with a structure similar to that of the sample image sub-blocks are searched for matching in the preset image, and the sample image sub-blocks and the image sub-blocks with the similar structure are combined into a data matrix.
That is, image sub-block matching is performed in the entire image, image sub-blocks having a similar structure to the sample image sub-blocks are searched in the global scope, and they are combined into a data matrix.
Further, in an embodiment of the present invention, before performing the matching process, the searching process needs to extract the sample image sub-blocks according to a specified step size and preset an initial value T as a threshold for measuring the similarity between the image sub-blocks, wherein when the searching range is within the range, the searching process needs to extract the sample image sub-blocks and preset an initial value T as a threshold for measuring the similarity between the image sub-blocksWhen the similarity between the image sub-block and the sample image sub-block satisfies T, the image sub-block is selected as the image sub-block with the similar structure to the sample image sub-block. The similarity measure includes, but is not limited to, Manhattan distance (l)1Norm), euclidean distance (l)2Norm) and normalized euclidean distance.
That is, only when the similarity with the sample image sub-block satisfies the threshold T, the image sub-block with the similar structure to the sample image sub-block can be selected, and the image sub-block with the similar structure can be accurately found.
It should be noted that the search range in searching for image sub-blocks with a similar structure to the sample image sub-block in the preset image for matching is a non-local range within the global range, and whether the image sub-block with a similar structure to the sample image sub-block is selected is only determined whether the similarity meets the threshold requirement.
It can be understood that the search range is not limited to the local range around the sample image sub-block, but also includes the non-local range within the global range, and the search range is selected as long as the similarity requirement is met, so that the image sub-blocks with similar structures in the image can be utilized to the greatest extent to achieve the purpose of structural sparse enhancement.
In step S104, a low-rank regularization constraint is performed on the data matrix, and a minimization constraint of the simulated measurement value and the real measurement value is combined to obtain an optimized and reconstructed objective function.
That is, the objective function consists of a low rank regularization constraint of the data matrix and a minimization constraint of the simulated measurements along with the real measurements.
Further, in an embodiment of the present invention, the low-rank regularization constraint of the data matrix uses a weighted kernel norm instead of a kernel norm to transform the original convex optimization problem into a non-convex optimization problem, so that the low-rank regularization constraint precision is higher.
Wherein the form of the weighted kernel norm is:
wherein σjThe jth singular value representing the internal matrix X; omegajRepresenting the weight corresponding to the jth singular value.
Further, the low-rank regularization constraint of the data matrix and the minimization constraint of the simulated measurement value and the real measurement value are used to obtain an optimized and reconstructed objective function in the form of:
wherein, ykIs the measured value of the k channel; phikA downsampled matrix for a kth channel; x is the number ofkIs the target image of the k channel.
In brief, in the low-rank regularization constraint of the data matrix, a weighted kernel norm is used to replace a kernel norm, and the original convex optimization problem is converted into a non-convex optimization problem, so that the low-rank regularization constraint precision is higher; then, in the process of demosaicing, combining the low-rank regularization constraint of the data matrix with the minimization constraint of the simulated measurement value and the real measurement value to obtain a new optimized reconstruction objective function.
In step S105, the objective function is solved to obtain an estimated value of the target image.
That is, the objective function of the optimized reconstruction is solved to obtain a final objective image estimation value.
Further, in one embodiment of the present invention, an auxiliary variable L is introduced in the solution of the objective functioni. The objective function after the introduction of the auxiliary variable becomes
Decomposing the objective function after introducing the auxiliary variable to obtain the following formula
And alternately performing low-rank estimation of the data matrix and demosaic reconstruction of the target image on the two equations to finally obtain an estimation value of the target image.
It should be noted that, although the optimal reconstruction objective function without introducing auxiliary variables can ensure higher reconstruction accuracy, it is mathematically difficult to solve. By means of an auxiliary variable LiAnd decomposing the new objective function, and further quickly and accurately solving the estimation value of the target image.
In step S106, the estimated value of the target image is used as a new preset image, and the above steps are iterated circularly until a specified number of times or the algorithm converges, so as to obtain a target demosaiced image.
Specifically, after one-time demosaicing reconstruction based on the non-local statistical eigen is completed, the result is used as an initial value of the next iteration, block matching, low-rank estimation and demosaicing are performed again, and the steps are performed in a circulating iteration mode until the specified times or algorithm convergence is achieved, so that the demosaicing reconstruction accuracy of the image is improved.
It should be noted that, when solving the demosaicing result, the solution of the demosaicing optimization model can be equivalent to a closed solution of a suboptimal problem, and the solution can be directly solved by using a conjugate gradient algorithm, so that the calculation is simple, convenient and fast.
The operation principle of the embodiment of the present invention will be specifically described below with reference to specific examples, but the present invention is not limited to the following embodiments.
As shown in fig. 2, a scene is projected through a camera lens onto a pre-designed filter array Mask, which performs specified filtering on scene light in a spectral dimension, and then hits on a detector to obtain a measurement value. The filter array Mask has the effect that only light with specified wavelength is allowed to pass through specified pixel points, so that the aim of simultaneously collecting information of a plurality of spectral channels is fulfilled.
As shown in fig. 3, the filter array Mask may be arranged in a uniform random distribution pattern in addition to the regular arrangement pattern in the figure. It should be noted that the number of Mask channels adapted in the embodiment of the present invention is not limited to the 4 channels shown in the figure, and the number of channels may be expanded downward or upward to generate a filter array with any number of channels.
As shown in fig. 4, measured values Measurements obtained after filtering a scene by Mask are used as input, and after the input, a total measured value is split into a plurality of sub-measured values according to channels, and demosaicing operations are respectively performed. The final output is a complete demosaiced gray-scale image for each channel. If desired, the summation can be continued in the spectral dimension to obtain a color image output.
As shown in FIG. 5, overall, the embodiment of the present invention models the demosaicing problem as a decompression perception problem, and the imaging model of each channel can be expressed as
yk＝Φkxk+η (1)
Wherein, ykIs the measured value of the k channel; phikA down-sampling matrix of the kth channel, namely a Mask of the kth channel; x is the number ofkIs the true value of the k channel; η is the noise of the kth channel. With the traditional method of decompressing the perception problem, the imaging model can be solved by solving the following unconstrained optimization problem:
by measuring y for each channel imagekUsing a simple compressed sensing demosaicing method (including but not limited to DCT \ TV \ GAP-TV), the target image x of each channel can be obtainedkAnd the estimated value is used as an iteration initial value of the demosaicing method based on the non-local statistical characteristics. Block matching, low rank estimation and demosaicing are then performed on the preset image: firstly, searching image subblocks with similar structures to form a data matrix by block matching; then, performing low-rank estimation on the data matrix to enhance the structural sparsity; and finally, the low-rank estimation is used as constraint to perform demosaicing processing.
Implementation of the Block matching phaseThe method is that sample image sub-block x is extracted with fixed step length on the iterative initial value of the imagei' (i ═ 1,2, 3.., N). For each sample image sub-block xi' all of them search image sub-blocks with similar structure within their wide search window as specified, and the judgment criterion of similarity is as follows
Wherein the content of the first and second substances,
the j image sub-block in the search window of the i sample image sub-block; t is a preset threshold value. Each similar image sub-block found will form a data matrix with the sample image sub-block
The low-rank estimation stage is implemented by solving a traditional low-rank optimization model
The term' nuclear norm | · | | |) in (a) is replaced with a weighted nuclear norm. The replaced low rank optimization model becomes
Wherein, | | Li||ω,*A weighted kernel norm of the formula
ωjL is more than or equal to 0iEach singular value σ of the matrixjThe corresponding weight. Lambda [ alpha ]>0 is a regularization parameter. After the optimization model of the low-rank estimation of the data matrix is changed to formula 5, the low-rank estimation update of each data matrix can use weighted singular valuesAnd solving by a threshold method.
The implementation method of the demosaicing stage is that after low-rank estimation is completed on all data matrixes, the low-rank estimation is used as a decompression perception optimization model of regularization constraint term modification formula 2, and the decompression perception optimization model is as follows:
wherein the content of the first and second substances,
is at xkThe data matrixes extracted from the same positions are the same as the positions of the structurally similar blocks selected during block matching, except that the image used in the block matching stage is a known iteration initial value image, and the image used here is a reconstructed image x to be solvedk. Aiming at the optimization model of the formula 6, the optimization model can be converted into a closed solution problem of a quadratic optimization problem, and a conjugate gradient method or an alternating direction multiplier method is used for quick updating.
After the process is completed, an image reconstruction value with higher quality compared with a simple compressed sensing demosaicing method is obtained. And then, using the high-quality image reconstruction value as an iteration initial value to continue the processes of block matching, low-rank estimation and demosaicing. Continuous cyclic update of low rank estimate LiAnd demosaiced image xk. This is a complementary process, LiCan increase xkDemosaicing quality of xkCan improve LiLow rank accuracy of. Such a loop iteration process will continue until a specified number of times or the algorithm converges.
According to the demosaicing method based on the non-local statistical eigen provided by the embodiment of the invention, the demosaicing problem is modeled as the compression perception problem of the non-local statistical eigen, and the demosaicing method which is easy to control the number of the reconstructed spectral channels, high in reconstructed image precision and strong in reconstruction algorithm robustness is obtained by fully utilizing the non-local statistical characteristics and the structural sparsity of a natural image, so that the reconstruction of a high-quality demosaicing image is realized, the reconstruction precision is improved, and the calculation process is simple, convenient and fast.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, or may be interconnected within and/or interacting with one another. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may mean that the first feature is directly on or obliquely above the second feature, or that only the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (7)
1. A demosaicing method based on non-local statistical eigen is characterized by comprising the following steps:
a scene is filtered by a filter matrix to obtain a total measurement value, and the total measurement value is separated according to a spectrum channel to obtain a plurality of sub-measurement values;
respectively carrying out initialization estimation on the plurality of sub-measurement values to obtain a preset image of each channel;
setting sample image sub-blocks, searching image sub-blocks with similar structures to the sample image sub-blocks in the preset image for matching, and combining the sample image sub-blocks and the image sub-blocks with similar structures into a data matrix;
performing low-rank regularization constraint on the data matrix, and combining minimization constraint of a simulated measurement value and a real measurement value to obtain an optimized and reconstructed target function; the performing low-rank regularization constraints on the data matrix comprises: after low-rank estimation is completed on all data matrixes, the low-rank estimation is used as a regularization constraint term;
solving the objective function to obtain an estimated value of the objective image; and:
taking the estimated value of the target image as a new preset image, taking the new preset image as an initial value of next iteration, performing block matching, low-rank estimation and demosaicing again, and circularly iterating the steps until the specified times or algorithm convergence, so as to obtain a target demosaiced image;
the low-rank regularization constraint of the data matrix uses a weighted nuclear norm instead of a nuclear norm, the weighted nuclear norm being of the form:
wherein σjThe jth singular value representing the internal matrix X; omegajRepresenting the weight corresponding to the j-th singular value; the objective function is of the form:
wherein, ykIs the measured value of the k channel; phikA downsampled matrix for a kth channel; x is the number ofkIs the target image of the k channel; eta is the noise of the channel;
when the objective function is solved, introducing an auxiliary variable, decomposing the objective function, and alternately performing low-rank estimation on the data matrix and demosaic reconstruction on the target image to finally obtain an estimated value of the target image; the introduced auxiliary variable is LiThe objective function after the introduction of the auxiliary variable becomes
Decomposing the objective function after introducing the auxiliary variable to obtain the following formula
Wherein the content of the first and second substances,
is at xkThe data matrix extracted from the same position is extracted,
a weighted kernel norm of the formula
ωjL is more than or equal to 0iEach singular value σ of the matrixjCorresponding weight, λ>0 is a regularization parameter;
and alternately performing low-rank estimation of the data matrix and demosaic reconstruction of the target image on the two equations to finally obtain an estimation value of the target image.
2. The method of claim 1, wherein the initialized estimation method of the preset image comprises interpolation demosaicing or compressed sensing demosaicing.
3. The method of claim 2, wherein the interpolation demosaicing comprises nearest neighbor interpolation, bilinear interpolation, and adaptive interpolation.
4. The method according to claim 2, wherein the compressed sensing demosaicing method comprises a compressed sensing method under discrete cosine transform, a compressed sensing method under total variation minimization and a compressed sensing method under total variation minimization based on generalized alternative projection.
5. The method according to claim 1, wherein before performing the matching process, the sample image sub-blocks are extracted according to a specified step length and an initial value T is preset as a similarity threshold between the image sub-blocks, wherein when the similarity between the image sub-blocks in the search range and the sample image sub-blocks satisfies T, the image sub-blocks are selected as image sub-blocks with a similar structure to the sample image sub-blocks.
6. The method of claim 5, wherein the similarity measures include Manhattan distance, Euclidean distance, and normalized Euclidean distance.
7. The method according to claim 1 or 5, wherein the searching range in searching for the image sub-blocks with the similar structure to the sample image sub-blocks in the preset image for matching is a non-local range in a global range, and whether the image sub-blocks with the similar structure to the sample image sub-blocks are selected depends only on whether the similarity meets a threshold requirement.
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