CN111651720B - Multispectral reconstruction method and device based on L4 norm optimization - Google Patents
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Abstract
The application provides a multispectral reconstruction method and a multispectral reconstruction device based on L4 norm optimization, wherein the method comprises the following steps: acquiring a multispectral data set; performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space; carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct a target function; solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix; and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space. Therefore, the L4 norm optimization is utilized to carry out component analysis on the high-dimensional data, the characteristic of the obtained base vector is obvious, the reconstruction efficiency is improved, the reconstruction is carried out under the regularization constraint, the precision is improved, and the algorithm robustness is enhanced.
Description
Technical Field
The application relates to the technical field of computer vision and computational photography, in particular to a multispectral reconstruction method and device based on L4 norm optimization.
Background
The spectrum represents the intrinsic information of the object, which represents the reflection/projection rate of the object to light wave in different wave bands, and the multispectral dimension is often more than 10 times of the dimension of the traditional color space, and is generally obtained by reconstructing from partial measurement values by using a multispectral reconstruction algorithm. The multispectral reconstruction has very important application value in the fields of satellite remote sensing, detection, medicine and the like.
The multispectral reconstruction method in the related art includes: pseudo-inverse, basis function, R-matrix theory, regression, and the like. These methods are less noise resistant and robust.
Disclosure of Invention
The present application is directed to solving, at least in part, one of the technical problems in the related art.
Therefore, the multispectral reconstruction method based on L4 norm optimization is provided, high-dimensional data are subjected to component analysis by utilizing L4 norm optimization, the obtained base vector features are obvious, the reconstruction efficiency is improved, reconstruction is performed under regularization constraint, the precision is improved, and the algorithm robustness is enhanced.
The application provides a multispectral reconstruction device based on L4 norm optimization.
An embodiment of one aspect of the present application provides a multispectral reconstruction method based on L4 norm optimization, including:
acquiring a multispectral dataset;
performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space;
carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct a target function;
solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix;
and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space.
The L4 norm optimization model is as follows:
Wherein, R (n, p) = [ y1 y2 … yn ] is the multispectral data set, the sample size is p, and each sample comprises n sampling points; b is the base vector space, X is a coefficient matrix, R = BX, and O (n; R) is an orthogonal set.
Optionally, the performing component analysis on the multispectral dataset by using an L4 norm optimization model to form a basis vector space includes:
step a, initializing a matrix A 0 E is O (n, R) and is used as an L4 norm maximization operator;
step b, loop T =0,1, … T, calculating gradient:
and projection->
A t+1 ＝UV * ；
Step c, ending circulation and outputting the base vector matrix
Optionally, the constructing the target function by performing regularization constraint on the spectrum to be reconstructed through a preset regularization algorithm includes:
establishing a multispectral reflectivity and channel response relation model as follows:
wherein λ is the wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (. Lamda.), f i The spectral power distribution function of the illumination light source, the transmissivity of the ith channel filter of the multispectral imaging system, the spectral transfer function of the lens and the spectral sensitivity function of the multispectral camera are unknown quantities; n is a radical of an alkyl radical i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
based on regularization constraints, establishing the objective function: min E (| g 0-P) * a0‖ 2 +λ‖P * ‖ 2 )。
Optionally, the solving the objective function, and characterizing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix includes:
solving the objective function as: p = a0 g0 T (g0g0 T +λI) -1 ；
And characterizing the spectrum to be reconstructed by using a basis vector space, and solving a basis vector coefficient matrix: a is ′ ＝a0 g0 T (g0g0 T +λI) -1 g', λ are regularization factors.
According to the basis vector coefficient matrix and the basis vector space, the spectrum for reconstructing the spectrum to be reconstructed is as follows: r is ′ ＝Ba ′ ＝Ba0 g0 T (g0g0 T +λI) -1 g′。
Another embodiment of the present application provides a multispectral reconstruction device based on L4 norm optimization, including:
the acquisition module is used for acquiring a multispectral data set;
the analysis module is used for performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space;
the building module is used for conducting regularization constraint on the spectrum to be reconstructed through a preset regularization algorithm to build a target function;
the solving module is used for solving the objective function, and characterizing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix;
and the reconstruction module is used for reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space.
In another aspect, an embodiment of the present application provides a home appliance, including: memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method for multispectral reconstruction based on L4 norm optimization as described in an embodiment of the aforementioned aspect when the program is executed.
In yet another aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, which when executed by a processor, implements the L4 norm optimization-based multispectral reconstruction method described in the foregoing method embodiments.
The technical scheme provided by the embodiment of the application can have the following beneficial effects:
by acquiring a multi-spectral dataset; performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space; carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct a target function; solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix; and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space. Therefore, the L4 norm optimization is utilized to carry out component analysis on the high-dimensional data, the obtained base vector features are obvious, the reconstruction efficiency is improved, reconstruction is carried out under the regularization constraint, the precision is improved, and the algorithm robustness is enhanced.
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The foregoing and/or additional aspects and advantages of the present application 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 schematic flowchart of a multispectral reconstruction method based on L4 norm optimization according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a process of component analysis based on L4 norm optimization according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a process of solving a transformation matrix under a regularization constraint according to an embodiment of the present application;
FIG. 4 is a general schematic diagram of a multi-spectral reconstruction in an embodiment of the present application;
fig. 5 is a diagram of simulation results of the embodiment of the present application.
Fig. 6 is a schematic structural diagram of an L4 norm optimization-based multispectral reconstruction device according to an embodiment of the present disclosure.
Detailed Description
Reference will now be made in detail to embodiments of the present application, 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 accompanying drawings are illustrative and intended to explain the present application and should not be construed as limiting the present application.
The multispectral reconstruction method and device based on L4 norm optimization according to the embodiment of the present application are described below with reference to the accompanying drawings.
In particular, the spectral curve of a natural object is generally relatively smooth and can be considered as a linear combination of several basis vectors. Therefore, in practical applications, effective dimension reduction and reconstruction are needed for solving the problems of data redundancy, high dimension and large calculation amount. The high-dimensional data is represented by linear combination of low-dimensional data, and the reconstruction precision can be kept while the dimension is reduced.
The high-order norm optimization develops rapidly in the research of the last two years, and under the constraint of the low-order norm, the sparsity of the target function can be improved by maximizing the high-order norm. The idea breaks through the previous NP limitation of L1 norm and L0 norm and provides a new optimization selection. Since the 1970 s, the characteristics of the L4 norm were used to find (orthogonal) functions with similar characteristics. There is theorem proving that local maximization points can be found by utilizing L4 norm maximization in spherical harmonics. The blind convolution method proves that the dictionary which is chemically extracted by utilizing the l4 norm maximum of the target function is close to a real dictionary, the geometric characteristic is good, and all saddle points are negative curvatures. In 2019, research articles propose a method for realizing orthogonal complete dictionary learning based on L4 maximization, and the method breaks through the limitation of one-column and one-column updating learning in the traditional method, realizes integral learning of the dictionary, promotes data sparsity, reduces calculation amount and iteration times, and is high in speed and efficiency. In addition, fourth order statistical accumulations have been widely used for blind source separation or Independent Component Analysis (ICA). And through theoretical analysis, the L4 norm optimization is closely related to a principal component analysis method and an independent component analysis method, and has potential advantages in the aspect of component analysis.
The multispectral reconstruction method based on L4 norm optimization has the characteristics of high signal-to-noise ratio, high precision, low cost, good adaptability and the like.
Fig. 1 is a schematic flowchart of a multispectral reconstruction method based on L4 norm optimization according to an embodiment of the present disclosure.
As shown in fig. 1, the method comprises the steps of:
The multispectral dataset of the application can be selected according to requirements, such as Munsell color chart spectrum datasets of different materials, munsell color chart spectrum datasets under specific illumination conditions, german Lauer (RLA) color chart datasets and the like.
And 102, performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space.
In the embodiment of the present application, the L4 norm optimization model is:
Wherein, R (n, p) = [ y1 y2 … yn ] is a multispectral data set, the sample size is p, and each sample comprises n sampling points; b is a base vector space, X is a coefficient matrix, R = BX, and O (n; R) is an orthogonal set.
In this embodiment of the present application, a component analysis is performed on the multispectral data set by using an L4 norm optimization model, and a basis vector space is formed by:
step a, initializing a matrix A 0 E is O (n, R) and is used as an L4 norm maximization operator;
step b, circulating T =0,1, … T, calculating gradient:
and projection->
A t+1 ＝UV * ；
Step c, ending circulation and outputting the basis vector matrix
And 103, carrying out regularization constraint on the spectrum to be reconstructed through a preset regularization algorithm to construct an objective function.
And 104, solving the target function, and representing the spectrum to be reconstructed by using the basis vector space to obtain a basis vector coefficient matrix.
In the embodiment of the present application, a model of the relationship between the multispectral reflectivity and the channel response is established as follows:
wherein λ is the wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (. Lamda.), f i (lambda), o (lambda), s (lambda) are unknown quantities which are respectively the spectral power distribution function of the illumination light source and the transmissivity of the ith channel filter of the multi-spectral imaging systemA spectral transfer function of the lens, a spectral sensitivity function of the multispectral camera; n is a radical of an alkyl radical i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
based on regularization constraints, an objective function is established: min E (II g 0-P) * a0‖ 2 +λ‖P * ‖ 2 )。
In the embodiment of the present application, solving the objective function, and characterizing the spectrum to be reconstructed by using the basis vector space to obtain the basis vector coefficient matrix includes:
solving the objective function as: p = a0 g0 T (g0g0 T +λI) -1 (ii) a And (3) characterizing the spectrum to be reconstructed by using a basis vector space, and solving a basis vector coefficient matrix: a' = a0 g0 T (g0g0 T +λI) -1 g', λ are regularization factors.
It should be noted that, in the embodiment of the present application, the regularization methods used include, but are not limited to, gikhonov (Tikhonov) regularization, L1 regularization, L2 regularization, and the like regularization methods, and the calculation of the sample coefficient matrix may be implemented by sparse reconstruction methods, including, but not limited to, methods such as basis tracking (BP), orthogonal Matching Pursuit (OMP), and the like, and an appropriate sparse reconstruction is selected, so that the sample is reconstructed with high accuracy.
And 105, reconstructing the spectrum to be reconstructed according to the base vector coefficient matrix and the base vector space.
In the embodiment of the present application, according to the basis vector coefficient matrix and the basis vector space, the spectrum to be reconstructed is reconstructed as follows: r' = Ba0 g0 T (g0g0 T +λI) -1 g′。
It should be noted that, in the embodiment of the present application, the reconstruction algorithm includes, but is not limited to, sparse reconstruction based on a priori knowledge, full-variational reconstruction, and the like.
In the multispectral reconstruction method based on L4 norm optimization, a multispectral data set is obtained; performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space; carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct a target function; solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix; and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space. Therefore, the L4 norm optimization is utilized to carry out component analysis on the high-dimensional data, the characteristic of the obtained base vector is obvious, the reconstruction efficiency is improved, the reconstruction is carried out under the regularization constraint, the precision is improved, and the algorithm robustness is enhanced.
2-5, fig. 2 is a schematic diagram of a process of analyzing components based on L4 norm optimization according to an embodiment of the present application; FIG. 3 is a schematic diagram of a process of solving for a transformation matrix under a regularization constraint according to an embodiment of the present application; FIG. 4 is a general schematic diagram of a multi-spectral reconstruction in an embodiment of the present application; fig. 5 is a diagram of simulation results according to an embodiment of the present application.
Specifically, fig. 4 shows an overall flow of multispectral reconstruction in the embodiment of the present application, and a schematic diagram of an L4 norm optimization analysis process is shown in fig. 2. Multispectral data is selected and a multispectral dataset used for training is established. The method comprises the steps of performing component analysis on high-dimensional data through L4 norm optimization, establishing a complete basis vector space, solving the L4 norm maximization of a target function to obtain the basis vector space of a characteristic spectral reflectivity data set, and calculating a sample coefficient matrix through a sparse reconstruction method, wherein the sparse reconstruction method comprises but is not limited to methods such as basis tracking (BP) and Orthogonal Matching Pursuit (OMP). Selecting proper sparsity reconstruction to reconstruct a sample at high precision, wherein the coefficient matrix of the sample is a 0 Satisfies the following conditions:
the process of establishing the objective function under the regularization constraint is shown in fig. 3, and in order to improve the algorithm robustness, regularization items are introduced, including but not limited to methods such as gipanofu (Tikhonov) regularization, L1 regularization, L2 regularization and the like. In a specific example, using the gihonov regularization algorithm, the derivation of the reconstructed objective function is as follows:
establishing a multispectral reflectivity and channel response relation model as follows:
wherein λ is the wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (. Lamda.), f i The spectral power distribution function of the illumination light source, the transmissivity of the ith channel filter of the multispectral imaging system, the spectral transfer function of the lens and the spectral sensitivity function of the multispectral camera are unknown quantities; n is i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
based on regularization constraints, an objective function is established: min E (II g 0-P) * a0‖ 2 +λ‖P * ‖ 2 )。
And solving an objective function, using the basis vector space to characterize the spectrum to be reconstructed, and solving a basis vector coefficient matrix.
a) Solving the objective function P = a0 g0 T (g0g0 T +λI) -1 ；
b) And (3) characterizing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix, wherein lambda is a regular factor: a' = a0 g0 T (g0g0 T +λI) -1 g′；
And reconstructing the target spectrum according to the coefficient matrix and the base vector space.
Spectrum is reconstructed using basis vectors:
R′＝Ba′＝Ba0 g0 T (g0g0 T +λI) -1 g′。
in order to verify the effectiveness of the method, the color chart spectral data of different materials are adopted as the training set to be simulated, the reconstruction result of the color chart data to be tested is shown in fig. 5, and compared with the principal component analysis method, the multispectral reconstruction method based on the L4 norm optimization has the advantages of high reconstruction effect precision and obvious advantages.
In order to implement the above embodiments, the present application further provides a multispectral reconstruction device based on L4 norm optimization.
Fig. 6 is a schematic structural diagram of an L4 norm optimization-based multispectral reconstruction device according to an embodiment of the present disclosure.
As shown in fig. 6, the apparatus includes: an acquisition module 601, an analysis module 602, a construction module 603, a solution module 604, and a reconstruction module 605.
The obtaining module 601 is configured to obtain a multispectral dataset.
An analysis module 602, configured to perform component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space.
The building module 603 is configured to perform regularization constraint on the spectrum to be reconstructed by using a preset regularization algorithm to build an object function.
And a solving module 604, configured to solve the objective function, and characterize the spectrum to be reconstructed by using the basis vector space, so as to obtain a basis vector coefficient matrix.
A reconstructing module 605, configured to reconstruct the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space.
Further, in a possible implementation manner of the embodiment of the present application, the L4 norm optimization model is:
Wherein, R (n, p) = [ y1 y2 … yn ] is the multispectral data set, the sample size is p, and each sample comprises n sampling points; b is the base vector space, X is a coefficient matrix, R = BX, and O (n; R) is an orthogonal set.
Further, in a possible implementation manner of the embodiment of the present application, the performing component analysis on the multispectral data set by using the L4 norm optimization model to form a basis vector space includes an analysis module, which is specifically configured to:
step a, initializing a matrix A 0 E is O (n, R) and is used as an L4 norm maximization operator;
step b, loop T =0,1, … T, calculating gradient:
and projection->
A t+1 ＝UV * ；
Step c, ending circulation and outputting the basis vector matrix
Further, in a possible implementation manner of the embodiment of the present application, the building module is specifically configured to:
establishing a multispectral reflectivity and channel response relation model as follows:
wherein λ is the wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (. Lamda.), f i The spectral power distribution function of the illumination light source, the transmissivity of the ith channel filter of the multispectral imaging system, the spectral transfer function of the lens and the spectral sensitivity function of the multispectral camera are unknown quantities; n is i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
based on regularization constraints, the objective function is established: min E (II g 0-P) * a0‖ 2 +λ‖P * ‖ 2 )。
Further, in a possible implementation manner of the embodiment of the present application, the solving module is specifically configured to:
solving the objective function P = a0 g0 T (g0g0 T +λI) -1 ；
And characterizing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix, wherein lambda is a regular factor: a' = a0 g0 T (g0g0 T +λI) -1 g′；
Further, in a possible implementation manner of the embodiment of the present application, the reconstruction module is specifically configured to:
and (3) spectrum reconstruction:
R′＝Ba′＝Ba0 g0 T (g0g0 T +λI) -1 g′。
it should be noted that the foregoing explanation of the method embodiment is also applicable to the apparatus of this embodiment, and is not repeated herein.
In the multispectral reconstruction device based on L4 norm optimization, a multispectral data set is obtained; performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space; carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct a target function; solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix; and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space. Therefore, the L4 norm optimization is utilized to carry out component analysis on the high-dimensional data, the characteristic of the obtained base vector is obvious, the reconstruction efficiency is improved, the reconstruction is carried out under the regularization constraint, the precision is improved, and the algorithm robustness is enhanced.
In order to implement the foregoing embodiments, an embodiment of the present application provides a home appliance, including: the device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the multispectral reconstruction method based on L4 norm optimization according to the embodiment of the method executed by the terminal device.
In order to implement the foregoing embodiments, the present application provides a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the L4 norm optimization-based multispectral reconstruction method described in the foregoing method embodiments.
In the description of the present specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means 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 present application. 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. Furthermore, 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.
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 application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing steps of a custom logic function or process, and alternate implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Further, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are exemplary and should not be construed as limiting the present application and that changes, modifications, substitutions and alterations in the above embodiments may be made by those of ordinary skill in the art within the scope of the present application.
Claims (8)
1. A multispectral reconstruction method based on L4 norm optimization is characterized by comprising the following steps:
acquiring a multispectral data set;
performing component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space, and representing the basis vector space by using a basis vector matrix, wherein the L4 norm optimization model is as follows:
Wherein, R (n, p) = [ y1 y2 … yn ] is the multispectral data set, the sample size is p, and each sample comprises n sampling points; b is the basis vector space, X is a coefficient matrix, R = BX, and O (n; R) is an orthogonal group;
carrying out regularization constraint on a spectrum to be reconstructed by a preset regularization algorithm to construct an objective function, wherein the objective function is as follows: min E (II g 0-P) * a0‖ 2 +λ‖P * ‖ 2 )；
Solving the target function, and representing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix;
and reconstructing the spectrum to be reconstructed according to the basis vector coefficient matrix and the basis vector space.
2. The method of claim 1, wherein the basis vector matrix is determined by steps comprising:
step a, initializing a matrix A 0 E is O (n, R) and is used as an L4 norm maximization operator;
step b, circulating T =0,1, … T, calculating gradient:
and projection->
A t+1 ＝UV * ；
Step c, ending circulation and outputting the basis vector matrix
3. The method of claim 1, wherein the regularization constraining of the spectrum to be reconstructed by a preset regularization algorithm to construct an objective function comprises:
establishing a multispectral reflectivity and channel response relation model as follows:
wherein λ is wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (λ), f i The spectral power distribution function of the illumination light source, the transmissivity of the ith channel filter of the multispectral imaging system, the spectral transfer function of the lens and the spectral sensitivity function of the multispectral camera are unknown quantities; n is a radical of an alkyl radical i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
and establishing the objective function based on regularization constraints.
4. The method of claim 1, wherein solving the objective function to characterize the spectrum to be reconstructed using a basis vector space to obtain a basis vector coefficient matrix comprises:
solving the objective function as: p = a0 g0 T (g0g0 T +λI) -1 ；
And characterizing the spectrum to be reconstructed by using a basis vector space, and solving a basis vector coefficient matrix: a' = a0 g0 T (g0g0 T +λI) -1 g', λ are regularization factors.
5. The method according to claim 1, wherein the spectrum to be reconstructed is reconstructed from the basis vector coefficient matrix and the basis vector space by:
R′＝Ba′＝Ba0 g0 T (g0g0 T +λI) -1 g′。
6. an L4 norm optimization-based multispectral reconstruction device, comprising:
the acquisition module is used for acquiring a multispectral data set;
an analysis module, configured to perform component analysis on the multispectral data set by using an L4 norm optimization model to form a basis vector space, and express the basis vector space by using a basis vector matrix, where the L4 norm optimization model is:
Wherein, R (n, p) = [ y1 y2 … yn ] is the multispectral data set, the sample size is p, and each sample comprises n sampling points; b is the base vector space, X is a coefficient matrix, R = BX, and O (n; R) is an orthogonal group;
the building module is used for conducting regularization constraint on a spectrum to be reconstructed through a preset regularization algorithm to build an objective function, and the objective function is as follows: min E (| | g 0-P) * a0|| 2 +λ||P * || 2 )；
The solving module is used for solving the objective function and characterizing the spectrum to be reconstructed by using a basis vector space to obtain a basis vector coefficient matrix;
and the reconstruction module is used for reconstructing the spectrum to be reconstructed according to the base vector coefficient matrix and the base vector space.
7. The apparatus of claim 6, wherein the analysis module determines the basis vector matrix by:
step a, initializing a matrix A 0 E is O (n, R) and is used as an L4 norm maximization operator;
step b, loop T =0,1, … T, calculating gradient:
and projection->
A t+1 ＝UV * ；
Step c, ending circulation and outputting the basis vector matrix
8. The apparatus of claim 6, wherein the building block is specifically configured to:
establishing a multispectral reflectivity and channel response relation model as follows:
wherein λ is the wavelength; λ min is the minimum wavelength; λ max is the maximum wavelength; g (λ) is the channel response; r (λ) is the object reflectivity; l (. Lamda.), f i The spectral power distribution function of the illumination light source, the transmissivity of the ith channel filter of the multispectral imaging system, the spectral transfer function of the lens and the spectral sensitivity function of the multispectral camera are unknown quantities; n is i Corresponding noise;
mixing l (lambda), f i (λ), o (λ), s (λ) are considered as a whole q, with noise neglected: g = QR;
it is assumed that the coefficient matrix a0 and the channel response function g0 have a correspondence: pg0= a0;
and building the objective function based on regularization constraints.
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