CN113298232B - Infrared spectrum blind self-deconvolution method based on deep learning neural network - Google Patents

Infrared spectrum blind self-deconvolution method based on deep learning neural network Download PDF

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CN113298232B
CN113298232B CN202110548772.9A CN202110548772A CN113298232B CN 113298232 B CN113298232 B CN 113298232B CN 202110548772 A CN202110548772 A CN 202110548772A CN 113298232 B CN113298232 B CN 113298232B
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鞠婷
朱虎
邓丽珍
程维文
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses an infrared spectrum blind self-deconvolution method based on a deep learning neural network, which comprises the following steps: and inputting the degraded infrared spectrum into the constructed generation network model, and recovering the potential clean infrared spectrum. Constructing and generating a network model, comprising: establishing and generating a network model; establishing an infrared spectrum degradation formula, and adding a total variation regularization function to optimize the generative network model; using a joint optimization algorithm to include raw infrared spectraxAnd fuzzy corekUpdating the parameters; inputting the degraded infrared spectrum into a generation network model for iterative training; the iterative training cannot be stopped until a condition is satisfied, and a potential clean infrared spectrum is obtained, as well as an error rate root mean square error RMSE, a correlation coefficient CC, and an self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum.

Description

Infrared spectrum blind self-deconvolution method based on deep learning neural network
Technical Field
The invention relates to an infrared spectrum blind self-deconvolution method based on a deep learning neural network, and belongs to the technical field of infrared spectrum deconvolution processing.
Background
With the development of science and technology and the convergence of various industries, infrared spectroscopy has become one of the most important tools for analyzing chemical structures. The infrared spectrum can be used for researching the structure and chemical bonds of molecules, such as the measurement of force constant and the criterion of molecular symmetry, and can also be used as a method for characterizing and identifying chemical species, and has high accuracy. Over the last decades, it has achieved many excellent performances and is used in various fields, for example: liquid detection, drug detection, chemical structure analysis, biological materials, medical images, food quality, and the like. However, in the process of acquiring the infrared spectrum, the infrared spectrum is often affected by many objective factors, such as the spreading effect of the Point Spread Function (PSF), the frequency band overlapping, random noise, and the like, which all cause the frequency bands of the infrared spectrum to overlap. The infrared spectra of these complex mixtures, which are subject to degradation, make it difficult to obtain accurate molecular information. The reduced ability to perform qualitative and quantitative analyses makes it more difficult to put infrared spectroscopy techniques into practice. To solve this problem, the deconvolution method has received great attention in recent years to recover the degraded spectrum.
In real-world research, the presence of random noise is an important factor in the degradation of infrared spectra, and reconstruction is an active and challenging research topic. Deconvolution of the infrared spectrum is aimed at eliminating spectral broadening effects such as gaussian blur kernel and lorentzian blur kernel. There are many methods for deconvolution of infrared spectra, which are mainly classified into three categories: non-blind deconvolution (NBD), Blind Deconvolution (BD) and semi-blind deconvolution (SBD).
The blurred infrared spectrum was initially recovered clearly by non-blind deconvolution, but given the precise information of the point spread function, the earliest technique of non-blind deconvolution was fourier self-deconvolution (FSD) by blurred infrared spectra. Many other non-blind deconvolution techniques have since been developed, which have achieved good results in terms of infrared spectrum deconvolution. However, non-blind deconvolution relies on much relevant information, and to reduce the influence of these factors, a semi-blind deconvolution (SBD) method is generated, which assumes that the PSF is a parametric function based on a priori knowledge. The two previous methods result in the inability to reconstruct a clean infrared spectrum if the blur kernel information is lost during deconvolution. However, blind deconvolution methods are generally used without knowing the exact blur kernel information, recovering a clean spectrum from the blurred infrared spectrum, and at the same time estimating the blur kernel. Blind deconvolution is also one of the most challenging tasks, just because blind deconvolution does not know the information of the blur kernel in advance.
The traditional method of blind deconvolution is the a posteriori probability based MAP method, but this method does not work well in some ways. In recent years, some neural networks for deconvolution processing have been proposed, such as stacked denoising autocoders, Convolutional Neural Networks (CNNs), feed-forward-only neural networks, and full convolution neural networks. Deep learning is performed through a large number of training iterations. The mapping of potential clean infrared spectra or fuzzy kernels is learned from a vast training data set, but existing deep deblurring networks are limited in dealing with a variety of complex and large-sized fuzzy kernels.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art, provide an infrared spectrum blind self-deconvolution method based on a deep learning neural network, and provide a method for combining a posterior probability (MAP) method with deep learning. Adding Total Variation (TV) regularization can solve the problem of trained overfitting.
In order to achieve the above object, the present invention provides an infrared spectrum blind self-deconvolution method based on a deep learning neural network, comprising: and inputting the degraded infrared spectrum into the constructed generation network model, and recovering the potential clean infrared spectrum.
Preferably, the building of the generative network model comprises:
establishing and generating a network model;
establishing an infrared spectrum degradation formula, and adding a total variation regularization function to optimize the generative network model;
updating parameters including the original infrared spectrum x and the fuzzy kernel k by using a joint optimization algorithm;
inputting the degraded infrared spectrum into a generation network model for iterative training;
the iterative training cannot be stopped until a condition is satisfied, and a potential clean infrared spectrum is obtained, as well as an error rate root mean square error RMSE, a correlation coefficient CC, and an self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum.
Preferably, the creating a generative network model comprises:
the formula for generating the network model is as follows:
Figure GDA0003725309330000021
in the formula, G x Generation of networks for potentially clean infrared spectra, G k Generating a network for the fuzzy core, z x Sample data for degraded infrared spectrum, z k Sample data of the blur kernel, y is a blurred infrared spectrum,
Figure GDA0003725309330000022
and
Figure GDA0003725309330000023
representing the ith generated potential clean infrared spectrum and the jth obtained blur kernel.
Preferably, the infrared spectrum degradation formula is:
Figure GDA0003725309330000024
in the formula, y is a fuzzy infrared spectrum, k represents a fuzzy kernel, x represents an original infrared spectrum, n represents additive noise,
Figure GDA0003725309330000038
representing a convolution operation.
Preferentially adding a total variation regularization function to optimize the generated network model, wherein the method comprises the following steps:
in order to prevent the full connected network from generating overfitting in estimating the fuzzy kernel, an additional full variation regularization aiming at the fuzzy kernel is introduced, and formula (1) is transformed into (3):
Figure GDA0003725309330000031
where λ and τ in denote regularization parameters controlled by the noise level σ, and TV () denotes a fully variant regularization function.
Preferentially, updating parameters including an original infrared spectrum x and a fuzzy kernel k by using a joint optimization algorithm, and inputting the degraded infrared spectrum into a generation network model for t times of iterative training; the iterative training cannot be stopped until a condition is satisfied, a potential clean infrared spectrum is obtained, and the error rate root mean square error RMSE, the correlation coefficient CC, and the self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum include:
4.1, inputting the nth degraded infrared spectrum into a generated network model, wherein N belongs to [1, N ], and N and N are positive integers;
4.2 initializing uniformly distributed infrared spectrum sample data z x And fuzzy kernel sample data z k Restoring it to the default value;
iterating for multiple times until the iteration times reach the set value T;
the multiple iterations are:
t is accumulated from 1 to T in sequence, the iteration times are circularly solved from 1 to T, the gradient descending operation is carried out on the objective function (3) in each iteration,
calculating gradient of t-1 iteration at t-th iteration
Figure GDA0003725309330000032
And
Figure GDA0003725309330000033
t∈[1，T]，
updating by alternating direction multiplier algorithm
Figure GDA0003725309330000034
And
Figure GDA0003725309330000035
according to the formula
Figure GDA0003725309330000036
And
Figure GDA0003725309330000037
calculate the parameter k andx, calculating error rate Root Mean Square Error (RMSE), Correlation Coefficient (CC) and self-Weighted Correlation Coefficient (WCC) of all the iterated potential clean infrared spectrums and the original infrared spectrums;
and judging whether the degraded infrared spectrum input into the generated network model is the last degraded infrared spectrum, if not, adding 1 to the value of n, and operating the step 4.1, otherwise, ending the operation.
Preferably, λ is set to 0.1 × σ.
The invention achieves the following beneficial effects:
two generation networks G are respectively established aiming at clean infrared spectrum and fuzzy core x And G k . Generator network G with infrared spectrum deployed under excitation of DIP network x The generator network is made up of asymmetric auto-encoders with hopping connections to capture the main content of the potentially clean infrared spectrum. The asymmetric self-encoder of the jump connection is an improvement of an automatic encoder, and has good advantages compared with a common encoder: first, they allow the signal to propagate back directly to the bottom layer, thus solving the problem of gradient vanishing, making it easier to train deep networks, thus achieving an improvement in recovery performance. Second, these jumped connections transfer the details of the infrared spectrum from the convolutional layer to the deconvolution layer, which helps to recover a clean infrared spectrum.
A Fully Connected Network (FCN) model is used as a priori of a fuzzy core, and a fully connected layer has strong fitting capacity and can be fitted with quite complex functions. At the same time, the extracted information is mapped to the peak details of the recovered spectrum. In order to satisfy the non-negative equality constraint of the fuzzy core, in the fuzzy core network G k The output layer of (a) deploys a sorted Softmax nonlinear function to satisfy the normalization constraint of the fuzzy kernel.
The noise level in the neuroblind deconvolution model is explicitly considered by an additional Total Variation (TV) regularization and a regularization parameter. Meanwhile, in order to prevent the situation that the full-connected network generates overfitting in the estimation of the fuzzy kernel, an additional TV regular aiming at the fuzzy kernel is also introduced. These regularization operations can effectively prevent the restored infrared spectrum from generating an overfitting phenomenon.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a comparison graph of error analysis in a single-mode blurred nuclear infrared spectroscopy dataset according to the method of the present invention;
FIG. 3 is a graph showing the comparison of the error analysis of the mixed fuzzy nuclear infrared spectroscopy data set by the method of the present invention;
FIG. 4 is a comparison graph of deconvolution error analysis of infrared spectra under different regularized optimizations in accordance with the present invention;
FIG. 5 is a comparison graph of the error analysis of the data set of the real infrared spectrum according to the method of the present invention.
Detailed Description
The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
In this example, python and MATLAB are used as implementation platforms.
The method disclosed by the invention realizes the recovery of a potential clean infrared spectrum from a degraded infrared spectrum by the method shown in figure 1, and the infrared spectrum blind deconvolution method disclosed by the invention is compared with other traditional infrared spectrum deconvolution methods on the same data set through experiments. The method comprises the following specific steps:
step 1: establishing infrared spectrum blind self-deconvolution generation network model G x 、G k 。
1. Building a Generation network G x
The blind self-deconvolution neural network architecture proposed by the present invention comprises an asymmetric automatic encoder network with hopping connections and a Fully Connected (FCN) network. Conventional blind deconvolution methods are mostly based on the Maximum A Posteriori (MAP) framework. The equation is expressed as shown in formula (2):
Figure GDA0003725309330000051
wherein P is r (y | k, x) is the likelihood corresponding to the fidelity term, P r (x) And P r (k) Separately for clean infrared spectra and ambiguitiesA priori modeling of the kernel. The traditional way of establishing a priori for x is usually done by hand, which certainly is not enough in terms of description of clean infrared spectra and blur kernels. The fidelity term of the MAP network framework can be obtained by converting equation (1):
Figure GDA0003725309330000052
meanwhile, in order to improve the generalization capability of the whole convolutional neural network, the invention carries out optimization by adding a regularization term, so that the formula (2) is converted into the formula (3):
Figure GDA0003725309330000053
where λ and τ correspond to compromise regularization parameters for infrared spectra and blur kernel, respectively.
Under the excitation of a DIP network, the infrared spectrum generator network G is deployed in the invention x The generator network is made up of asymmetric auto-encoders with hopping connections to capture the main content of the potentially clean infrared spectrum. The self-encoder is a network and plays a crucial role in the maintenance of deep learning. The use of an auto-encoder has advantages in feature extraction and processing time. While the asymmetric self-encoder of the jump connection is an improvement of the auto-encoder, which helps to restore a clean infrared spectrum. In the inventive experiment, the first 5 layers of the encoder were skipped over the last 5 layers connected to the decoder. Finally, a potentially clean infrared spectrum is generated using the convolved output layers. To satisfy the range constraint of x, Sigmoid nonlinearity is applied to the output layer. For a single encoder-decoder, n is inside f The filter of the layer, inside the filter is a convolution kernel of k × 1 and a filling convolution of p × 1. We fix the filter size in the last convolution to 1 x 1. The slope of the leakyreu is 0.2, downsampling is achieved using stride-2, and upsampling is achieved using 1 × bilinear interpolation.
2. Building a Generation network G k
Generators formed by asymmetric autoencodersThe prior on the fuzzy core is not well obtained by the networks of the generators. The blur kernel k also typically contains much less information than the potentially clean image x and can be generated well by a simpler generation network. Therefore, in order to obtain better fuzzy kernel priors, the invention adopts a Fully Connected Network (FCN) model as the prior of the fuzzy kernel, and the extracted information is mapped to the peak details of the recovery spectrum. In order to satisfy the non-negative equality constraint of the fuzzy core, the invention generates the network G k The output layer of (a) deploys a sorted Softmax nonlinear function to satisfy the normalization constraint of the fuzzy kernel. By fixing the network structure (G) sampled from a uniform distribution k And G x ) And input (z) k And z x ) The blind deconvolution is thus formulated as a pair G k And G x Unconstrained neural optimization of network parameters. Therefore, k and x in formula (3) are replaced by G k And G x And removing regularization terms
Figure GDA0003725309330000054
And ψ (x). Due to the deployed Softmax nonlinear function, the invention further introduces the nonnegative equation constraint of the fuzzy kernel k, and the size in x is also constrained in the range [0,1 ]]And (4) the following steps. Wherein z is x And z k Is sampled from a uniform distribution, and i and (.) j Then the ith and jth elements. Equation (3) becomes equation (4):
Figure GDA0003725309330000061
step 2: according to an infrared spectrum degradation formula, a loss function is established, and in order to solve the over-fitting problem, a Total Variation (TV) regularization function is added to the infrared spectrum and the fuzzy kernel respectively to optimize an overall objective function.
Latent clean infrared spectrum generation network G x It is proposed based on the DIP theory basis, which consists of an asymmetric auto-encoder with a jump connection. Although the G is x The network has high resistance, but relies heavily on one iteration in the performance of infrared spectrum deconvolutionAnd additional averaging of different optimization runs. Moreover, only the loss function is used as the objective function, and the restored infrared spectrum generates an overfitting phenomenon. The present invention then introduces total variation regularization (TV). The total variation regularization is the average of all sample errors over the entire training data set, and such regularization can be used for denoising, deconvolution, image inpainting, and the like. It supports three noise models: poisson, Gaussian and Laplace, which realize denoising, deconvolution and image restoration by solving the TV recovery problem. The main steps are as follows:
(1) and (4) establishing an energy general function and a constraint condition from an actual image problem.
(2) And solving an E-L equation through a variational principle.
(3) An approximate solution, i.e. a numerical solution of the partial differential equation, is found under initial conditions.
The present invention explicitly considers the noise level in the neuropblinded deconvolution model by an additional Total Variation (TV) regularization and a regularization parameter. Meanwhile, in order to prevent the situation that the full-connected network generates overfitting in the estimation of the fuzzy kernel, an additional TV regular aiming at the fuzzy kernel is also introduced. Then equation (4) is transformed to (5), which is shown below:
Figure GDA0003725309330000062
where λ, τ denote the regularization parameters controlled by the noise level σ. Although generating network G x More powerful, but G x The combination with another infrared spectrum prior is generally advantageous for the deconvolution properties of the infrared spectrum. In addition, the introduction of noise level dependent regularization parameters λ, τ can greatly improve the robustness of processing blurred infrared spectra with various noise levels. The present invention sets λ to 0.1 × σ.
And step 3: the parameters are updated using a joint optimization algorithm.
The whole learning process of the formula (5) is unsupervised learning, and the Joint Optimization (Joint Optimization) is used for optimizing the formula (5). Because the entire optimization equation is unconstrained optimization, unconstrained optimization is highly non-convex. If alternating optimization ADMM (alternating direction multiplier) is used, the optimization equation will be stuck at the pole. Joint Optimization (Joint Optimization) may lead to better convergence of the loss function compared to ADMM (alternating direction multiplier) Optimization. The algorithm flow is as follows:
updating parameters including an original infrared spectrum x and a fuzzy kernel k by using a joint optimization algorithm, and inputting each degraded infrared spectrum into a generation network model for t times of iterative training; the iterative training cannot be stopped until a condition is satisfied, a potential clean infrared spectrum is obtained, and the error rate root mean square error RMSE, the correlation coefficient CC and the self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum comprise:
4.1, inputting the nth degraded infrared spectrum into a generated network model, wherein N belongs to [1, N ], and N and N are positive integers;
4.2 initializing uniformly distributed infrared spectrum sample data z x And fuzzy kernel sample data z k Restoring it to the default value;
iterating for multiple times until the iteration time reaches the set value T;
the multiple iterations are:
t is accumulated from 1 to T in sequence, the iteration times are circularly solved from 1 to T, the gradient descending operation is carried out on the objective function (3) in each iteration,
calculating gradient of t-1 iteration at t-th iteration
Figure GDA0003725309330000071
And
Figure GDA0003725309330000072
t∈[1，T]，
updating by alternating direction multiplier algorithm
Figure GDA0003725309330000073
And
Figure GDA0003725309330000074
according to the formula
Figure GDA0003725309330000075
And
Figure GDA0003725309330000076
calculating parameters k and x, and calculating error rate root mean square error RMSE, correlation coefficient CC and self-weighted correlation coefficient WCC of all the iterated potential clean infrared spectrums and the original infrared spectrums;
and judging whether the degraded infrared spectrum input into the generated network model is the last degraded infrared spectrum, if not, adding 1 to the value of n, and operating the step 4.1, otherwise, ending the operation.
And fourthly, outputting: the output of the whole algorithm is generated by a model
Figure GDA0003725309330000077
And
Figure GDA0003725309330000078
and 4, step 4: and inputting the degraded infrared spectrum into a network system for training.
1. Data set preparation
The training dataset for the experiments performed in the present invention was 1225 artificially generated noisy contaminated infrared spectroscopy dataset. The method of obtaining the training data set is based on a method of degenerating a spectral model. Different fuzzy kernels such as Gaussian fuzzy kernel, Lorentz fuzzy kernel and the like and noise are added into a clean infrared spectrum to simulate a spectrum degradation process; the raw clean infrared spectrum is obtained from a high precision infrared spectrometer. Because the present invention uses a single infrared spectroscopy unsupervised network to generate a clean infrared spectrum, batch processing of training data is not required. Generating a network G x And G k Only the degraded fuzzy ir spectrum is required for training, and no real ir spectrum is required.
2. Parameter initialization and training process
The experimental parameters of the invention are initialized as follows: the Learning Rate (LR) is 0.01, and the total variation regularization weight (tv _ weight) is 0 e-6. According to the iterative algorithm, the invention trains a Joint Optimization (Joint Optimization) algorithm to update parameters during the experiment. The procedure for updating the parameters (x, k) is shown in step 3. And finally, obtaining average errors RMSE, CC and WC of all iterations according to the calculated k and x.
And 5: experimental results and analysis.
The same data set (artificial and true infrared) was compared by different deconvolution methods. First, the present invention and conventional infrared spectral deconvolution are trained and compared on a single blurred nuclear infrared spectral data set. The result is shown in figure 2, and the invention can recover clearer texture details on single-mode blurred nuclear infrared spectrum.
Secondly, the present invention and the traditional infrared spectrum deconvolution are trained and compared on the mixed fuzzy nuclear infrared spectrum data set. The result is shown in figure 3, and the invention can recover clearer texture details on the mixed fuzzy nuclear infrared spectrum.
Then, the invention trains and compares under different regular functions of the same data set. The result is shown in figure 4, and the invention can recover clearer texture details under the two TV regularities of infrared spectrum and fuzzy kernel.
Finally, the present invention and conventional infrared spectroscopy deconvolution are trained and compared on a true infrared spectroscopy dataset. The result is shown in fig. 5, and the invention can recover clearer texture details on the real infrared spectrum.
In conclusion, the infrared spectrum blind deconvolution method based on the deep learning neural network can recover a clearer potential clean infrared spectrum. Compared with the traditional method, the method has the advantage that the recovery on the texture details is clearer.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (3)

1. An infrared spectrum blind self-deconvolution method based on a deep learning neural network is characterized by comprising the following steps:
inputting the degraded infrared spectrum into the constructed generation network model, and recovering a potential clean infrared spectrum;
constructing and generating a network model, comprising:
establishing and generating a network model;
establishing an infrared spectrum degradation formula, and adding a total variation regularization function to optimize the generative network model;
updating parameters including the original infrared spectrum x and the fuzzy kernel k by using a joint optimization algorithm;
inputting the degraded infrared spectrum into a generation network model for iterative training;
the iterative training can not be stopped until the condition is met, and a potential clean infrared spectrum, an error rate Root Mean Square Error (RMSE), a correlation coefficient CC and an self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum are obtained;
the infrared spectrum degradation formula is as follows:
Figure FDA0003725309320000011
in the formula, y is a fuzzy infrared spectrum, k represents a fuzzy kernel, x represents an original infrared spectrum, n represents additive noise,
Figure FDA0003725309320000012
represents a convolution operation;
adding a total variation regularization function to optimize the generated network model, which comprises the following steps:
in order to prevent the full connected network from generating overfitting in estimating the fuzzy kernel, an additional full variation regularization aiming at the fuzzy kernel is introduced, and formula (1) is transformed into (3):
Figure FDA0003725309320000013
where λ and τ in the middle represent regularization parameters controlled by the noise level σ, and TV () represents a full-variational regularization function;
updating parameters including an original infrared spectrum x and a fuzzy kernel k by using a joint optimization algorithm, and inputting each degraded infrared spectrum into a generation network model for t times of iterative training; the iterative training cannot be stopped until a condition is satisfied, a potential clean infrared spectrum is obtained, and the error rate root mean square error RMSE, the correlation coefficient CC, and the self-weighted correlation coefficient WCC of the potential clean infrared spectrum and the original infrared spectrum include:
4.1, inputting the nth degraded infrared spectrum into a generated network model, wherein N belongs to [1, N ], and N and N are positive integers;
4.2 initializing uniformly distributed infrared spectrum sample data z x And fuzzy kernel sample data z k Restoring it to the default value;
iterating for multiple times until the iteration time reaches the set value T;
the multiple iterations are:
t is accumulated from 1 to T in sequence, the iteration times are circularly solved from 1 to T, the gradient descending operation is carried out on the objective function (3) in each iteration,
calculating gradient of t-1 iteration at t-th iteration
Figure FDA0003725309320000021
And
Figure FDA0003725309320000022
updating by alternating direction multiplier algorithm
Figure FDA0003725309320000023
And
Figure FDA0003725309320000024
according to the formula
Figure FDA0003725309320000025
And
Figure FDA0003725309320000026
calculating parameters k and x, and calculating error rate root mean square error RMSE, correlation coefficient CC and self-weighted correlation coefficient WCC of all the iterated potential clean infrared spectrums and the original infrared spectrums;
and judging whether the degraded infrared spectrum input into the generated network model is the last degraded infrared spectrum, if not, adding 1 to the value of n, and operating the step 4.1, otherwise, ending the operation.
2. The infrared spectrum blind self-deconvolution method based on the deep learning neural network of claim 1, wherein the establishing of the generative network model comprises:
the formula for generating the network model is as follows:
Figure FDA0003725309320000027
in the formula, G x Generation of networks for potentially clean infrared spectra, G k Generating a network for the fuzzy core, z x Sample data for degraded infrared spectrum, z k Sample data of the blur kernel, y is a blurred infrared spectrum,
Figure FDA0003725309320000028
and
Figure FDA0003725309320000029
representing the ith generated potential clean infrared spectrum and the jth acquired blur kernel.
3. The deep learning neural network-based infrared spectrum blind self-deconvolution method of claim 1, wherein λ is set to 0.1 x σ.
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