CN109544656B - Compressed sensing image reconstruction method and system based on generation countermeasure network - Google Patents
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Abstract
The invention discloses a compressed sensing image reconstruction method based on a generation countermeasure network, which comprises the following steps: s1, constructing a generated countermeasure network model based on a neural network according to a measurement vector obtained by sampling an original image and the size of a reconstructed image, and designing an objective function for optimizing parameters of the generated countermeasure network model; s2, presetting parameters for training when the countermeasure network model is generated; s3, alternately training a generator and a discriminator by adopting a back propagation algorithm according to the objective function; s4, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding image reconstructed by the measurement vector; otherwise, the steps S2-S4 are executed in a returning mode. The invention uses the strong mapping capability of the generator to preliminarily reconstruct the original image, and uses the countermeasure training of the generator and the discriminator to ensure that the pixel distribution of the image reconstructed by the generator is closer to the original image, thereby achieving the purpose of accurately reconstructing the original image under the low sampling rate.
Description
Technical Field
The invention relates to the technical field of image information processing, in particular to a compressed sensing image reconstruction method and system based on a generated countermeasure network.
Background
Compressed sensing (Compressed Sensing, CS) is a novel signal acquisition theory, integrates the traditional sampling and compression processes, can directly acquire measurement data far lower than Nyquist sampling rate, can reduce sampling cost and storage resources, and meanwhile, the coding end of a compressed sensing model only needs to perform linear random measurement, and the complex optimization process of reconstructing signals is completed at the decoding end.
The imaging systems reconstruct images using iterative optimization algorithms on a small number of observed measurements based on compressed sensing theory. However, these reconstruction algorithms all need to perform complex iterative operation, the reconstruction time is long, and the quality of the reconstructed image is relatively poor under the lower sampling rate, which hinders the deep development and industry application of compressed sensing imaging.
Disclosure of Invention
The invention aims to: in order to overcome the defects of the prior art, the invention provides a compressed sensing image reconstruction method based on a generation countermeasure network, which can solve the problems of longer reconstruction time and poorer quality of reconstructed images.
The technical scheme is as follows: the invention relates to a compressed sensing image reconstruction method based on a generation countermeasure network, which comprises the following steps:
s1, constructing a neural network-based generation countermeasure network model according to a measurement vector obtained by image sampling and the size of a reconstructed image, and designing an objective function for optimizing parameters of the generation countermeasure network model;
s2, presetting parameters for training when the countermeasure network model is generated;
s3, alternately training a generator and a discriminator by adopting a back propagation algorithm according to the objective function;
s4, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding image reconstructed by the measurement vector; otherwise, the steps S2-S4 are executed in a returning mode.
Preferably, in S1, the measurement vector is expressed as:
wherein y represents a measurement vector, phi is a measurement matrix, x represents a data line vector which is changed into a data matrix of an image to be sampled after being changed into vectorization, M represents the size of the measurement vector, and N is the number of pixels of the image to be sampled.
Preferably, in the step S1, the formula for generating the countermeasure network model is:
wherein G is a generator, D is a discriminator, y is a measurement vector, and x representsThe data matrix of the image to be sampled becomes a vector of data rows that becomes vectorized,
reconstruction loss->
Regular for total variation->
To combat losses in the discriminator network.
Preferably, substituting the reconstruction loss, the total variation regularization and the counterloss correspondence formula of the discriminator network into the formula for generating the counternetwork model to obtain objective functions for optimizing parameters of the generator and the discriminator respectively;
the objective function of the generator is expressed as:
the objective function of the discriminator is:
wherein,,
the generator reconstructs an image, i and j are pixel positions of the original image, p data And p y Is the statistical distribution of the original image and the random measurement vector, and γ is the loss weight of the discriminator.
Preferably, in S3, the activation function used in training the generator is Selu, and the activation function used in training the discriminator is lrinlu.
The invention also discloses a system for realizing the compressed sensing image reconstruction method based on the generation countermeasure network, which comprises the following steps:
the network model construction module is used for constructing a neural network-based generation countermeasure network model according to the measurement vector obtained by image sampling and the size of the reconstructed image, and designing an objective function for optimizing parameters of the generation countermeasure network model;
the parameter presetting module is used for presetting parameters for training the generation of the countermeasure network model;
the generator training module is used for alternately training the generator and the discriminator by adopting a back propagation algorithm according to the objective function;
the convergence judging module is used for judging whether the generated countermeasure network model converges or not, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding original image reconstructed by the measurement vector; otherwise, returning to the parameter preset module.
Preferably, in the network model construction module,
the measurement vector is expressed as:
wherein y represents a measurement vector, phi is a measurement matrix, x represents a data row vector which is changed after the data matrix of the image to be sampled becomes vectorized, M represents the size of the measurement vector, and N is the pixel number of the image to be sampled.
Preferably, in the network model building module, the formula for generating the countermeasure network model is:
wherein G is a generator, D is a discriminator, y is a measurement vector, x represents a data line vector which becomes vectorized after the data matrix of the original image becomes vectorized,
the reconstruction is lost to the process,/>
regular for total variation->
To combat losses in the discriminator network.
Preferably, substituting the reconstruction loss, the total variation regularization and the counterloss correspondence formula of the discriminator network into the formula for generating the counternetwork model to obtain objective functions for optimizing parameters of the generator and the discriminator respectively;
the objective function of the generator is expressed as:
the objective function of the discriminator is:
wherein,,
the generator reconstructs an image, i and j are pixel positions of the original image, p data And p y Is the statistical distribution of the original image and the random measurement vector, and γ is the loss weight of the discriminator.
Preferably, in the generator training module, the activation function used in training the generator is Selu, and the activation function used in training the discriminator is lrinlu.
The beneficial effects are that: the invention establishes a compressed sensing image reconstruction method based on a generation countermeasure network by utilizing a compressed sensing theory, and the model initially reconstructs an original image by utilizing the strong mapping capability of the generator under the condition of low sampling rate of the image, and simultaneously, further enhances the capability of the generator by utilizing countermeasure training of the generator and the discriminator, so that the pixel distribution of the image reconstructed by the generator is closer to the original image, and the purpose of accurately reconstructing the original image under the low sampling rate is achieved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a comparison result of a plurality of algorithms for a reconstructed image and an original image of a CelebA face data set according to the present invention, wherein fig. 2a is a schematic diagram of a comparison result of a reconstructed image and an original image obtained by a ReconNet algorithm, fig. 2b is a comparison result of a reconstructed image and an original image obtained by a CSGAN algorithm, fig. 2c is a schematic diagram of a comparison result of a reconstructed image and an original image obtained by a DCGAN algorithm, and fig. 2d is a schematic diagram of a comparison result of a reconstructed image and an original image obtained by a method according to the present invention;
FIG. 3 is a graph of the mean square error comparison result of the Reconnet algorithm, the CSGAN algorithm, the DCGAN algorithm, and the reconstructed image and the original image obtained by the present algorithm, which are related in the present invention;
FIG. 4 is a graph of the results of comparing the peak signal-to-noise ratio and the image structure similarity index of the reconstructed image and the original image obtained by the Reconnet algorithm, the CSGAN algorithm and the DCGAN algorithm;
FIG. 5 is a graph of time versus results for the Reconnet algorithm, the CSGAN algorithm, the DCGAN algorithm, and the present algorithm to reconstruct an image, as referred to in the present invention;
fig. 6 is a schematic diagram of a system configuration according to the present invention.
Detailed Description
As shown in fig. 1, the present invention provides a compressed sensing image reconstruction method based on generation of an countermeasure network, comprising:
Measurement vector y=Φx+ζ, y∈r M ，Φ∈R M×N ，x∈R N Y represents a measurement vector, phi is a measurement matrix, x represents a data line vector which is changed into a vectorization after a picture data matrix is changed into vectorization, M represents the size of the measurement vector, and N is the number of pixels of an original image.
And 2, constructing and generating an countermeasure network model according to the size of the measurement vector and the size of the reconstructed image, and designing an objective function for optimizing parameters of the network model.
The size of the measurement vector determines the size of the input of the generator, and the size of the reconstructed image determines the final output size of the generator. The generating an countermeasure network model is as follows:
wherein G is a generator, D is a discriminator, and the reconstruction loss is
The total variation is regular as
The countermeasures against loss of the discriminator network are +.>
Substituting the reconstruction loss, the total variation regularization and the counterloss of the discriminator network into the network model to obtain objective functions respectively optimizing parameters of the generator and the discriminator, wherein the objective functions of the generator are respectively +.>
The objective function of the discriminator is
The generator reconstructs an image, i and j are pixel positions of the original image, p data And p y Is the statistical distribution of the original image and the random measurement vector, and γ is the loss weight of the discriminator.
The preset parameters comprise model learning rate alpha during training, iteration times L, training batch size S, loss weight gamma of the discriminator during training of the generator, depth and layer number of the generator and the discriminator network, activation function of the generator and class of the generator of the discriminator.
And 4, alternately training the generator and the discriminator by adopting a back propagation algorithm according to the objective function.
Specifically, step 4 specifically includes:
step 41, selecting S training images { x } in training set (1) ,…,x (s) And get the corresponding measurement vector { y } (1) ,…,y (s) }；
Step 42, updating the parameter ω in the discriminator by a back propagation algorithm.
First, calculate discriminator loss
Second, the generator parameter θ is fixed, and the discriminator parameter ω++ω·rmsprop (ω, d) is updated ω ). Wherein RMSProp is one of the gradient descent algorithms.
Step 43, constructing the generator loss function required by training the generator network according to the model
Calculating a loss function of S training images in a batch, fixing a discriminator parameter omega, and updating a generator parameter theta by adopting an RMSProp gradient descent algorithm: theta-alpha-RMSProp (theta, g) θ )。
Step 44, sequentially performing step 41, step 42 and step 43 on all images of the whole training set, and performing a total of L iterations.
And step 5, if the network model is converged, the trained network can directly realize the compressed sensing task of the segment opposite end, the output of the model is the corresponding image reconstructed by the measurement vector, otherwise, the step 3 is executed in a return mode, and the steps 3-5 are circulated.
Specifically, the step 5 specifically includes:
step 51, it is determined whether the generator network and the discriminator network converge. Iterative training in a networkIn the course, when the discriminator loses d ω Sum generator g θ And when the values are reduced and respectively gradually increased to a certain value, the network is judged to be converged.
Step 52, after the measurement vector obtained after sampling the measurement matrix Φ is input to the converged generator network, the output of the generator is the corresponding reconstructed image.
Step 53, if the iterative training does not converge, returning to execute step 3.
In order to verify the effect of the invention, the invention is subjected to simulation experiments, the specification of a test image is 64 multiplied by 64, a training and testing model is trained on a CelebA face data set, and related parameters are set: the model learning rate α=0.002, the iteration number l=30, the number of pictures per input s=16, γ=0.01, and the process of the network of generator and discriminator from input to output is shown in tables 1 and 2 below.
Training depth and activation function of table 1 generator
Table 2 training depth and activation function of discriminator
The evaluation of the experiment uses both qualitative and quantitative analysis methods.
Fig. 2 shows a comparison of the image reconstruction effect of the three algorithms of the present invention and ReconNet, CSGAN, DCGAN at sample block numbers of 20, 100 and 500, respectively. The sample block is the size of the measurement vector y, and as can be seen from fig. 2, the reconstruction effect of the invention is obviously better than that of the three algorithms ReconNet, CSGAN, DCGAN for the same four face images.
Regarding quantitative analysis comparisons, MSE, PSNR, and SSIM are used to evaluate image quality, and the reconstruction time (in milliseconds) of a single image is used to evaluate the reconstruction speed of the algorithm. Where MSE is the mean square error (Mean Squared Error), i.e. the average error of a single pixel in the image, PSNR is the peak signal to noise ratio (Peak Signal to Noise Ratio), SSIM is the structural similarity (structural similarity index), which is calculated as follows:
wherein range represents the dynamic range of the image pixel values, μ is the mean, σ is the variance, c 1 ＝(k 1 L) 2 ,c 1 ＝(k 1 L) 2 Is a constant for maintaining stability, L is the dynamic range of pixel values, k 1 ＝0.01，k 2 ＝0.03。
When quantitative comparison is carried out, 4 test pictures are selected from the test set, sampling is carried out by using a measurement matrix phi, the test pictures are input into each model, a reconstructed image is calculated and output through the model, the reconstructed image is compared with a corresponding original image, and corresponding MSE, PSNR and SSIM values are calculated.
Fig. 3 shows the MSE (under log2 scaling) comparison values for the algorithms of the invention and ReconNet, CSGAN, DCGAN, TWLST, LASSO, respectively, in the test set of CelebA, with an abscissa of Number of Measurements (number of samples) and an ordinate of the error per pixel, i.e. the mean square error (Reconstruction error per pixel); fig. 4 shows the PSNR and SSIM comparison values for the algorithm of the present invention and ReconNet, CSGAN, DCGAN at different sample blocks. Fig. 5 shows a comparison of the mean time (in milliseconds) for the present algorithm and ReconNet, CSGAN, DCGAN, twIST and LASSO algorithms to reconstruct an image in the mnist, fmnist and CelebA test sets, respectively.
The present invention also provides a compressed perceived image reconstruction system based on a generation countermeasure network, as shown in fig. 6, comprising:
the network model construction module is used for constructing a neural network-based generation countermeasure network model according to the measurement vector obtained by image sampling and the size of the reconstructed image, and designing an objective function for optimizing parameters of the generation countermeasure network model;
the parameter presetting module is used for presetting parameters for training the generation of the countermeasure network model;
the generator training module is used for alternately training the generator and the discriminator by adopting a back propagation algorithm according to the objective function;
the convergence judging module is used for judging whether the generated countermeasure network model converges or not, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding original image reconstructed by the measurement vector; otherwise, returning to the parameter presetting module.
The system is realized based on a compressed sensing image reconstruction method for generating an countermeasure network, and the specific technology is similar to the method, and the invention is not repeated here. The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be covered by the present invention
In summary, compared with the conventional compressed sensing, the method has the advantages of long reconstruction iteration time and poor reconstruction quality at a low sampling rate. The invention utilizes deep learning to establish a compressed sensing image reconstruction model based on generation of an antagonism network, enables a generator G to reconstruct an image, uses a discriminator D to improve pixel distribution of the reconstructed image, reduces reconstruction errors, enables reconstruction of a complex image at a low sampling rate to have a better effect, and has a better reconstruction effect on a more complex color image, and has certain advantages from the aspects of reconstruction errors, similarity and efficiency and visual effect.
Claims (4)
1. A compressed perceived image reconstruction method based on a generation countermeasure network, comprising:
s1, constructing a generated countermeasure network model based on a neural network according to a measurement vector obtained by sampling an original image and the size of a reconstructed image, and designing an objective function for optimizing parameters of the generated countermeasure network model;
the measurement vector y=Φx+ζ, y ε R M ，Φ∈R M×N ，x∈R N ；
Wherein y represents a measurement vector, phi is a measurement matrix, x represents a data line vector which is changed into a vectorized data matrix of an image to be sampled, M represents the size of the measurement vector, and N is the number of pixels of the image to be sampled;
the generating an countermeasure network model is as follows:
J(D,G)＝min G max D [l rec (G(y))+l reg (G(y))+l GAN (G(y),D)]
wherein G is a generator, D is a discriminator, and the reconstruction loss is
l reg For total variation regularization, the countermeasures of the discriminator network are +.>
Substituting the reconstruction loss, the total variation regularization and the antagonism loss of the discriminator network into the network model to obtain objective functions respectively optimizing parameters of the generator and the discriminator, wherein the objective functions respectively comprise:
the objective function of the discriminator is
The generator reconstructs an image, i and j are pixel positions of the original image, p data And p y Statistical distribution of original image and random measurement vector, gamma is loss weight of discriminator;
s2, presetting parameters for training when the countermeasure network model is generated;
s3, alternately training a generator and a discriminator by adopting a back propagation algorithm according to the objective function;
s4, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding image reconstructed by the measurement vector; otherwise, the steps S2-S4 are executed in a returning mode.
2. The compressed sensing image reconstruction method based on a generation countermeasure network according to claim 1, wherein in S3, an activation function used in training the generator is Selu, and an activation function used in training the discriminator is lrinlu.
3. A system implemented in accordance with the compressed perceived image reconstruction method of claim 1 or 2, comprising:
the network model construction module is used for constructing a generated countermeasure network model based on a neural network according to the measurement vector obtained by sampling the original image and the size of the reconstructed image, and designing an objective function for optimizing parameters of the generated countermeasure network model;
the parameter presetting module is used for presetting parameters for training the generation of the countermeasure network model;
the generator training module is used for alternately training the generator and the discriminator by adopting a back propagation algorithm according to the objective function;
the convergence judging module is used for judging whether the generated countermeasure network model converges or not, if the generated countermeasure network model converges, the trained network can directly realize a compressed sensing task, and the model is output as a corresponding original image reconstructed by the measurement vector; otherwise, returning to the parameter preset module;
the measurement vector y=Φx+ζ, y ε R M ，Φ∈R M×N ，x∈R N ，
Wherein y represents a measurement vector, phi is a measurement matrix, x represents a data line vector which is changed into a vectorized data matrix of an image to be sampled, M represents the size of the measurement vector, and N is the number of pixels of the image to be sampled;
the generating an countermeasure network model is as follows:
J(D,G)＝min G max D [l rec (G(y))+l reg (G(y))+l GAN (G(y),D)]
wherein G is a generator, D is a discriminator, and the reconstruction loss is
l reg For total variation regularization, the countermeasures of the discriminator network are +.>
Substituting the reconstruction loss, the total variation regularization and the antagonism loss of the discriminator network into the network model to obtain objective functions respectively optimizing parameters of the generator and the discriminator, wherein the objective functions respectively comprise:
4. A compressed sensing image reconstruction system based on a generation countermeasure network according to claim 3, wherein in the generator training module, an activation function used in training the generator is Selu, and an activation function used in training the discriminator is lrilu.
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