CN111091495A - High-resolution compressive sensing reconstruction method for laser image based on residual error network - Google Patents

High-resolution compressive sensing reconstruction method for laser image based on residual error network Download PDF

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CN111091495A
CN111091495A CN201910952609.1A CN201910952609A CN111091495A CN 111091495 A CN111091495 A CN 111091495A CN 201910952609 A CN201910952609 A CN 201910952609A CN 111091495 A CN111091495 A CN 111091495A
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image
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秦翰林
李莹
延翔
马琳
杨硕闻
刘燕
杨毓鑫
乐阳
林凯东
李兵斌
周慧鑫
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Xidian University
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Abstract

The invention discloses a high-resolution compressed sensing reconstruction method for a laser image based on a residual error network, which comprises the steps of measuring a matrix W and a real laser image block xiMultiplying to obtain a compressed sensing measurement yi(ii) a The compressed sensing measure yiBy convex optimization based linear mapping network FfOutputting initial estimated image blocks of a fully connected layer output reconstructed image
Figure DDA0002226249410000011
The initial estimated image block
Figure DDA0002226249410000012
By means of a residual network Fr(. output prediction residual image block
Figure DDA0002226249410000013
For the initial estimation image block
Figure DDA0002226249410000014
And pre-estimating residual image block
Figure DDA0002226249410000015
And reconstructing, and splicing all reconstructed image blocks to obtain a desired high-quality laser image reconstruction result. The invention properly increases the depth of the network through the jump connection, so that the network model is easier to optimize, the convergence of the training process is faster and more stable, and the reconstruction quality is better.

Description

High-resolution compressive sensing reconstruction method for laser image based on residual error network
Technical Field
The invention belongs to the field of compressed sensing laser image reconstruction, and particularly relates to a high-resolution compressed sensing reconstruction method for a laser image based on a residual error network.
Background
The compressed sensing theory utilizes the characteristic that signals have sparsity, and finally recovers the signals through discrete samples obtained by random sampling under the condition that the sampling rate is far less than the Nyquist sampling rate, so that the compressed sensing theory draws wide attention once put forward, and has great application value in the fields of communication, mode recognition, biomedicine, optical imaging, image processing and the like. The traditional reconstruction method based on compressed sensing comprises a greedy algorithm, a convex optimization algorithm, an iterative algorithm and the like, the method recovers images by solving an optimization problem, and the algorithm is serious in time consumption, low in reconstruction speed and low in reconstruction precision, so that the problems of low frame frequency, poor real-time performance and the like in practical application are caused.
Aiming at the problems of time consumption, low reconstruction accuracy and the like of the algorithm, with the continuous development of deep learning in recent years, in order to reduce the computational complexity of reconstruction, a Convolutional Neural Network (CNN) based method is also introduced into compressed sensing reconstruction, and the CNN based reconstruction method is initially inspired by a CNN super-resolution algorithm, and finally obtains a high-quality reconstruction result by obtaining initial rough estimation and performing subsequent operations such as super-resolution optimization and the like. However, in the current CNN-based compressed sensing reconstruction method, nonlinear mapping is performed through convolution operation when a one-dimensional sparse signal is mapped into a two-dimensional image, and the principle of compressed sensing is not considered; and the algorithm network structure and model parameters for super-resolution reconstruction are complex, the training process takes a long time, the reconstruction result is not ideal, and further improvement space exists.
Disclosure of Invention
In view of the above, the main object of the present invention is to provide a high-resolution compressive sensing reconstruction method for a laser image based on a residual error network.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the embodiment of the invention provides a high-resolution compressive sensing reconstruction method for a laser image based on a residual error network, which comprises the following steps:
by measuring matrix W and real laser image block xiMultiplying to obtain a compressed sensing measurement yi；
The compressed sensing measure yiBy based on convex advantagesLinearized mapping network FfOutputting initial estimated image blocks of a fully connected layer output reconstructed image
Figure BDA0002226249390000021
The initial estimated image block
Figure BDA0002226249390000022
By means of a residual network Fr(. output prediction residual image block
Figure BDA0002226249390000023
For the initial estimation image block
Figure BDA0002226249390000024
And pre-estimating residual image block
Figure BDA0002226249390000025
And reconstructing, and splicing all reconstructed image blocks to obtain a desired high-quality laser image reconstruction result.
In the above scheme, the real laser image x is processed in blocks to obtain a plurality of real laser image blocks xiMultiplying the real laser image blocks by a measurement matrix W to obtain a compressed sensing measurement yi。
In the above scheme, the compressed sensing measurement yiBy convex optimization based linear mapping network FfOutputting an initial estimated image block of a fully connected layer output reconstructed image block
Figure BDA0002226249390000026
The method specifically comprises the following steps:
the mapping process to recover the real laser image x from the compressed sensing measurement value y is denoted as x-Wy, where W ∈ Rn×mIs a measurement matrix;
converting the mapping matrix into a solution mapping matrix WfTo the optimization problem of
Figure BDA0002226249390000027
Wherein, yi∈Rn×1And xi∈Rn×1Respectively representing the compressed perceptual measurement and the corresponding original signal, { (y)1,x1),(y2,x2),…,(yN,xN) Denotes training data, X ═ X1,x2,…,xN]，Y＝[y1,y2,…,yN]；
Obtaining a mapping matrix W using a loss functionf：
Figure BDA0002226249390000028
Wherein, Ff(yi,Wf) Is yiInputting the output after passing through the linear mapping network;
compressed sensing measurement vector y corresponding to any original image blockiBy the mapping matrix WfThen all the image blocks can be obtained
Figure BDA0002226249390000029
The mapping process is represented as:
Figure BDA00022262493900000210
in the above scheme, the method further comprises mapping the mapping matrix WfOptimizing, specifically: training an optimization network by a random gradient descent method until the network converges and obtaining an optimal mapping matrix Wf。
In the above scheme, the image blocks are initially estimated
Figure BDA00022262493900000211
As a residual network FrObtaining estimated residual image block by inputting
Figure BDA0002226249390000031
Wherein, WrAre parameters of the residual network.
In the above scheme, the initial estimation image block is processed
Figure BDA0002226249390000032
And pre-estimating residual image block
Figure BDA0002226249390000033
Reconstructing, and splicing all reconstructed image blocks to obtain a desired high-quality laser image reconstruction result, specifically: the initial estimation image block
Figure BDA0002226249390000034
And pre-estimating residual image block
Figure BDA0002226249390000035
Adding the two to obtain a corresponding laser image block reconstruction result:
Figure BDA0002226249390000036
all reconstructed image blocks
Figure BDA0002226249390000037
Splicing to obtain a complete laser reconstruction image x*。
In the above scheme, the network F is mapped through the linear mappingfThe parameters of (a) initialize the residual network, representing the final desired laser image reconstruction as:
Figure BDA0002226249390000038
wherein the content of the first and second substances,
Figure BDA0002226249390000039
compared with the prior art, the method comprises the steps of firstly outputting an initial estimation result of a reconstructed image through a linear mapping network by utilizing convex optimization constraint, inputting the initial estimation result into a residual error reconstruction network, gradually reducing the difference value between the initial estimation image and a real laser image by utilizing the residual error network, and adding the output results of the initial estimation image and the real laser image to obtain a final expected laser reconstructed image with higher quality; because the invention introduces the residual error network, the depth of the network is properly increased through jump connection, so that the network model is easier to optimize, the convergence of the training process is faster and more stable, and the reconstruction quality is better.
Drawings
FIG. 1 is a high-resolution compressive sensing reconstruction network model diagram of a laser image based on a residual error network according to the present invention;
FIG. 2 is a network model diagram of a single reconstruction unit of the residual error reconstruction network according to the present invention;
FIG. 3 is a simulation result of the method of the present invention when the measurement rate is 0.01, (3a), (3b) represent the output results of two different sets of laser images, respectively;
FIG. 4 is a simulation result of the method of the present invention when the measurement rate is 0.10, where (4a) and (4b) represent the output results of two different laser images, respectively;
fig. 5 shows the simulation results of the method of the present invention when the measurement rate is 0.25, and (5a) and (5b) represent the output results of two different laser images, respectively.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a high-resolution compressive sensing reconstruction method for a laser image based on a residual error network, which is realized by the following steps:
step 1: obtaining compressed sensing measurement y by multiplying measurement matrix W with real laser image blocki；
Specifically, the real laser image x is subjected to blocking processing to obtain a plurality of real laser image blocks xiMultiplying the real laser image blocks by a measurement matrix W to obtain a compressed sensing measurement yi∈Rn×1；
Step 2: the compressed sensing measure yiBy convex optimization based linear mapping network FfFull connected layer output of (a) initial estimated image blocks of a reconstructed image
Figure BDA0002226249390000041
Specifically, in the compressive sensing theory, the mapping process for recovering the real laser image x from the compressive sensing measurement value y can be represented as x ═ Wy, where W ∈ Rn×mIs a measurement matrix.
This equation is a sick equation, with no unique solution, and therefore translates it into solving the mapping matrix WfBy estimating
Figure BDA0002226249390000042
The minimum, namely:
Figure BDA0002226249390000043
wherein { (y)1,x1),(y2,x2),…,(yN,xN) Denotes training data, X ═ X1,x2,…,xN]，Y＝[y1,y2,…,yN]。
The mapping network adopts a loss function shown as a formula (2) to obtain an optimal mapping matrix Wf：
Figure BDA0002226249390000044
Wherein, Ff(yi,Wf) Is yiThe output after the input passes through the linear mapping network.
Mapping network Ff(. to) is a full connection layer, all samples are trained by a random gradient descent (SGD) training method to obtain a corresponding optimal mapping matrix Wf。
Compressed sensing measurement vector y of any image block through linear mapping networkiAll can obtain better initial estimation image block
Figure BDA0002226249390000045
The mapping process is represented as:
Figure BDA0002226249390000046
and step 3: the initial estimated image block
Figure BDA0002226249390000051
By means of a residual network Fr(. output prediction residual image block
Figure BDA0002226249390000052
(3a) Solving a residual error:
specifically, because the difficulty in solving the optimal solution of the formula (3) is high, the linear mapping is generally adopted for approximate solution, and because the quality of the approximate result is poor, further optimization is required to further reduce the size of the solution
Figure BDA0002226249390000053
And xiThe difference between the two signals is estimated by introducing a residual error network, and the residual error diCan be expressed as:
Figure BDA0002226249390000054
the residual error reconstruction network of the present invention comprises a plurality of residual error reconstruction units, each unit comprising three convolutional layers having convolutional kernel sizes of 11 × 11, 1 × 1 and 7 × 7, respectively, each convolutional layer being followed by a linear activation (ReLU) layer except for the last convolutional layer.
By initially estimating image blocks
Figure BDA0002226249390000055
To input, residual error network
Figure BDA0002226249390000056
Generating pre-estimated residual image blocks
Figure BDA0002226249390000057
Wherein WrIs a parameter of the residual network, the process can be expressed as:
Figure BDA0002226249390000058
further, training the residual error reconstruction network by a random gradient descent (SGD) training method to obtain an optimal parameter WfAnd Wr：
Figure BDA0002226249390000059
In the training process, in order to avoid the overfitting condition, the invention adds the attenuation weight coefficient to the error function to restrain a larger weight so as to lead the error function to be stably converged.
The method adopts a fixed learning strategy in the initial stage of a training stage, obtains a loss function and an accuracy curve chart after the training is finished, adjusts the learning rate according to the convergence condition, modifies the learning strategy into a stepping type after a plurality of times of training, and obtains corresponding parameters according to the formula (7).
lr＝base_lr*gammafloor(iter/stepsize)(7)
Wherein the gamma parameter is set to 0.5, and the base _ lr parameter is set to 10-2. And when a better result is obtained by training, storing the current model, and performing high-resolution reconstruction on the target laser image by using the model parameters.
And 4, step 4: for the initial estimation image block
Figure BDA00022262493900000510
And pre-estimating residual image block
Figure BDA00022262493900000511
And carrying out reconstruction to obtain a desired high-quality laser image reconstruction result.
Specifically, output results of the linear mapping network are mapped
Figure BDA0002226249390000062
And residual network output
Figure BDA0002226249390000063
Add to obtainTo the final desired high quality laser reconstructed image block
Figure BDA0002226249390000064
This process can be expressed as:
Figure BDA0002226249390000065
after all the original image blocks are subjected to the steps, the obtained reconstructed image blocks are spliced to obtain a final complete laser reconstructed image
Figure BDA0002226249390000066
The method of the invention fully considers the characteristics of the reconstruction solution of the compressed sensing laser image, adopts convex optimization constraint, outputs a better initial estimation image through a linear mapping network, inputs the result into a residual error reconstruction network for further optimization, obtains a residual error image between the initial estimation and a real laser image, and adds the initial estimation and the real laser image to obtain the expected high-resolution laser image reconstruction result.
In order to prove the effectiveness of the method, three values of the compression measurement rate of 0.01, 0.10 and 0.25 are respectively selected for verification, fig. 3, fig. 4 and fig. 5 clearly show the reconstruction results of the method when the compression measurement rate is 0.01, 0.10 and 0.25, and table 1 shows the peak signal-to-noise ratio (PSNR) values of the two groups of laser image output results when the compression measurement rate is 0.01, 0.10 and 0.25 respectively.
TABLE 1 PSNR values of two groups of laser image output results at different measurement rates
Figure BDA0002226249390000061
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (7)

1. A high-resolution compressive sensing reconstruction method for a laser image based on a residual error network is characterized by comprising the following steps:
by measuring matrix W and real laser image block xiMultiplying to obtain a compressed sensing measurement yi；
The compressed sensing measure yiBy convex optimization based linear mapping network FfOutputting initial estimated image blocks of a fully connected layer output reconstructed image
Figure FDA0002226249380000011
The initial estimated image block
Figure FDA0002226249380000012
By means of a residual network Fr(. output prediction residual image block
Figure FDA0002226249380000013
For the initial estimation image block
Figure FDA0002226249380000014
And pre-estimating residual image block
Figure FDA0002226249380000015
And reconstructing, and splicing all reconstructed image blocks to obtain a desired high-quality laser image reconstruction result.
2. The residual network-based high-resolution compressive sensing reconstruction method for laser images as claimed in claim 1, wherein the real laser image x is partitioned to obtain a plurality of real laser image blocks xiMultiplying the real laser image blocks by a measurement matrix W to obtain a compressed sensing measurement yi。
3. The residual error network-based laser image high-resolution compressed sensing reconstruction method according to claim 1 or 2, wherein the compressed sensing measurement y isiBy convex optimization based linear mapping network FfOutputting an initial estimated image block of a fully connected layer output reconstructed image block
Figure FDA0002226249380000016
The method specifically comprises the following steps:
the mapping process to recover the real laser image x from the compressed sensing measurement value y is denoted as x-Wy, where W ∈ Rn×mIs a measurement matrix;
converting the mapping matrix into a solution mapping matrix WfTo the optimization problem of
Figure FDA0002226249380000017
Wherein, yi∈Rn×1And xi∈Rn ×1Respectively representing the compressed perceptual measurement and the corresponding original signal, { (y)1,x1),(y2,x2),…,(yN,xN) Denotes training data, X ═ X1,x2,…,xN]，Y＝[y1,y2,…,yN]；
Obtaining a mapping matrix W using a loss functionf：
Figure FDA0002226249380000018
Wherein, Ff(yi,Wf) Is yiInputting the output after passing through the linear mapping network;
compressed sensing measurement vector y corresponding to any original image blockiBy the mapping matrix WfThen all the image blocks can be obtained
Figure FDA0002226249380000019
The mapping process is represented as:
Figure FDA00022262493800000110
4. the residual error network-based laser image high-resolution compressed sensing reconstruction method according to claim 3, wherein the method is characterized in thatThen, the method further comprises mapping the matrix WfOptimizing, specifically: training an optimization network by a random gradient descent method until the network converges and obtaining an optimal mapping matrix Wf。
5. The residual network-based laser image high-resolution compressed sensing reconstruction method according to claim 4, wherein the initial estimation image blocks are used as the initial estimation image blocks
Figure FDA0002226249380000021
As a residual network FrObtaining estimated residual image block by inputting
Figure FDA00022262493800000211
Figure FDA0002226249380000022
Wherein, WrAre parameters of the residual network.
6. The residual network-based high-resolution compressed sensing reconstruction method for laser images according to claim 5, wherein the initial estimation image blocks are subjected to image reconstruction
Figure FDA0002226249380000023
And pre-estimating residual image block
Figure FDA0002226249380000024
Reconstructing, and splicing all reconstructed image blocks to obtain a desired high-quality laser image reconstruction result, specifically: the initial estimation image block
Figure FDA0002226249380000025
And pre-estimating residual image block
Figure FDA0002226249380000026
Adding the two to obtain a corresponding laser image block reconstruction result:
Figure FDA0002226249380000027
all reconstructed image blocks
Figure FDA0002226249380000028
Splicing to obtain a complete laser reconstruction image x*。
7. The residual error network-based laser image high-resolution compressed sensing reconstruction method according to claim 6, characterized in that the linear mapping network F is usedfThe parameters of (a) initialize the residual network, representing the final desired laser image reconstruction as:
Figure FDA0002226249380000029
wherein the content of the first and second substances,
Figure FDA00022262493800000210
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