CN117319656B - Quantized signal reconstruction method based on depth expansion - Google Patents

Quantized signal reconstruction method based on depth expansion Download PDF

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CN117319656B
CN117319656B CN202311625159.8A CN202311625159A CN117319656B CN 117319656 B CN117319656 B CN 117319656B CN 202311625159 A CN202311625159 A CN 202311625159A CN 117319656 B CN117319656 B CN 117319656B
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张军
王庐华
陈溢鑫
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Guangdong University of Technology
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Abstract

The invention discloses a quantized signal reconstruction method based on depth expansion, and relates to the technical field of signal processing. Firstly, acquiring image data, preprocessing the image data, dividing the preprocessed image data into a training set and a verification set, then introducing unconstrained optimization problems, and constructing a quantized compressed sensing reconstruction model, wherein the quantized compressed sensing reconstruction model comprises a signal acquisition module and a signal reconstruction module, based on the unconstrained optimization problems, the signal acquisition module is used for acquiring image signals in the training set, the acquired image signals are transmitted to the signal reconstruction module to perform optimization training on the quantized compressed sensing reconstruction model, the verification set is used for verifying the trained quantized compressed sensing reconstruction model to obtain a trained quantized compressed sensing reconstruction model, and the quality of signal reconstruction can be improved while the real-time performance of signal reconstruction can be ensured in the process of signal reconstruction by the trained quantized compressed sensing reconstruction model.

Description

Quantized signal reconstruction method based on depth expansion
Technical Field
The invention relates to the technical field of signal processing, in particular to a quantized signal reconstruction method based on depth expansion.
Background
With the rapid development of technology, the transmission and acquisition requirements of information in modern life represent exponential explosive growth. How to store, transmit and process large-scale data in an efficient and economical manner becomes a hotspot concern to current practitioners. Currently, a relatively advanced method is to use quantized compressed sensing (Quantized Compressed sensing, QCS) technology, which breaks through the limitation requirement on the sampling rate in the classical Shannon-Nyquist sampling law, and can accurately reconstruct a signal at a sampling rate far lower than that required by the former. However, such reconstruction problems can be more challenging than those in classical theory, since quantization can lead to irreversible information loss.
In order to deal with the distortion problem caused by quantization operations, one common approach is to simply treat the quantization distortion as additive gaussian noise. Thus, the reconstruction of the quantized signal can be roughly seen as a signal reconstruction problem in noisy environments in the traditional compressed sensing (Compressed sensing, CS) domain, i.e. the signal can be reconstructed using a BPDN (base tracking noise reduction) decoder:
（BPDN）；
however, the solution obtained by this method does not guarantee that the quantization consistency principle is satisfied, and the quantization distortion is actually uniformly distributed instead of gaussian.
To solve the above problems, a classical quantized compressed sensing reconstruction method, BPDQ, is proposed by Jacques et al P Theoretical demonstration of 2 Norms, L P Norms (P)>2) The quantization distortion can be modeled more truly, and the algorithm performance can be improved along with the increase of the key parameter P. However, as the main body and the constraint condition of the BPDQP belong to non-smooth non-micromanipulation functions, jacques propose to solve sparse signals by using a specific monotonic operator splitting method, namely a Douglas-Rachford (DR) splitting method, so that the reconstruction accuracy is greatly improved, but the method for solving the nested loop iteration also sequentially brings high computational complexity, and parameters of the method need to be manually adjusted, so that the problems of insufficient performance release and low signal reconstruction efficiency are caused, and the signal reconstruction workload is caused to be large.
Disclosure of Invention
In order to solve the problems that in the existing signal reconstruction technology, the calculation complexity is high, the signal reconstruction efficiency is low, the signal reconstruction instantaneity cannot be guaranteed, and the signal reconstruction workload is large.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
a quantized signal reconstruction method based on depth expansion, comprising the steps of:
s1: acquiring image data, preprocessing the image data, and dividing the preprocessed image data into a training set, a verification set and image data to be reconstructed;
s2: introducing unconstrained optimization problems, and constructing a quantized compressed sensing reconstruction model, wherein the quantized compressed sensing reconstruction model comprises a signal acquisition module and a signal reconstruction module, based on the unconstrained optimization problems, acquiring image signals in a training set by using the signal acquisition module, transmitting the acquired image signals to the signal reconstruction module to perform optimization training on the quantized compressed sensing reconstruction model, and verifying the trained quantized compressed sensing reconstruction model by using a verification set to obtain a trained quantized compressed sensing reconstruction model;
s3: carrying out signal reconstruction on the image data to be reconstructed by using the trained quantized compressed sensing reconstruction model, and outputting a signal reconstruction result;
s4: and evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model according to the output signal reconstruction result.
In the technical scheme, the acquired image data is preprocessed, the reliability of the image data can be improved, then the unconstrained optimization problem is introduced, the built quantized compressed sensing reconstruction model is optimized, trained and verified by utilizing the preprocessed image data, the trained quantized compressed sensing reconstruction model can effectively reconstruct the image data to be reconstructed, the unconstrained optimization problem is introduced, the frame structure design of the model can be reasonably guided, the model training time is shortened, the whole model has the interpretability logically, and the signal reconstruction precision of the quantized compressed sensing reconstruction model is improved; the signal reconstruction structure of the quantized compressed sensing reconstruction model is evaluated, so that the effectiveness of signal reconstruction of the quantized compressed sensing reconstruction model can be ensured, and the workload of signal reconstruction is reduced.
Further, the preprocessing of the image data in step S1 is as follows:
randomly cutting and sampling the acquired image data, dividing the preprocessed image data into a training set T1 and a verification set T2, wherein,，/>representing the number of training sets.
According to the technical scheme, the acquired image data is randomly cut and sampled, so that the randomness of the data is ensured in the process of training and testing the quantized compressed sensing reconstruction model, and further, the trained quantized compressed sensing reconstruction model can reconstruct the random image data, and therefore, the signal reconstruction performance of the quantized compressed sensing reconstruction model is ensured.
Further, the specific process of introducing the unconstrained optimization problem in step S2 is as follows:
introduction of classicalA paradigm, expressed as:
；
will beThe inequality constraint of the paradigm expands the power P to establish an optimization problem, and the expression is:
；
converting the optimization problem into an unconstrained optimization problem by using a Lagrangian multiplier method, wherein the expression is as follows:
；
wherein,representing the basis tracking dequantizer, < >>Representing a quantified measure,/->Representing sparse signals, ++>Representation->Norms (F/F)>Representing a measurement matrix->Representing regularization parameters; for an image signal with sparse representation in a certain sparse transform domain D +.>Converting unconstrained optimization problems into:
；
and inputting the solution of the unconstrained optimization problem into a quantized compressed sensing reconstruction model, and mapping the solution process into a neural network architecture by using the quantized compressed sensing reconstruction model for solution.
Further, in the quantized compressed sensing reconstruction model constructed in step S2:
the signal acquisition module comprises a sampling unit, a quantization unit and an initialization unit;
the sampling unit is used for performing compression sampling on the image data to obtain a linear measurement value of the image data, and transmitting the linear measurement value to the quantization unit;
the quantization unit is used for carrying out quantization processing on the linear measured value after the compressed sampling and transmitting the linear measured value after the quantization processing to the initialization unit;
the initialization unit constructs an initial signal estimated value according to the quantized linear measured value and transmits the initial signal estimated value to the signal reconstruction module;
the signal reconstruction module comprises a plurality of sub-network units, which are used for solving an unconstrained optimization problem according to an initial signal estimation value, and further carrying out signal reconstruction on the initialized image signal, wherein each sub-network unit comprises a plurality of convolution blocks formed by stacking convolution layers with convolution kernels of 3×3 and convolution layers with convolution kernels of 3×3×32, and the convolution layers with the convolution kernels of 3×3 and 3×3×32 are separated by an activation function ReLU.
According to the technical scheme, unconstrained optimization is introduced, the model framework structure design can be reasonably guided, the model training time is reduced, the whole model has the interpretability in logic, the signal reconstruction precision of the quantized compressed sensing reconstruction model is improved, and the constructed quantized compressed sensing reconstruction model effectively carries out signal reconstruction on image data to be reconstructed by utilizing the mutual coordination among the sampling unit, the quantization unit, the initialization unit and a plurality of sub-network units.
Further, the specific process of collecting the image signals in the training set by using the signal collecting module in step S2 is as follows:
s21: the sampling unit is used for compressing and sampling the image data in the training set T1 to obtain a linear measurement value of the image dataThe expression is:
；
wherein,representing the image signal +_>Representing a measurement matrix;
s22: alignment measurement using quantization unitPerforming quantization operation to obtain quantized measurement value->The expression is:
；
wherein,representing a uniform quantization operator;
s23: using an initialization unit to measure the matrixAnd quantifying the measured value->Combining to obtain an image signal->Is +.>The expression is:
；
wherein,representing a random Gaussian matrix subjected to row orthogonalization processing;
s24: estimate the initial signalTransmitting to a signal reconstruction module for iterative update to obtain a reconstruction signal to be solved +.>Is expressed as:
；
；
wherein,krepresenting the number of iterations of the method,representing step size>Representing data fidelity term->Derivative of>Representing the transform domain.
Further, the specific process of performing optimization training on the quantized compressed sensing reconstruction model in step S2 is as follows:
the reconstruction signal to be solvedThe solving process of (2) is mapped into a neural network architecture, for +.>Solving, wherein the process is as follows:
estimate the initial signalAs input to the neural network architecture, convolutional blocks in the sub-network elements are utilized to replace sparse variationsDomain change D, p->And carrying out iterative update solution, wherein the expression is as follows:
；
is provided withAnd->Is +.>And->The expression is:
the method comprises the steps of carrying out a first treatment on the surface of the Then there are:
；
using soft threshold algorithm pairsSolving to obtain +.>The expression is:
；
wherein, ，/>representing a 3 x 3 convolutional layer with 3A transform module formed by stacking x 3 x 32 convolution layers;
using loss functionsOptimizing parameters in the quantized compressed sensing reconstruction model, and obtaining a solution +.f for each iteration of the quantized compressed sensing reconstruction model by using a verification set T2>Verification is performed when the loss function->And (3) obtaining the quantized compressed sensing reconstruction model after training when the value convergence of (a) or the iteration number reaches an upper limit value.
Further, when the training set T1 is used for optimizing the quantized compressed sensing reconstruction model, an adaptive optimizer Adam is adopted.
Further, in step S2, the method for mapping the unconstrained optimization problem to the neural network architecture for solving is as follows: the shrink threshold algorithm is iterated.
Further, in the process of training the quantized compressed sensing reconstruction model, a loss function expression is used as follows:
；
；
；
wherein,representing image signal +.>And reconstruct Signal->Error between->Representation->And->Symmetrical constraint between->Representing the number of training sets->Representing each data +.>Size of->Representing the total number of iterations.
In the above technical solution, in the process of training the quantized compressed sensing reconstruction model by using the training set T1, image data is first compressed and sampled, so as to obtain a linear measurement valueAnd is a linear measurement->Performing quantization operation to obtain quantized measurement value->Subsequently +.>Initializing to obtain input for solving the unconstrained optimization problem, and mapping the process for solving the unconstrained optimization problem into a neural network architecture to solve, thereby compressing the quantizationThe method comprises the steps that a perception reconstruction model is optimized and trained, the neural network architecture can further improve the accuracy and quality of signal reconstruction of the quantized compressed perception reconstruction model, a convolution layer of 3×3 and a convolution layer of 3×3×32 are utilized to train the quantized compressed perception reconstruction model, more characteristics can be extracted, further the accuracy of signal reconstruction of the quantized compressed perception reconstruction model is improved, finally, a verification set and a loss function are utilized to verify and optimize parameters of the quantized compressed perception reconstruction model, in addition, an adaptive optimizer Adam is utilized to adaptively adjust the learning rate and adjust the momentum, the signal reconstruction performance of the quantized compressed perception reconstruction model is improved, further the trained quantized compressed perception reconstruction model is obtained, the quality and accuracy of signal reconstruction can be improved while the timeliness is guaranteed in the process of signal reconstruction of the trained quantized compressed perception reconstruction model, and further the workload of signal reconstruction is reduced.
Further, the process of evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model in step S4 is as follows:
randomly cutting and sampling image data to be reconstructed, inputting the image data obtained by cutting and sampling into a trained quantized compressed sensing reconstruction model for signal reconstruction, and outputting a signal reconstruction result; according to the signal reconstruction result output by the quantized compressed sensing reconstruction model, adopting the signal to noise ratioAs a performance evaluation index of the quantized compressed sensing reconstruction model, the expression is:
；
where L represents the length of the image, W represents the width of the image,and->Respectively representing the gray scale of the original image and the reconstructed image at the same pointValues.
In the technical scheme, the signal reconstruction structure of the quantized compressed sensing reconstruction model is evaluated, so that the effectiveness of signal reconstruction of the quantized compressed sensing reconstruction model can be ensured, and the workload of signal reconstruction is reduced.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a quantized signal reconstruction method based on depth expansion, which comprises the steps of firstly preprocessing acquired image data, improving the reliability of the image data, then introducing unconstrained optimization problems, and carrying out optimization training and verification on a constructed quantized compressed sensing reconstruction model by utilizing the preprocessed image data, so that the trained quantized compressed sensing reconstruction model can effectively reconstruct signals of the image data to be reconstructed, introducing unconstrained optimization problems, reasonably guiding the frame structure design of the model, reducing the training time of the model, enabling the whole model to have logic interpretability, and improving the signal reconstruction precision of the quantized compressed sensing reconstruction model; the signal reconstruction structure of the quantized compressed sensing reconstruction model is evaluated, so that the effectiveness of signal reconstruction of the quantized compressed sensing reconstruction model can be ensured, and the workload of signal reconstruction is reduced.
Drawings
Fig. 1 is a flowchart of a quantized signal reconstruction method based on depth expansion according to an embodiment of the present application;
FIG. 2 is a block diagram of a quantized compressed sensing reconstruction model according to an embodiment of the present application;
fig. 3 is a schematic diagram of signal reconstruction of a quantized compressed sensing reconstruction model provided in an embodiment of the present application at different sampling rates;
fig. 4 is a schematic diagram comparing a quantized compressed sensing reconstruction model provided in an embodiment of the present application with other model signal reconstruction results.
Detailed Description
In order that the invention may be readily understood, a more complete description of the invention will be rendered by reference to the appended drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
Embodiment one:
the embodiment provides a quantized signal reconstruction method based on depth expansion, referring to fig. 1, including the following steps:
s1: acquiring image data, preprocessing the image data, and dividing the preprocessed image data into a training set, a verification set and image data to be reconstructed;
s2: introducing unconstrained optimization problems, and constructing a quantized compressed sensing reconstruction model, wherein the quantized compressed sensing reconstruction model comprises a signal acquisition module and a signal reconstruction module, based on the unconstrained optimization problems, acquiring image signals in a training set by using the signal acquisition module, transmitting the acquired image signals to the signal reconstruction module to perform optimization training on the quantized compressed sensing reconstruction model, and verifying the trained quantized compressed sensing reconstruction model by using a verification set to obtain a trained quantized compressed sensing reconstruction model;
s3: carrying out signal reconstruction on the image data to be reconstructed by using the trained quantized compressed sensing reconstruction model, and outputting a signal reconstruction result;
s4: and evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model according to the output signal reconstruction result.
The preprocessing of the image data in step S1 is as follows:
randomly cutting and sampling the acquired image data, dividing the preprocessed image data into a training set T1 and a verification set T2, wherein,，/>representing the number of training sets.
It can be understood that the obtained image data is randomly cut and sampled, so as to ensure the randomness of the data in the process of training and testing the quantized compressed sensing reconstruction model, and further ensure that the quantized compressed sensing reconstruction model obtained by training can perform signal reconstruction on the random image data, thereby ensuring the signal reconstruction performance of the quantized compressed sensing reconstruction model.
In the embodiment, the acquired image data is preprocessed, the reliability of the image data can be improved, then the unconstrained optimization problem is introduced, the optimization training and verification are carried out on the constructed quantized compressed sensing reconstruction model by utilizing the preprocessed image data, the trained quantized compressed sensing reconstruction model can effectively reconstruct the image data to be reconstructed, the unconstrained optimization problem is introduced, the frame structure design of the model can be reasonably guided, the model training time is reduced, the whole model has the interpretability in logic, and the signal reconstruction precision of the quantized compressed sensing reconstruction model is improved; the signal reconstruction structure of the quantized compressed sensing reconstruction model is evaluated, so that the effectiveness of signal reconstruction of the quantized compressed sensing reconstruction model can be ensured, and the workload of signal reconstruction is reduced.
Embodiment two:
the present embodiment further describes steps S2 to S4 in the first embodiment, referring to fig. 2, and specifically describes the following:
the specific process of introducing the unconstrained optimization problem in the step S2 is as follows:
introduction of classicalA paradigm, expressed as:
；
will beThe inequality constraint of the paradigm expands the power P to establish an optimization problem, and the expression is:
；
converting the optimization problem into an unconstrained optimization problem by using a Lagrangian multiplier method, wherein the expression is as follows:
；
wherein,representing the base tracking dequantizer (i.e. Basis Pursuit DeQuantizer of moment P), a base tracking dequantizer>Representing a quantified measure,/->Representing sparse signals, ++>Representation->Norms (F/F)>Representing a measurement matrix->Representing regularization parameters; for sparse representation in a sparse transform domain DIs>Converting unconstrained optimization problems into:
；
and inputting the solution of the unconstrained optimization problem into a quantized compressed sensing reconstruction model, and mapping the solution process into a neural network architecture by using the quantized compressed sensing reconstruction model for solution.
In the quantized compressed sensing reconstruction model constructed in step S2:
the signal acquisition module comprises a sampling unit, a quantization unit and an initialization unit;
the sampling unit is used for performing compression sampling on the image data to obtain a linear measurement value of the image data, and transmitting the linear measurement value to the quantization unit;
the quantization unit is used for carrying out quantization processing on the linear measured value after the compressed sampling and transmitting the linear measured value after the quantization processing to the initialization unit;
the initialization unit constructs an initial signal estimated value according to the quantized linear measured value and transmits the initial signal estimated value to the signal reconstruction module;
the signal reconstruction module comprises a plurality of sub-network units, which are used for solving an unconstrained optimization problem according to an initial signal estimation value, and further carrying out signal reconstruction on the initialized image signal, wherein each sub-network unit comprises a plurality of convolution blocks formed by stacking convolution layers with convolution kernels of 3×3 and convolution layers with convolution kernels of 3×3×32, and the convolution layers with the convolution kernels of 3×3 and 3×3×32 are separated by an activation function ReLU.
It can be understood that unconstrained optimization problem is introduced, the model framework structure design can be reasonably guided, the model training time is reduced, the whole model has the interpretability in logic, the accuracy of signal reconstruction of the quantized compressed sensing reconstruction model is improved, and the constructed quantized compressed sensing reconstruction model effectively carries out signal reconstruction on image data to be reconstructed by utilizing the mutual coordination among a sampling unit, a quantization unit, an initialization unit and a plurality of sub-network units.
The specific process of collecting the image signals in the training set by using the signal collecting module in step S2 is as follows:
s21: the sampling unit is used for compressing and sampling the image data in the training set T1 to obtain a linear measurement value of the image dataThe expression is:
；
wherein,representing the image signal +_>Representing a measurement matrix;
s22: alignment measurement using quantization unitPerforming quantization operation to obtain quantized measurement value->The expression is:
；
wherein,representing a uniform quantization operator;
s23: using an initialization unit to measure the matrixAnd quantifying the measured value->Combining to obtain an image signal->Is +.>The expression is:
；
wherein,representing a random Gaussian matrix subjected to row orthogonalization processing;
s24: estimate the initial signalTransmitting to a signal reconstruction module for iterative update to obtain a reconstruction signal to be solved +.>Is expressed as:
；
；
wherein,krepresenting the number of iterations of the method,representing step size>Representing data fidelity term->Is of (1)Count (n)/(l)>Representing the transform domain.
By way of example only, and not by way of limitation,representing data fidelity term->Can be obtained by the derivative of
；
Wherein, ，/>，/>representing an element-by-element multiplication operator,representing a sign function->The number of (2) is P-1;
considering the complexity of the mapping network, limiting the range of values of P to be positive even numbers avoids the influence of absolute values and sign functions, i.eNote that whenP = 2The time model can degrade intoBPDNThus->Can be abbreviated as:
；
wherein the method comprises the steps ofThe number of (2) isP-1。
The specific process of performing optimization training on the quantized compressed sensing reconstruction model in step S2 is as follows:
the reconstruction signal to be solvedThe solving process of (2) is mapped into a neural network architecture, for +.>Solving, wherein the process is as follows:
estimate the initial signalAs an input to the neural network architecture, a convolutional block in a sub-network element is used to replace the sparse transform domain D, p->And carrying out iterative update solution, wherein the expression is as follows:
；
is provided withAnd->Is +.>And->The expression is:
；
then there are:
；
using soft threshold algorithm pairsSolving to obtain +.>The expression is:
；
exemplary whereinAnd then the soft threshold function is utilized to obtain the following steps:
；
is the slaveSolution of->Introduces->Is defined as +.>，/>And->Having a symmetrical structure, i.e.)>Wherein->Representing the unit operator, it is therefore possible to obtain:
；
wherein, ，/>a transform module in which a 3×3 convolution layer and a 3×3×32 convolution layer are stacked;
using loss functionsOptimizing parameters in the quantized compressed sensing reconstruction model, and obtaining a solution +.f for each iteration of the quantized compressed sensing reconstruction model by using a verification set T2>Verification is performed when the loss function->When the value convergence or the iteration number reaches the upper limit value, obtaining a quantized compressed sensing reconstruction model after training is completed;
for example, in the training model stage, we choose 91 pictures as in the ISTA-Net, and randomly cut all the pictures, and finally generate 88912 image blocks of 33 x 33 as training set.
When the training set T1 is used for optimizing and training the quantized compressed sensing reconstruction model, an adaptive optimizer Adam is adopted, and the initial learning rate is set to be 1e-5.
In step S2, the method for mapping the unconstrained optimization problem to the neural network architecture for solving is as follows: the shrink threshold algorithm is iterated.
In the process of training the quantized compressed sensing reconstruction model, the learnable parameters of the BPDQP-Net (namely the quantized compressed sensing reconstruction model) comprise step sizesContraction threshold->And convolution module->And->The loss function expression used is:
；
；
；
wherein,representing image signal +.>And reconstruct Signal->Error between->Representation->And->Symmetrical constraint between->Representing the number of training sets->Representing each data +.>Size of->Representing the total number of iterations.
The process of evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model in step S4 is as follows:
randomly cutting and sampling image data to be reconstructed, inputting the image data obtained by cutting and sampling into a trained quantized compressed sensing reconstruction model for signal reconstruction, and outputting a signal reconstruction result; according to the signal reconstruction result output by the quantized compressed sensing reconstruction model, adopting the signal to noise ratioAs a performance evaluation index of the quantized compressed sensing reconstruction model, the expression is:
；
where L represents the length of the image, W represents the width of the image,and->Respectively representing the gray values of the original image and the reconstructed image at the same point.
In this embodiment, in the process of training the quantized compressed sensing reconstruction model by using the training set T1, image data is first compressed and sampled, so as to obtain a linear measurement valueAnd is a linear measurement->Performing quantization operation to obtain quantized measurement value->Subsequently +.>Performing initialization operation to obtain input for solving an unconstrained optimization problem, mapping a process for solving the unconstrained optimization problem into a neural network architecture to solve the neural network architecture, so that optimization training is performed on the quantized compressed sensing reconstruction model, the neural network architecture can further improve the accuracy and quality of signal reconstruction of the quantized compressed sensing reconstruction model, the quantized compressed sensing reconstruction model is trained by a convolution layer of 3×3 and a convolution layer of 3×3×32, more characteristics can be extracted, the accuracy of signal reconstruction of the quantized compressed sensing reconstruction model is further improved, finally, verification and parameter optimization are performed on the quantized compressed sensing reconstruction model by a verification set and a loss function, in addition, an adaptive optimizer Adam is used for adaptively adjusting the learning rate and adjusting momentum, the signal reconstruction performance of the quantized compressed sensing reconstruction model is improved, the trained quantized compressed sensing reconstruction model is obtained, and the quality and accuracy of signal reconstruction can be improved while the time of the trained quantized compressed sensing reconstruction model is ensured in the process of signal reconstruction; the signal reconstruction structure of the quantized compressed sensing reconstruction model is evaluated, so that the effectiveness of signal reconstruction of the quantized compressed sensing reconstruction model can be ensured, and the workload of signal reconstruction is reduced.
Embodiment III:
the embodiment of the invention provides a quantized signal reconstruction method based on depth expansion for validity experimental verification, which comprises the following steps:
91 pictures which are the same as those in ISTA-Net are selected, all the pictures are randomly cut, and 88912 image blocks with the size of 33 x 33 are finally generated to serve as a training set; in the test stage, a Set11 data Set and a Caltech-256 data Set are selected, wherein the Set11 data sets comprise 11 gray-scale pictures in total, the other Set comprises 3067 color pictures, 300 color pictures are randomly extracted from the gray-scale pictures, and the color pictures are cut into image blocks with the size of 128 x 128 for testing, and a signal-to-noise ratio (SNR) is selected as an index for evaluating the quality of a model and defined as follows:
wherein L and W respectively represent the length and width dimensions of the image,and->Representing the gray values of the original image and the reconstructed image at this point, respectively.
Testing BPDQ when the level of equivalence is limited to 5bits P Reconstruction of Net on Set11 dataset, setting the sampling rate to η[0.125,0.625]And sets a plurality of P values at each sampling rate to show the effect of the values on the model, the reconstruction effect is shown in FIG. 3, from which it can be seen that when the sampling rate is low, η +.>[0.125,0.25]When the quantized compressed perceptual reconstruction model performs best at p=2 (BPDN), it is necessary to increase the value of P to increase the reconstruction performance when the sampling rate is further increased, which is characteristic of BPDQ P The method remains consistent.
To further evaluate BPDQ P The reconstruction performance of Net, incorporating BPDQ P Comparing with QCoSaMP algorithm including BPDQ P All algorithms including Net use gaussian random matrix as sampling matrix; furthermore, for BPDQ P And qcasamp algorithm using Discrete Cosine Transform (DCT) matrix as sparse dictionary. As shown in Table 1, table 1 shows the optimal reconstruction effect of each algorithm at different sampling rates, it can be seen that the depth-based expansion of BPDQ P Net is far better than optimization-based BPDQ at each sampling rate P The algorithm and greedy-based qcasamp algorithm show the partial reconstruction results of each algorithm at a sampling rate of 0.625 in a visual form, as shown in fig. 4.
Table 1:
the average SNR performance of the algorithms at different sampling rates over the Set11 dataset is compared (quantization level is fixed at 5 Bits).
In addition, 300 pictures were randomly selected on the Caltech-256 dataset for testing the reconstruction performance of each algorithm at different quantization levels, in this experiment the sampling rate of each algorithm was fixed at 0.625, with a quantization level interval of 2 to 5 bits. As shown in Table 2, table 2 shows the reconstructed performance of each algorithm, where BPDQ P And BPDQ P The respective best P values employed by Net, obviously, the BPDQ proposed in the present application P Net can still maintain a significant performance lead.
Table 2:
SNR performance at different quantization levels for each algorithm over the Caltech-256 dataset (sample rate is fixed at 0.625).
Finally, the reconstruction efficiency of each algorithm was compared, specifically, the quantization level was fixed at 3bits, and the average run time required by each algorithm to reconstruct a picture on the Caltech-256 dataset was tested in order to compare the different P values for BPDQ P BPDN (p=2) was introduced in this experiment, and as shown in table 3, a comparison of the reconstruction times for each algorithm is shown in table 3. It is apparent that the BPDQ proposed in the present application P The fastest Net reconstruction speed compared toThe second qqos amp was 6 times faster. Furthermore, by comparing BPDN and BPDQ P (p=6 in this experiment) it was found that the reconstruction time required by the algorithm increases dramatically as P increases.
Table 3:
average run time comparisons (in seconds) of the methods over the Caltech-256 dataset.
The foregoing description is only illustrative of the present invention and is not intended to limit the scope of the invention, and all equivalent structures or equivalent processes or direct or indirect application in other related technical fields are included in the scope of the present invention.

Claims (8)

1. A quantized signal reconstruction method based on depth expansion, comprising the steps of:
s1: acquiring image data, preprocessing the image data, and dividing the preprocessed image data into a training set, a verification set and image data to be reconstructed;
s2: introducing unconstrained optimization problems, and constructing a quantized compressed sensing reconstruction model, wherein the quantized compressed sensing reconstruction model comprises a signal acquisition module and a signal reconstruction module, based on the unconstrained optimization problems, acquiring image signals in a training set by using the signal acquisition module, transmitting the acquired image signals to the signal reconstruction module to perform optimization training on the quantized compressed sensing reconstruction model, and verifying the trained quantized compressed sensing reconstruction model by using a verification set to obtain a trained quantized compressed sensing reconstruction model;
s3: carrying out signal reconstruction on the image data to be reconstructed by using the trained quantized compressed sensing reconstruction model, and outputting a signal reconstruction result;
s4: evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model according to the output signal reconstruction result;
the preprocessing of the image data in step S1 is as follows:
randomly cutting and sampling the acquired image data, dividing the preprocessed image data into a training set T1 and a verification set T2, wherein,，/>representing the number of training sets>Representing the first of the training set T1iA picture is taken of the picture,representation and->Corresponding quantized measurements;
the specific process of introducing the unconstrained optimization problem in the step S2 is as follows:
introduction of classicalA paradigm, expressed as:
；
will beThe inequality constraint of the paradigm expands the power P to establish an optimization problem, and the expression is:
；
converting the optimization problem into an unconstrained optimization problem by using a Lagrangian multiplier method, wherein the expression is as follows:
；
wherein,representing a quantified measure,/->Representing sparse signals, ++>Representation->Norms (F/F)>Representing a measurement matrix->Representing regularization parameters; for an image signal with sparse representation in a certain sparse transform domain D +.>Converting unconstrained optimization problems into:
；
and inputting the solution of the unconstrained optimization problem into a quantized compressed sensing reconstruction model, and mapping the solution process into a neural network architecture by using the quantized compressed sensing reconstruction model for solution.
2. The depth-expansion-based quantized signal reconstruction method according to claim 1, wherein in the quantized compressed perceptual reconstruction model constructed in step S2:
the signal acquisition module comprises a sampling unit, a quantization unit and an initialization unit;
the sampling unit is used for performing compression sampling on the image data to obtain a linear measurement value of the image data, and transmitting the linear measurement value to the quantization unit;
the quantization unit is used for carrying out quantization processing on the linear measurement value and transmitting the linear measurement value after the quantization processing to the initialization unit;
the initialization unit constructs an initial signal estimated value according to the quantized linear measured value and transmits the initial signal estimated value to the signal reconstruction module;
the signal reconstruction module comprises a plurality of sub-network units, which are used for solving an unconstrained optimization problem according to an initial signal estimation value, and further carrying out signal reconstruction on the initialized image signal, wherein each sub-network unit comprises a plurality of convolution blocks formed by stacking convolution layers with convolution kernels of 3×3 and convolution layers with convolution kernels of 3×3×32, and the convolution layers with the convolution kernels of 3×3 and 3×3×32 are separated by an activation function ReLU.
3. The depth-expansion-based quantized signal reconstruction method according to claim 2, wherein the specific process of acquiring the image signals in the training set by using the signal acquisition module in step S2 is as follows:
s21: the sampling unit is used for compressing and sampling the image data in the training set T1 to obtain a linear measurement value of the image dataThe expression is:
；
wherein,representing the image signal +_>Representing a measurement matrix;
s22: alignment measurement using quantization unitPerforming quantization operation to obtain quantized measurement value->The expression is:
；
wherein,representing a uniform quantization operator;
s23: using an initialization unit to measure the matrixAnd quantifying the measured value->Combining to obtain an image signal->Is +.>The expression is:
；
wherein,representing a random Gaussian matrix subjected to row orthogonalization processing;
s24: estimate the initial signalTransmitting to a signal reconstruction module for iterative update to obtain a reconstruction signal to be solved +.>Is expressed as:
；
；
wherein,krepresenting the number of iterations of the method,representing step size>Representing data fidelity term->Derivative of>Representing the transform domain.
4. The depth-expansion-based quantized signal reconstruction method according to claim 3, wherein the specific process of performing optimization training on the quantized compressed sensing reconstruction model in step S2 is as follows:
the reconstruction signal to be solvedThe solving process of (2) is mapped into a neural network architecture, for +.>Solving, wherein the process is as follows:
estimate the initial signalAs an input to the neural network architecture, a convolutional block in a sub-network element is used to replace the sparse transform domain D, p->And carrying out iterative update solution, wherein the expression is as follows:
；
is provided withAnd->Is +.>And->The expression is:
the method comprises the steps of carrying out a first treatment on the surface of the Then there are:
；
using soft threshold algorithm pairsSolving to obtain +.>The expression is:
；
wherein, ，/>a transform module in which a 3×3 convolution layer and a 3×3×32 convolution layer are stacked, is described as +.>Representation->Left inverse of (1), and->With symmetrical structure->Representing an AND->Related scalar quantities;
using loss functionsOptimizing parameters in the quantized compressed sensing reconstruction model, and obtaining a solution +.f for each iteration of the quantized compressed sensing reconstruction model by using a verification set T2>Verification is performed when the loss function->When the value of convergence or the iteration number reaches the upper limit value, the training is completedAnd quantizing the compressed sensing reconstruction model.
5. The depth-expansion-based quantized signal reconstruction method according to claim 4, wherein an adaptive optimizer Adam is used when the quantized compressed perceptual reconstruction model is optimally trained using a training set T1.
6. The depth-based quantized signal reconstruction method according to claim 5, wherein in step S2, the method of mapping the unconstrained optimization problem into a neural network architecture for solving is as follows: the shrink threshold algorithm is iterated.
7. The depth-based quantized signal reconstruction method according to claim 6, wherein the loss function expression used in training the quantized compressed perceptual reconstruction model is:
；
；
；
wherein,representing image signal +.>And reconstruct Signal->Error between->Representation->And (3) withSymmetrical constraint between->Representing the number of training sets->Representing each data +.>Size of->Represents the total number of iterations, +.>Representing a non-negative regularization parameter.
8. The depth-based quantized signal reconstruction method according to claim 7, wherein the process of evaluating the signal reconstruction performance of the quantized compressed sensing reconstruction model in step S4 is as follows:
randomly cutting and sampling image data to be reconstructed, inputting the image data obtained by cutting and sampling into a trained quantized compressed sensing reconstruction model for signal reconstruction, and outputting a signal reconstruction result; according to the signal reconstruction result output by the quantized compressed sensing reconstruction model, adopting the signal to noise ratioAs a performance evaluation index of the quantized compressed sensing reconstruction model, the expression is:
；
where L represents the length of the image, W represents the width of the image,and->Respectively representing the gray values of the original image and the reconstructed image at the same point.
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