A soft threshold weighted phase recovery method, device and storage medium based on TWF

Abstract

The present invention discloses a soft threshold weighted phase recovery method, device and storage medium based on TWF. The method comprises: inputting an image signal into a sampling system to obtain an observation value; calculating an initial measurement value according to the obtained observation value by using a truncated spectrum method; substituting the initial measurement value into a soft threshold weighted iteration formula to obtain a measurement value; calculating a recovery error of the measurement value, and outputting the measurement value if the recovery error is lower than a threshold, otherwise substituting the measurement value into a soft threshold weighted iteration formula to obtain the next round of measurement values ​​until the recovery error is lower than the threshold. Compared with the prior art, the method has stronger image recovery quality and excellent convergence.

Description

Technical Field

[0001] The present invention specifically relates to a TWF-based soft threshold weighted phase recovery method, device and storage medium, and belongs to the technical field of image processing. Background Art

[0002] With the development of computers and big data, people's requirements for image information are also increasing. The sampling frequency of existing image sampling systems is generally lower than the frequency of light waves. Sampling can only obtain the amplitude signal of the original image, resulting in the loss of phase signal.

[0003] Phase recovery is one of the important research areas in the field of image processing. It is widely used in X-ray crystallography, acoustics, astronomical imaging, authentication and encryption of optical images, target reconstruction of synthetic aperture radar, photographic imaging of holographic technology, ultra-high resolution electron stack diffraction, channel estimation, etc. Phase recovery is a technology that uses the amplitude or intensity information of the signal to restore the phase information when the phase information of the signal is missing, thereby recovering the complete signal.

[0004] The phase recovery problem usually involves the original image passing through a known sampling system to obtain the amplitude signal of the image signal, while the phase signal is lost. The purpose of the phase recovery method is to recover the phase signal or the original image signal from the amplitude signal.

[0005] Since the convergence of the GS method and error reduction method commonly used in traditional phase recovery methods is extremely dependent on the selection of initial values, once the initial value deviates from the true value, the final result is likely to fall into local optimization rather than the global optimal solution. Methods based on convex optimization such as PhaseLift and PhaseMax convert the phase recovery problem from solving a one-dimensional vector into a semidefinite programming problem, which can accurately recover the signal, but the computational complexity will increase exponentially as the data scale increases. Non-convex methods such as WF and TWF ensure the convergence of iterations through proofs and improve the recovery quality, but their convergence speed and image quality still need to be improved. Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a soft threshold weighted phase recovery method, device and storage medium based on TWF to improve the image restoration quality and convergence speed.

[0007] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0008] In a first aspect, the present invention provides a soft threshold weighted phase recovery method based on TWF, comprising the following steps:

[0009] Input image signals into the sampling system to obtain observation values;

[0010] Based on the obtained observations, the initial measurements are calculated using the truncated spectrum method;

[0011] Substitute the initial measured value into the soft threshold weighted iterative formula to obtain the measured value;

[0012] Calculate the recovery error of the measured value. If the recovery error is lower than the threshold, output the measured value. Otherwise, substitute the measured value into the soft threshold weighted iteration formula to obtain the next round of measured values ​​until the recovery error is lower than the threshold.

[0013] In combination with the first aspect, further, the steps of calculating the initial measurement value using the truncated spectrum method are as follows:

[0014] According to the sampling system matrix and observation values, the semi-positive definite conjugate matrix is ​​obtained, which is calculated as follows:

[0015]

[0016] Among them, Y is a semi-positive conjugate matrix, m is the number of sampling times, and vector a i is the i-th row of the sampling system matrix, is the vector a i The transpose of y i represents the observed value obtained from the i-th measurement, α y is the preset value, λ0 is the square root of the mean of the observed values; is the cutoff coefficient, when The value of the cutoff coefficient is 1, otherwise it is 0;

[0017] Through the semi-positive definite conjugate matrix, the principal eigenvector of the semi-positive definite conjugate matrix is ​​obtained, and the initial measurement value is calculated.

[0018] Furthermore, the calculation formula of the initial measurement value is as follows:

[0019]

[0020] Among them, z0 represents the initial measurement value, is the principal eigenvector of the semi-positive definite conjugate matrix Y, and n is the dimension of the input signal vector.

[0021] Furthermore, the soft threshold weighted iterative formula is calculated as follows:

[0022]

[0023] Among them, z t+1 represents the measured value obtained at the t+1th iteration, z t represents the measured value obtained at the tth iteration, μ represents the iteration step length, represents the soft-threshold weighted regularized gradient of the measurement obtained at iteration t.

[0024] Furthermore, the soft threshold weighted regularization gradient is calculated as follows:

[0025]

[0026] in, represents the regularized gradient, k(z) represents the soft threshold weighting coefficient, z is the measured value, m is the number of samplings, and vector a i is the i-th row of the sampling system matrix, is the vector a i The transpose of y i represents the observed value obtained from the i-th measurement.

[0027] Furthermore, the soft threshold weighting coefficient is a decimal from 0 to 1, and is calculated as follows:

[0028]

[0029] Among them, η1, η2, and μ3 are all set parameters, η1=0.3, μ2=5, η3=5.

[0030] Furthermore, the recovery error is calculated as follows:

[0031]

[0032] Among them, R e is the recovery error, z is the measurement value, A is the sampling system matrix, and y is the observation value.

[0033] In a second aspect, the present invention provides a soft threshold weighted phase recovery device based on TWF, comprising an acquisition module: inputting an image signal into a sampling system to obtain an observation value;

[0034] Initial calculation module: used to calculate the initial measurement value based on the observed value using the truncated spectrum method;

[0035] Iterative calculation module: the initial measurement value is used as the input of the first iteration, and the measurement value of the first iteration is calculated using the soft threshold weighted iteration formula; in the i-th iteration, the measurement value output from the i-1 iteration is substituted into the soft threshold weighted iteration formula to calculate the measurement value of the i-th iteration, where i is greater than 1;

[0036] Judgment module: used to calculate the recovery error of the measured value. If the recovery error is lower than the threshold, the measured value is output; otherwise, the measured value is substituted into the soft threshold weighted iteration formula to obtain the next round of measurement values ​​until the recovery error is lower than the threshold.

[0037] In combination with the second aspect, further, the device includes a processor and a storage medium;

[0038] The storage medium is used to store instructions;

[0039] The processor is configured to operate according to the instructions to perform any one of the method steps.

[0040] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the program is executed by a processor to perform the steps of any one of the methods.

[0041] Compared with the prior art, the beneficial effects achieved by the present invention include:

[0042] The present invention is a soft threshold weighted phase recovery method based on TWF. The truncated spectrum method is used to calculate the initial measurement value. The soft threshold weighted coefficient is calculated by setting the soft threshold weighted iterative formula to weaken the influence of abnormal components and prevent the measurement value from overshooting. The convergence speed of the algorithm is guaranteed and the accuracy of the algorithm to restore the image is effectively improved, which is conducive to solving the phase recovery problem encountered in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flow chart of a TWF-based soft threshold weighted phase recovery method provided in an embodiment of the present invention;

[0044] Figure 2 These are three original images in the BSD dataset;

[0045] Figure 3 These are the effect images after the three original images are restored;

[0046] Figure 4 It is a convergence curve of the recovery error provided by the implementation of the present invention. DETAILED DESCRIPTION

[0047] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0048] like Figure 1 As shown, it is a flow chart of a soft threshold weighted phase recovery method based on TWF provided by an embodiment of the present invention. A soft threshold weighted phase recovery method based on TWF provided by the present invention comprises the following steps:

[0049] Step S1, input an image signal to a sampling system, perform a fast Fourier transform on the image signal, and obtain an observation value y;

[0050] Step S2, using the obtained observation values, calculating the initial measurement values ​​using the truncated spectrum method; specifically;

[0051] Step S2.1, obtain the semi-positive definite conjugate matrix Y through the measurement operator, the observation value and the truncation coefficient; the specific calculation is as follows:

[0052]

[0053] Where m is the number of sampling times, vector a i is the i-th row of the sampling system matrix A, is the vector a i The transpose of is the cutoff coefficient. The value of this coefficient is 1, otherwise it is 0. y is the default value, which can be optionally set to α y =3, It is expressed as the mean of the observed values ​​and is calculated as follows:

[0054]

[0055] Step S2.2: Calculate the principal eigenvector of matrix Y

[0056] Step S2.3: Use the principal eigenvector of matrix Y The initial measurement value z0 is calculated by using λ0. The specific calculation is as follows:

[0057]

[0058] Step S3: Taking the initial measurement value as the initial value, substitute it into the soft threshold weighted iteration formula to calculate the next round of measurement value; the specific calculation is as follows:

[0059]

[0060] where z t represents the measured value obtained at the tth iteration, μ represents the iteration step size, which can be optionally set to μ = 0.28, Represents the soft threshold weighted regularization gradient, which can be divided into the product of two parts, namely the regularization gradient and the soft threshold weighting coefficient. The specific calculation is as follows:

[0061]

[0062] in represents the regularization gradient, and k(z) represents the soft threshold weighting coefficient. The soft threshold weighting coefficient is a decimal from 0 to 1. The specific value is calculated based on the input measurement value z. The specific calculation is as follows:

[0063]

[0064] Among them, η1, η2, and μ3 are all set parameters. The three parameters can be optionally set to η1 = 0.3, μ2 = 5, and η3 = 5. The soft threshold weighting coefficient is intended to as well as It is limited within the range to reduce the impact of abnormal components on the gradient, so as to avoid overshoot during the convergence process, thereby rushing out of the convergence range of the true value and jumping to other local optimal solutions.

[0065] Step 4: Calculate the recovery error R of the measured value e , judge whether the restored error meets the requirements, if it meets the requirements, output the measured value, otherwise continue to step 3; the restored error is calculated based on the measured value and the observed value, and the specific calculation is as follows:

[0066]

[0067] When R e When the measured value z is lower than a certain set threshold, it can be considered that the measured value z has reached the recovery expectation. The threshold can be optionally set to 1×10 -5 The measurement value z that finally meets the recovery error requirement is the recovery result of the method.

[0068] Ideally, a method that can converge will eventually reach the threshold. However, for experimental feasibility, a time requirement is usually set for the iteration of the method. If the time requirement is not met, the iteration is terminated and the last measured value is used as the recovery result of this method. Therefore, the final recovery error R of the recovery result is shown in Table 1. e If the threshold is not met, Figure 3 You can learn more about the convergence process of each method.

[0069] Table 1 Image phase recovery experimental results

[0070]

[0071] As shown in Table 1, the phase recovery method STW shown in the present invention is compared with the recovery effect of the prior art. The input image signals used are from three classic images Barbara, Cameraman and Peppers in the data set BSD. Figure 2 As shown in Table 1, the recovery error R e It can be seen that both TWF and STW of the present invention reach the preset threshold requirements after a certain number of iterations, while the WF method is still greater than the threshold after reaching the maximum number of iterations, and the recovery error R of STW e Maintained at 1×10 -6 As shown below, STW outperforms the other two methods in terms of convergence. From the comparison of structural similarity (SSIM) and peak signal-to-noise ratio (PSNR), it can be seen that the restoration effect of STW method is better than WF and TWF.

[0072] from Figure 3 It can be seen from the restored image that the restored image by the method of the present invention has less noise and is smoother. Figure 4 The convergence curves of the three methods show that the convergence of STW is much better than that of WF method and is almost the same as that of TWF method. In summary, the phase recovery method provided by the present invention has obvious competitive advantages, so the present method performs well in solving the phase recovery problem and has special significance.

[0073] The present invention also provides a soft threshold weighted phase recovery device based on TWF, comprising:

[0074] Acquisition module: input image signals into the sampling system to obtain observation values;

[0075] Initial calculation module: used to calculate the initial measurement value based on the observed value using the truncated spectrum method;

[0076] Iterative calculation module: the initial measurement value is used as the input of the first iteration, and the measurement value of the first iteration is calculated using the soft threshold weighted iteration formula; in the i-th iteration, the measurement value output from the i-1 iteration is substituted into the soft threshold weighted iteration formula to calculate the measurement value of the i-th iteration, where i is greater than 1;

[0077] Judgment module: used to calculate the recovery error of the measured value. If the recovery error is lower than the threshold, the measured value is output; otherwise, the measured value is substituted into the soft threshold weighted iteration formula to obtain the next round of measurement values ​​until the recovery error is lower than the threshold.

[0078] The soft threshold weighted phase recovery device comprises a processor and a storage medium, wherein the storage medium is used to store instructions, and the processor is used to operate according to the instructions to execute the steps of a soft threshold weighted phase recovery method based on TWF.

[0079] The present invention provides a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to perform steps of a soft threshold weighted phase recovery method based on TWF.

[0080] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0081] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0082] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0083] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0084] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A soft threshold weighted phase recovery method based on TWF, characterized in that: The steps include: Input image signals into the sampling system to obtain observation values; Based on the obtained observations, the initial measurements are calculated using the truncated spectrum method; Substitute the initial measured value into the soft threshold weighted iterative formula to obtain the measured value; Calculate the recovery error of the measured value. If the recovery error is lower than the threshold, output the measured value. Otherwise, substitute the measured value into the soft threshold weighted iteration formula to obtain the next round of measured values ​​until the recovery error is lower than the threshold. The soft threshold weighted iterative formula is calculated as follows: ， in, represents the measurement value obtained at the t+1th iteration, represents the measured value obtained at the tth iteration, represents the iteration step length, represents the soft threshold weighted regularized gradient of the measurement value obtained at the tth iteration; The steps to calculate the initial measurement using the truncated spectrum method are as follows: According to the sampling system matrix and observation values, the semi-positive definite conjugate matrix is ​​obtained. The specific calculation is as follows: ， in, is a semi-positive conjugate matrix, m is the number of samplings, and the vector is the i-th row of the sampling system matrix, For vector The transpose of Indicates The observed value obtained from the measurement, is the default value, Take the square root of the mean of the observations; is the cutoff coefficient, when , the value of the truncation coefficient is 1, otherwise the value is 0; Through the semi-positive definite conjugate matrix, the principal eigenvector of the semi-positive definite conjugate matrix is ​​obtained, and the initial measurement value is calculated; The calculation formula of the initial measurement value is as follows: ， in, represents the initial measurement value, is a positive semidefinite conjugate matrix The main eigenvector of , n is the dimension of the input signal vector.

2. According to claim 1, a TWF-based soft threshold weighted phase recovery method is characterized in that: The soft threshold weighted regularization gradient is calculated as follows: ， in, represents the regularized gradient, represents the soft threshold weighting coefficient, is the measured value, is the sampling number, vector is the i-th row of the sampling system matrix, For vector The transpose of Indicates The observed value obtained from the measurement.

3. The TWF-based soft threshold weighted phase recovery method according to claim 2, characterized in that: The soft threshold weighting coefficient is a decimal from 0 to 1 and is calculated as follows: ， in, , , All are setting parameters. , , .

4. The TWF-based soft threshold weighted phase recovery method according to claim 1, characterized in that: The recovery error is calculated as follows: ， in, To recover the error, is the measured value, is the sampling system matrix, is the observed value.

5. A soft threshold weighted phase recovery device based on TWF, characterized in that: include Acquisition module: input image signals into the sampling system to obtain observation values; Initial calculation module: used to calculate the initial measurement value using the truncated spectrum method according to the observed value; the steps of calculating the initial measurement value using the truncated spectrum method are as follows: According to the sampling system matrix and observation values, the semi-positive definite conjugate matrix is ​​obtained. The specific calculation is as follows: ， in, is a semi-positive conjugate matrix, m is the number of samplings, and the vector is the i-th row of the sampling system matrix, For vector The transpose of Indicates The observed value obtained from the measurement, is the default value, Take the square root of the mean of the observations; is the cutoff coefficient, when , the value of the truncation coefficient is 1, otherwise the value is 0; Through the semi-positive definite conjugate matrix, the principal eigenvector of the semi-positive definite conjugate matrix is ​​obtained, and the initial measurement value is calculated; The calculation formula of the initial measurement value is as follows: ， in, represents the initial measurement value, is a positive semidefinite conjugate matrix The main eigenvector of , n is the dimension of the input signal vector; Iterative calculation module: the initial measurement value is used as the input of the first iteration, and the measurement value of the first iteration is calculated using the soft threshold weighted iteration formula; in the i-th iteration, the measurement value output from the i-1 iteration is substituted into the soft threshold weighted iteration formula to calculate the measurement value of the i-th iteration, where i is greater than 1; Judgment module: used to calculate the recovery error of the measured value. If the recovery error is lower than the threshold, the measured value is output. Otherwise, the measured value is substituted into the soft threshold weighted iteration formula to obtain the next round of measurement value until the recovery error is lower than the threshold. The soft threshold weighted iteration formula is calculated as follows: ， in, represents the measurement value obtained at the t+1th iteration, represents the measured value obtained at the tth iteration, represents the iteration step length, represents the soft-threshold weighted regularized gradient of the measurement obtained at iteration t.

6. A soft threshold weighted phase recovery device based on TWF, characterized in that: including processor and storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 4 are implemented.

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