CN111325682B - Phase recovery improvement method and device for self-correlation signal with interference - Google Patents
Phase recovery improvement method and device for self-correlation signal with interference Download PDFInfo
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Abstract
A phase recovery improvement method and device for a band interference autocorrelation signal, the method includes: extracting an initial Fourier amplitude of a target object from a known target object autocorrelation signal, and taking a random Fourier phase as an input to obtain a phase recovery reconstruction result; performing space domain denoising treatment on the reconstruction result, assigning a part smaller than the maximum energy setting percentage of the reconstruction result to zero to obtain a denoised reconstruction result, and calculating the mean square error between the Fourier amplitude of the denoised reconstruction result and the initial Fourier amplitude of the target object; repeating the steps by taking a plurality of different random Fourier phases as inputs to obtain a plurality of de-noised reconstruction results and a plurality of mean square errors; and taking the mean square error as a judging index of the quality of the reconstruction result, selecting the optimal reconstruction result from the plurality of denoised reconstruction results as a final output, and realizing the phase recovery of the target object. The invention can realize stable phase recovery for the self-correlation signal with interference.
Description
Technical Field
The invention relates to the field of computer vision and digital image processing, in particular to an improved phase recovery method and device for an auto-correlation signal with interference.
Background
The traditional phase recovery algorithm can be used for recovering and reconstructing the object to be observed from the autocorrelation signal of the object, namely, firstly, the Fourier transformation is utilized to extract the Fourier amplitude of the object from the autocorrelation signal; under the condition that the Fourier amplitude of the target object is known and the phase is unknown, taking the random phase as an initial guess of the Fourier phase of the target object, and iteratively recovering the real Fourier phase of the target object and reconstructing the spatial distribution of the target object. However, due to randomness of initial phase guess, the spatial distribution of the target object reconstructed by the traditional phase recovery algorithm and the actual fourier phase of the recovered target object have great instability, and particularly when partial interference exists in the autocorrelation signal of the target object, the reconstruction instability is larger, so that the phase recovery result is disordered, the accurate and effective spatial information of the target object is difficult to obtain from the single phase recovery result, and the applicability of the traditional phase recovery algorithm to the autocorrelation signal with interference is limited.
Disclosure of Invention
The main object of the present invention is to overcome at least one of the above technical drawbacks and to provide an improved method and device for phase recovery for an auto-correlation signal with interference.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a phase recovery method for a band-disturbance-oriented autocorrelation signal, said method comprising the steps of:
a1: extracting an initial Fourier amplitude of a target object from a known target object autocorrelation signal, and taking a random Fourier phase as an input to obtain a phase recovery reconstruction result;
a2: performing space domain denoising treatment on the reconstruction result, assigning a part smaller than the maximum energy setting percentage of the reconstruction result to zero to obtain a denoised reconstruction result, and calculating the mean square error between the Fourier amplitude of the denoised reconstruction result and the initial Fourier amplitude of the target object;
a3: repeating the steps A1 and A2 by taking a plurality of different random Fourier phases as inputs to obtain a corresponding plurality of de-noised reconstruction results and a corresponding plurality of mean square errors;
a4: and taking the mean square error as a judging index of the quality of the reconstruction result, selecting an optimal reconstruction result from the plurality of denoised reconstruction results as a final output, and realizing the phase recovery of the target object.
Further:
in step A2, the part smaller than 20% of the maximum energy of the reconstruction result is assigned zero.
In step A1, for the initial target object autocorrelation signal with interference, the process of extracting the initial fourier amplitude of the target object by fourier transform and evolution operation is as follows:
wherein ,
representing an initial target autocorrelation signal with interference, c representing the dryDisturbing signal, O represents the object to be reconstructed, < ->
Representing an autocorrelation operation. />
In step A1, the initial Fourier amplitude |F (O) | of the object is known, and the random Fourier phase theta is used m As an initial guess of the phase, iteratively reconstructing the spatial distribution O of the target object m And obtaining a phase recovery reconstruction result.
In step A2, for the reconstruction result O m Performing space domain denoising processing, and assigning a part of which the maximum energy is less than 20% of the reconstruction result to be zero to obtain a denoised reconstruction result P m According to the following formula:
wherein (x, y) represents the two-dimensional coordinate distribution of the target airspace.
In step A2, for the denoised reconstruction result P m Calculating the Fourier amplitude |F (P) m ) Mean square error between i and initial fourier magnitude of the object, F (O)
According to the following formula:
wherein, (s, t) represents the two-dimensional coordinate distribution of the Fourier domain of the target object; H. v represents the maximum range of the two-dimensional coordinates of the fourier domain of the object, respectively.
In step A3, a plurality of different random Fourier phases θ m Repeating steps A1 and A2 with m=1, 2, …, M as input to obtain a plurality of corresponding denoised reconstruction results P m M=1, 2, …, M and corresponding multiple mean square errors
In step A4, the mean square error is used as a criterion of the quality of the reconstruction result, and the optimal reconstruction result is selected from the plurality of denoised reconstruction results according to the following formula:
where m=1, 2, …, M represents the number of random fourier phases input.
In step A1, the initial target autocorrelation signal a with interference is taken as the known target autocorrelation signal.
A phase recovery device for a signal with interference autocorrelation, comprising at least one memory and at least one processor;
the memory stores at least one executable program;
the executable program, when executed by the processor, implements the method.
The invention has the following beneficial effects:
the invention provides a phase recovery method and a phase recovery device for an autocorrelation signal with interference, which can realize stable and effective reconstruction of spatial distribution of a target object and Fourier phase of the target object under the condition that the autocorrelation signal is known to have certain interference. The method comprises the steps of carrying out spatial domain denoising on a reconstruction result of a traditional phase recovery algorithm according to a certain percentage proportion of maximum energy, particularly preferably 20%, taking constraint as a constraint, calculating a Mean Square Error (MSE) between a Fourier amplitude of the denoised reconstruction result and a Fourier amplitude of an initial target object, taking the MSE as a judging standard of the denoised reconstruction result, and selecting an optimal reconstruction result from a plurality of denoising reconstruction results with different random phases as inputs so as to realize stable phase recovery and target reconstruction. By using the phase recovery method and the phase recovery device, stable phase recovery can be realized for the autocorrelation signal with interference.
Drawings
Fig. 1 is a flowchart of a phase recovery method for an auto-correlation signal with interference according to an embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail. It should be emphasized that the following description is merely exemplary in nature and is in no way intended to limit the scope of the invention or its applications.
Referring to fig. 1, an embodiment of the present invention provides a phase recovery method for an auto-correlation signal with interference, which includes the following steps:
a1: extracting an initial Fourier amplitude of a target object from a known target object autocorrelation signal, and taking a random Fourier phase as an input to obtain a phase recovery reconstruction result;
a2: performing space domain denoising treatment on the reconstruction result, assigning a part of which the maximum energy is less than 20% of the reconstruction result to be zero, obtaining a denoised reconstruction result, and calculating the mean square error between the Fourier amplitude of the denoised reconstruction result and the initial Fourier amplitude of the target object;
a3: repeating the steps A1 and A2 by taking a plurality of different random Fourier phases as inputs to obtain a corresponding plurality of de-noised reconstruction results and a corresponding plurality of mean square errors;
a4: and taking the mean square error as a judging index of the quality of the reconstruction result, selecting the optimal reconstruction result from a plurality of reconstruction results as a final output, and realizing the phase recovery of the target object.
In the step A1, the phase recovery method may be implemented using the initial target autocorrelation signal a with interference as a known target autocorrelation signal.
In a specific preferred embodiment, in step A1, for an initial target autocorrelation signal with interference, the process of extracting the initial fourier amplitude of the target using fourier transform and squaring operation is as follows:
wherein ,
an object autocorrelation signal representing an initial disturbance, c representing a disturbance signal, O representing an object to be reconstructed,/->
Representing an autocorrelation operation.
Further preferably, the initial Fourier amplitude |F (O) | of the object is known as the random Fourier phase θ m As an initial guess of the phase, iteratively reconstructing the spatial distribution O of the target object m And obtaining a phase recovery reconstruction result.
In a particularly preferred embodiment, in step A2, the fraction smaller than 20% of the maximum energy of the reconstruction result is assigned zero.
In a particularly preferred embodiment, in step A2, for the reconstruction result O m Performing space domain denoising processing, and assigning a part of which the maximum energy is less than 20% of the reconstruction result to be zero to obtain a denoised reconstruction result P m ：
Wherein (x, y) represents the two-dimensional coordinate distribution of the target airspace.
Further preferably, for the denoised reconstruction result P m Calculating the Fourier amplitude |F (P) m ) Mean square error between i and initial fourier magnitude of the object, F (O)
/>
Wherein, (s, t) represents the two-dimensional coordinate distribution of the Fourier domain of the target object; H. v represents the maximum range of the two-dimensional coordinates of the fourier domain of the object, respectively.
In a particularly preferred embodiment, in step A3, a plurality of different random Fourier phases θ m Repeating steps A1 and A2 with m=1, 2, …, M as input to obtain a plurality of corresponding denoised reconstruction results P m M=1, 2, …, M and corresponding multiple mean square errors
In step A4, the mean square error is used as a judging index of the quality of the reconstruction result, the optimal reconstruction result is selected from a plurality of reconstruction results, and the following formula is adopted:
where m=1, 2, …, M represents the number of random fourier phases input.
The phase recovery method for the self-correlation signal with interference provided by the embodiment of the invention can realize stable and effective reconstruction of the spatial distribution of the target object and the Fourier phase of the target object under the condition that the self-correlation signal with certain interference is known. The method comprises the steps of carrying out spatial domain denoising on a reconstruction result of a traditional phase recovery algorithm according to a certain percentage proportion of maximum energy, particularly preferably 20%, taking constraint as a constraint, calculating a Mean Square Error (MSE) between a Fourier amplitude of the denoised reconstruction result and a Fourier amplitude of an initial target object, taking the MSE as a judging standard of the denoised reconstruction result, and selecting an optimal reconstruction result from a plurality of denoising reconstruction results with different random phases as inputs so as to realize stable phase recovery and target reconstruction. By using the phase recovery method and the phase recovery device provided by the embodiment of the invention, stable phase recovery can be realized for the self-correlation signal with interference.
It should be noted that the specific preferred methods (such as phase recovery algorithm, generation of random phase, etc.) in the above embodiments are only illustrative, and the scope of the present invention is not limited to the methods.
The background section of the present invention may contain background information about the problems or environments of the present invention and is not necessarily descriptive of the prior art. Accordingly, inclusion in the background section is not an admission of prior art by the applicant.
The foregoing is a further detailed description of the invention in connection with specific/preferred embodiments, and it is not intended that the invention be limited to such description. It will be apparent to those skilled in the art that several alternatives or modifications can be made to the described embodiments without departing from the spirit of the invention, and these alternatives or modifications should be considered to be within the scope of the invention. In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "preferred embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Those skilled in the art may combine and combine the features of the different embodiments or examples described in this specification and of the different embodiments or examples without contradiction. Although embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the scope of the invention as defined by the appended claims.
Claims (6)
1. A method for phase recovery of an auto-correlation signal with interference, the method comprising the steps of:
a1: extracting an initial Fourier amplitude of a target object from an initial target object autocorrelation signal with interference, and taking a random Fourier phase as input to obtain a phase recovery reconstruction result;
a2: performing space domain denoising treatment on the reconstruction result, assigning a part which is smaller than 20% of the maximum energy of the reconstruction result to be zero, obtaining a denoised reconstruction result, and calculating the mean square error between the Fourier amplitude of the denoised reconstruction result and the initial Fourier amplitude of the target object;
in step A2, for the reconstruction result O m Performing space domain denoising processing, and assigning a part of which the maximum energy is less than 20% of the reconstruction result to be zero to obtain a denoised reconstruction result P m According to the following formula:
wherein, (x, y) represents two-dimensional coordinate distribution of the airspace of the target object;
a3: repeating the steps A1 and A2 by taking a plurality of different random Fourier phases as inputs to obtain a corresponding plurality of de-noised reconstruction results and a corresponding plurality of mean square errors;
a4: and taking the mean square error as a judging index of the quality of the reconstruction result, selecting an optimal reconstruction result from the plurality of denoised reconstruction results as a final output, and realizing the phase recovery of the target object.
2. The phase recovery method for an auto-correlation signal with interference according to claim 1, wherein in step A1, for an initial target auto-correlation signal with interference, the process of extracting an initial fourier amplitude of the target by using fourier transform and squaring operation is as follows:
wherein ,
an object autocorrelation signal representing an initial disturbance, c representing a disturbance signal, O representing an object to be reconstructed,/->
Representing an autocorrelation operation.
3. The phase recovery method for an auto-correlation signal with interference according to claim 2, wherein in step A1, the initial fourier amplitude |f (O) | of the target object is known, and the random fourier phase θ is used m As an initial guess of the phase, iteratively reconstructing the spatial distribution O of the target object m And obtaining a phase recovery reconstruction result.
4. The phase recovery method for an interfering autocorrelation signal of claim 1 wherein in step A2, for the denoised reconstruction result P m Calculating the Fourier amplitude |F (P) m ) Mean square error between i and initial fourier magnitude of the object, F (O)
According to the following formula:
wherein, (s, t) represents the two-dimensional coordinate distribution of the Fourier domain of the target object; H. v represents the maximum range of the two-dimensional coordinates of the fourier domain of the object, respectively.
5. The phase recovery method for an interfering autocorrelation signal of claim 4 wherein in step A3, a plurality of different random fourier phases θ are used m Repeating steps A1 and A2 with m=1, 2, … and m as input to obtain a plurality of corresponding denoised reconstruction results P m M=1, 2, …, M and corresponding multiple mean square errors
In step A4, toThe mean square error is used as a judging index of the quality of the reconstruction result, the optimal reconstruction result is selected from the plurality of denoised reconstruction results, and the following formula is adopted:
where m=1, 2, …, M represents the number of random fourier phases input.
6. A phase recovery device for a signal with interference autocorrelation, comprising at least one memory and at least one processor;
the memory stores at least one executable program;
the executable program, when executed by the processor, implements the method of any one of claims 1 to 5.
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