CN113495241A - Phase unwrapping method and device and readable storage medium - Google Patents
Phase unwrapping method and device and readable storage medium Download PDFInfo
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Abstract
The technical scheme of the invention discloses a phase unwrapping method, a phase unwrapping device and a readable storage medium, wherein the method comprises the following steps: calculating to obtain a residual point distribution diagram according to a winding phase diagram of the image; calculating to obtain a phase quality map according to the winding phase map of the image; connecting residual points in the residual point distribution graph by using branch tangent lines, and reducing the quality of the residual points by N times; setting phase points outside the branch tangent lines as high-quality points; unwinding the high-quality points; obtaining the real phase of the residual point by utilizing local polynomial surface fitting; and unwrapping the residual error points according to the real phase. According to the invention, residual points are connected by branch tangent lines to remove 'balance' polarity, so that the high-quality points can be unwound along the region without passing through the branch tangent lines, the generation and transmission of unwinding errors can be avoided, and after the real phase of the residual points is obtained by correction, the residual points are unwound according to the real phase, thereby improving the accuracy of unwinding of the residual points.
Description
Technical Field
The present invention relates to the field of image processing technologies, and in particular, to a phase unwrapping method and apparatus, and a readable storage medium.
Background
In magnetic resonance imaging techniques, many techniques require the use of phase information of the image, such as: chemical shift imaging, blood flow imaging, magnetic resonance temperature imaging, B0 field imaging, and the like. However, the phase data obtained from complex magnetic resonance arrays is usually confined to the (- π, π ] interval, and in order to obtain the true phase, k 2 π values (k being an integer) must be added or subtracted, which is called phase unwrapping.
Since the 80 s of the last century, a large number of phase unwrapping algorithms have been proposed by foreign and domestic researchers in order to improve noise immunity, increase computation speed and improve unwrapping accuracy. These algorithms can be broadly classified into the following two categories: (1) a minimum norm algorithm and (2) a path-following algorithm.
The core of the minimum norm algorithm is to fit the true phase by minimizing the local difference of the true phase and the local difference of the wrapped phase. Among the unwrapping algorithms that utilize the minimum norm, the simplest one is the least squares fitting algorithm, minimizing the sum of the squares of the differences of the true phase and wrapped phase. The method for fitting the real phase can adopt a polynomial fitting model, a Markov model and the like, and the application of the models can change the complex unwrapping problem into a relatively easy numerical calculation problem. The least square method unwrapping algorithm based on the models can effectively deal with the noise problem of the image, and a good result can be still fitted in a region with poor quality. The least square method can be improved by introducing a weight value, the weight of a discontinuous area or a serious noise area is reduced, the weight of an area with good phase quality is improved, and the unwrapping effect is better. The model-based approach can then be further improved by using local models, such as local polynomial fits that more accurately fit local variations in the phase map. However, the de-winding based on the least square method causes global propagation of local errors due to the fact that the de-winding passes through a behavior discontinuous region containing residual points, and therefore global errors, effects and stability are poor.
The idea of the path following algorithm is: and (3) unwinding the phase diagram according to a certain path, and unwinding the region with good quality first and then unwinding the region with poor quality so as to avoid the interference and wrong accumulation and transmission of the region with poor quality to other regions. Path-following algorithms can be broadly classified into three types: (1) a path-dependent algorithm, (2) a residual compensation algorithm, and (3) a quality map guided path algorithm. The path-dependent algorithm calculates the true phase deviation by using the position of the edges in the image and the phase step of the jump, adding or subtracting this deviation from the wrapped phase. This algorithm is robust but computationally too computationally intensive. The residual error compensation algorithm judges whether residual error points exist or not by calculating the sum of cyclic differences of adjacent 4 points in the image data and the remainder of 2 pi. If the residual points exist, branch tangent lines are arranged to connect the residual points, and the branch tangent lines are avoided to be unwound by utilizing a flooding algorithm. This algorithm is fast, but not robust, and tends to produce closed non-unwrapped areas, i.e., "islands," of branch-cut lines. The method comprises the steps of firstly obtaining a phase quality map based on a quality map guided path following algorithm, carrying out descending order on the quality of points in the quality map, firstly unwrapping the point with the highest quality in the quality map, and finally unwrapping the point with the lowest quality in the quality map. Such an algorithm is computationally very efficient, but its results are heavily dependent on the quality of the quality map. The worse the quality of the quality map, the worse the effect of unwinding, and the poor stability.
The above is only for the purpose of assisting understanding of the technical aspects of the present invention, and does not represent an admission that the above is prior art.
Disclosure of Invention
The invention mainly aims to provide a phase unwrapping method, a phase unwrapping device and a readable storage medium, and aims to solve the technical problems of poor effect and poor stability of the existing phase unwrapping method.
In order to achieve the above object, the present invention provides a phase unwrapping method, comprising the steps of:
calculating to obtain a residual point distribution diagram according to a winding phase diagram of the image;
calculating to obtain a phase quality map according to the winding phase map of the image;
connecting residual points in the residual point distribution graph by using branch tangent lines, and reducing the quality of the residual points by N times;
setting phase points outside the branch tangent lines as high-quality points;
unwinding the high-quality points;
obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and unwrapping the residual error points according to the real phase.
Optionally, the step of obtaining the residual point distribution map by calculating according to the winding phase map of the image includes:
the four phase points of the winding phase diagram are connected to form a square, and the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
The winding phase difference value between two of the four phase points in the square is obtained through the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
the sum of the winding phase difference values between two of the four phase points is obtained as q,
if the q value is 0, the phase point ψm,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
Optionally, the specific process of obtaining the phase quality map by calculating according to the winding phase map of the image includes:
the quality value of the phase point (x, y) is:
Qx,yis the mass value of the phase point (x, y), k is the k value of the k x k matrix of the wound phase map, and (x, y) is the coordinate value of the phase point at k x k matrix, where
Corrected phase for phase point (x, y), psix,yIs the winding phase of the phase point (x, y).
Optionally, the step of unwrapping the high quality dots comprises:
dividing the high-quality points into a plurality of pairs of points by taking two adjacent high-quality points as a pair, and calculating the quality value of each pair of points;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the high-quality point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
Optionally, the specific process of obtaining the true phase of the residual point by using local polynomial surface fitting includes:
the true phase of the residual point is
Wherein X(x0，y0)Is the polynomial basis of the residual point (x0, y0), R (-) represents a rounding function,
is a column vector of fitting coefficients,. phix,yIs the winding phase of the phase point (x, y),
wherein the column vector is composed of fitting coefficients
The value of (d) is obtained by:
where Φ is a column vector consisting of the true phases of p unwrapped high-quality points, the p unwrapped high-quality points being high-quality points in a v × v window formed centered on a point (X0, y0), X being a matrix of p × (M +1) (N +1) consisting of the polynomial basis of the unwrapped high-quality points;
true phase of p unwrapped high quality points
Is derived from a polynomial function, wherein,
in the above formula, Cm,nCoefficients representing a polynomial function, M and N representing the order, + e, of the polynomial function in the x and y directions, respectivelyx,yIs the approximation error of the polynomial function.
Optionally, the step of unwrapping the residual error point according to the true phase includes:
dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair, and calculating the quality value of each point pair;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the residual error point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
Further, in order to achieve the above object, the present application also proposes a phase unwrapping device including:
the residual point distribution module is used for calculating to obtain a residual point distribution diagram according to the winding phase diagram of the image;
the quality map module is used for calculating a phase quality map according to the winding phase map of the image;
the branch tangent line module is used for connecting the residual points in the residual point distribution graph by using branch tangent lines and reducing the quality of the residual points by N times;
the high-quality point module is used for setting the phase point outside the branch tangent line as a high-quality point;
the first unwinding module is used for unwinding the high-quality point;
the real phase module is used for obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and the second unwrapping module is used for unwrapping the residual error points according to the real phase.
Optionally, the residual point distribution module includes:
a square submodule for forming a square by connecting four phase points of the winding phase diagram, the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
A difference submodule for obtaining a winding phase difference between two of the four phase points in the square by the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
a summation submodule for summing the winding phase differences between two of the four phase points to q,
a judgment sub-module, if the q value is 0, the phase point psim,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
Optionally, the first unwinding module comprises:
the first quality submodule is used for dividing the high-quality points into a plurality of point pairs by taking two adjacent high-quality points as a pair and calculating the quality value of each point pair;
the first sequencing submodule is used for sequencing a plurality of points according to the quality values;
the first primary unwinding submodule is used for taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points and adding the unwound pair of points into a first group;
the first deep unwinding submodule is used for judging whether the high-quality point in the Nth point is unwound or not before unwinding the Nth point, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
Optionally, the second unwinding module comprises:
the second quality submodule is used for dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair and calculating the quality value of each point pair;
the second sorting submodule is used for sorting the points according to the quality values;
the second primary unwinding submodule is used for taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points and adding the unwound pair of points into the first group;
the second deep unwinding submodule is used for judging whether the residual error point in the Nth point is unwound or not before unwinding the Nth point,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
Furthermore, in order to achieve the above object, the present application also proposes a readable storage medium having stored thereon a phase unwrapping program that, when executed by a processor, implements the steps of the phase unwrapping method as recited in any one of the above.
The technical scheme of the invention discloses a phase unwrapping method, which comprises the following steps: calculating to obtain a residual point distribution diagram according to a winding phase diagram of the image; calculating to obtain a phase quality map according to the winding phase map of the image; connecting residual points in the residual point distribution graph by using branch tangent lines, and reducing the quality of the residual points by N times; setting phase points outside the branch tangent lines as high-quality points; unwinding the high-quality points; obtaining the real phase of the residual point by utilizing local polynomial surface fitting; and unwrapping the residual error points according to the real phase. According to the method, the residual error point distribution diagram and the phase quality diagram are obtained, then the residual error points are connected by the branch tangent line to remove 'balance' polarity, so that the high-quality points can be unwound along the region which does not pass through the branch tangent line, the generation and transmission of unwinding errors can be avoided, after the real phase of the residual error points is obtained by correction, the residual error points are unwound according to the real phase, and the accuracy of unwinding of the residual error points is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a schematic diagram of a hardware structure of a backlight response testing apparatus for a display module according to the present invention;
FIG. 2 is a schematic flow chart of a phase unwrapping method in accordance with the present invention;
the reference numbers illustrate:
| reference numerals | Name (R) | Reference numerals | Name (R) |
| 101 | Processor with a memory having a plurality of memory cells | 103 | Memory device |
| 102 | Communication bus |
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a phase unwrapping device according to an embodiment of the present application, including: a processor 1001, such as a CPU, a communication bus 1002, and a memory 1003. Wherein a communication bus 1002 is used to enable connective communication between these components.
The memory 1003 may be a high-speed RAM memory or a non-volatile memory (e.g., a disk memory). As shown in fig. 1, a phase unwrapping program may be included in the memory 1003 as a computer storage medium; and processor 1001 may be configured to invoke the phase unwrapping program stored in memory 1003 and perform the following operations:
calculating to obtain a residual point distribution diagram according to a winding phase diagram of the image;
calculating to obtain a phase quality map according to the winding phase map of the image;
connecting residual points in the residual point distribution graph by using branch tangent lines, and reducing the quality of the residual points by N times;
setting phase points outside the branch tangent lines as high-quality points;
unwinding the high-quality points;
obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and unwrapping the residual error points according to the real phase.
Alternatively, the processor 1001 may be configured to call the phase unwrapping program stored in the memory 1003 and perform the following operations:
the step of obtaining the residual point distribution diagram by calculating according to the winding phase diagram of the image comprises the following steps:
the four phase points of the winding phase diagram are connected to form a square, and the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
The winding phase difference value between two of the four phase points in the square is obtained through the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
the sum of the winding phase difference values between two of the four phase points is obtained as q,
if the q value is 0, the phase point ψm,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
Alternatively, the processor 1001 may be configured to call the phase unwrapping program stored in the memory 1003 and perform the following operations:
the specific process of calculating and obtaining the phase quality map according to the winding phase map of the image comprises the following steps:
the quality value of the phase point (x, y) is:
Qx,yis the mass value of the phase point (x, y), k is the k value of the k x k matrix of the wound phase map, and (x, y) is the coordinate value of the phase point at k x k matrix, where
Corrected phase for phase point (x, y), psix,yIs the winding phase of the phase point (x, y).
Alternatively, the processor 1001 may be configured to call the phase unwrapping program stored in the memory 1003 and perform the following operations:
the step of unwrapping the high quality dots includes:
dividing the high-quality points into a plurality of pairs of points by taking two adjacent high-quality points as a pair, and calculating the quality value of each pair of points;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the high-quality point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
Alternatively, the processor 1001 may be configured to call the phase unwrapping program stored in the memory 1003 and perform the following operations:
the specific process of obtaining the true phase of the residual point by using the local polynomial surface fitting comprises the following steps:
the true phase of the residual point is
Wherein X(x0，y0)Is the polynomial basis of the residual point (x0, y0), R (-) represents a rounding function,
is a column vector of fitting coefficients,. phix,yIs the winding phase of the phase point (x, y),
wherein the column vector is composed of fitting coefficients
The value of (d) is obtained by:
where Φ is a column vector consisting of the true phases of p unwrapped high-quality points, the p unwrapped high-quality points being high-quality points in a v × v window formed centered on a point (X0, y0), X being a matrix of p × (M +1) (N +1) consisting of the polynomial basis of the unwrapped high-quality points;
true phase of p unwrapped high quality points
Is derived from a polynomial function, wherein,
in the above formula, Cm,nCoefficients representing a polynomial function, M and N representing the order, + e, of the polynomial function in the x and y directions, respectivelyx,yIs the approximation error of the polynomial function.
Alternatively, the processor 1001 may be configured to call the phase unwrapping program stored in the memory 1003 and perform the following operations:
the step of unwrapping the residual points according to the true phase includes:
dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair, and calculating the quality value of each point pair;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the residual error point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
Those skilled in the art will appreciate that the configuration of the device shown in fig. 1 is not intended to be limiting of the device and may include more or fewer components than those shown, or some components may be combined, or a different arrangement of components.
Referring to fig. 2, an embodiment of a phase unwrapping method according to the present invention is provided, the phase unwrapping method including:
step S10, calculating to obtain a residual point distribution diagram according to the winding phase diagram of the image;
in this embodiment, a residual point distribution diagram is obtained first, and because the residual points are contaminated points, the points "contaminated" by noise are separated first from the residual points and are released to be unwound finally.
Further, in this embodiment, the step S10 includes:
step S11, forming a square by connecting four phase points of the winding phase diagram, wherein the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
Step S12, obtaining a winding phase difference value between each two of the four phase points in the square by the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
step S13, the sum of the winding phase difference values between every two of the four phase points is obtained as q,
step S14, if the q value is 0, the phase point psim,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
In this embodiment, a square is formed by connecting four phase points of the winding phase diagram, and then the sum of winding phase differences between every two of the four phase points is used to determine whether the phase point is a residual error point. If the q value is positive, the phase point ψm,nThe residual error points with positive polarity and vice versa are connected by branch tangent lines to balance the polarity, so that the unwrapping can be carried out along the area without the branch tangent lines, and the generation and the transmission of unwrapping errors can be avoided.
Step S20, calculating a phase quality map according to the winding phase map of the image;
according to the mass-guided algorithm, the quality of the contaminated phase points is lower than that of the normal phase points, and thus by obtaining a phase-quality map, the contaminated phase points can be further distinguished from the normal phase points.
Further, in this embodiment, the specific process of step S20 includes:
the quality value of the phase point (x, y) is:
Qx,yis the mass value of the phase point (x, y), k is the k value of the k x k matrix of the wound phase map, and (x, y) is the coordinate value of the phase point at k x k matrix, where
Corrected phase for phase point (x, y), psix,yIs the winding phase of the phase point (x, y).
Step S30, connecting residual error points in the residual error point distribution graph by branch tangent lines, and reducing the quality of the residual error points by N times;
this embodiment reduces the quality of the points located on the branch tangent line by a factor of N, so that other high quality points can be unwrapped first, and then the quality map obtained after such processing is used to guide the unwrapping of the phase points. In this embodiment, the value N is 1000, and analysis of the obtained unwrapped phase map indicates that the phase values at the branch tangent and the 3 adjacent points are less accurate, so that the phase points of the branch tangent need to be phase-corrected and then unwrapped.
Step S40, setting the phase point outside the branch tangent line as a high-quality point;
step S50, unwinding the high-quality points;
in this embodiment, the high-quality point is unwrapped first, the phase value of the high-quality point is highly accurate, the phase value of the high-quality point does not need to be corrected, the high-quality point does not pass through the area of the branch tangent line, the phase value of the residual point on the branch tangent line is less accurate, and the generation and transmission of an unwrapping error can be avoided.
Further, in this embodiment, the step S50 includes:
dividing the high-quality points into a plurality of pairs of points by taking two adjacent high-quality points as a pair, and calculating the quality value of each pair of points;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the high-quality point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
In the embodiment, on the premise of being based on the quality map, the high-quality point is unwound by using the specific unwinding path, so that the unwinding efficiency of the high-quality point can be greatly improved.
Step S60, obtaining the real phase of the residual point by using local polynomial surface fitting;
the residual points on the tangent of the branch are regarded as polluted points, and the true phases of the polluted points are required to be solved by local polynomial fitting by taking the polluted points (x0, y0) as the center and combining p high-quality points which are subjected to unwrapping, so that the accuracy of unwrapping is improved.
Further, in this embodiment, the specific process of step S60 is as follows:
the true phase of the residual point is
Wherein X(x0，y0)Is the polynomial basis of the residual point (x0, y0), R (-) represents a rounding function,
is a column vector of fitting coefficients,. phix,yIs the winding phase of the phase point (x, y),
wherein the column vector is composed of fitting coefficients
The value of (d) is obtained by:
where Φ is a column vector consisting of the true phases of p unwrapped high-quality points, the p unwrapped high-quality points being high-quality points in a v × v window formed centered on a point (X0, y0), X being a matrix of p × (M +1) (N +1) consisting of the polynomial basis of the unwrapped high-quality points;
true phase of p unwrapped high quality points
Is derived from a polynomial function, wherein,
in the above formula, Cm,nRepresentsCoefficients of a polynomial function, M and N representing the order, + e, of the polynomial function in the x and y directions, respectivelyx,yIs the approximation error of the polynomial function.
And step S70, unwrapping the residual error points according to the real phase.
In this embodiment, the true phases of the points of the residual points are solved by local polynomial fitting, and then the residual points are unwrapped according to the true phases, so that the accuracy of unwrapping the residual points is improved.
Further, in this embodiment, the step S70 includes:
dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair, and calculating the quality value of each point pair;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the residual error point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
On the premise of being based on the quality map, the embodiment uses the specific unwrapping path to unwrapp the residual points, so that the unwrapping efficiency of the residual points can be greatly improved.
According to the method, the residual error point distribution diagram and the phase quality diagram are obtained, then the residual error points are connected by the branch tangent line to remove 'balance' polarity, so that the high-quality points can be unwound along the region which does not pass through the branch tangent line, the generation and transmission of unwinding errors can be avoided, after the real phase of the residual error points is obtained by correction, the residual error points are unwound according to the real phase, and the accuracy of unwinding of the residual error points is improved.
The present application also provides a phase unwrapping device, which includes:
the residual point distribution module is used for calculating to obtain a residual point distribution diagram according to the winding phase diagram of the image;
the quality map module is used for calculating a phase quality map according to the winding phase map of the image;
the branch tangent line module is used for connecting the residual points in the residual point distribution graph by using branch tangent lines and reducing the quality of the residual points by N times;
the high-quality point module is used for setting the phase point outside the branch tangent line as a high-quality point;
the first unwinding module is used for unwinding the high-quality point;
the real phase module is used for obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and the second unwrapping module is used for unwrapping the residual error points according to the real phase.
According to the method, the residual error point distribution diagram and the phase quality diagram are obtained, then the residual error points are connected by the branch tangent line to remove 'balance' polarity, so that the high-quality points can be unwound along the region which does not pass through the branch tangent line, the generation and transmission of unwinding errors can be avoided, after the real phase of the residual error points is obtained by correction, the residual error points are unwound according to the real phase, and the accuracy of unwinding of the residual error points is improved.
In this embodiment, the residual point distribution module includes:
a square submodule for forming a square by connecting four phase points of the winding phase diagram, the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
A difference submodule for obtaining a winding phase difference between two of the four phase points in the square by the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
a summation submodule for summing the winding phase differences between two of the four phase points to q,
a judgment sub-module, if the q value is 0, the phase point psim,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
In this embodiment, the first unwinding module includes:
the first quality submodule is used for dividing the high-quality points into a plurality of point pairs by taking two adjacent high-quality points as a pair and calculating the quality value of each point pair;
the first sequencing submodule is used for sequencing a plurality of points according to the quality values;
the first primary unwinding submodule is used for taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points and adding the unwound pair of points into a first group;
the first deep unwinding submodule is used for judging whether the high-quality point in the Nth point is unwound or not before unwinding the Nth point, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
In this embodiment, the second unwinding module includes:
the second quality submodule is used for dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair and calculating the quality value of each point pair;
the second sorting submodule is used for sorting the points according to the quality values;
the second primary unwinding submodule is used for taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points and adding the unwound pair of points into the first group;
the second deep unwinding submodule is used for judging whether the residual error point in the Nth point is unwound or not before unwinding the Nth point,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
The present application also proposes a readable storage medium having stored thereon a phase unwrapping program that, when executed by a processor, implements the steps of the phase unwrapping method according to the first subject matter. Since the third subject includes all the technical features of the first subject, the third subject can achieve the same technical effects as the first subject, and will not be described herein again.
The above description is only an alternative embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (10)
1. A phase unwrapping method comprising the steps of:
calculating to obtain a residual point distribution diagram according to a winding phase diagram of the image;
calculating to obtain a phase quality map according to the winding phase map of the image;
connecting residual points in the residual point distribution graph by using branch tangent lines, and reducing the quality of the residual points by N times;
setting phase points outside the branch tangent lines as high-quality points;
unwinding the high-quality points;
obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and unwrapping the residual error points according to the real phase.
2. The phase unwrapping method according to claim 1, wherein the step of calculating the residual point profile from the wrapped phase map of the image includes:
the four phase points of the winding phase diagram are connected to form a square, and the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
The winding phase difference value between two of the four phase points in the square is obtained through the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
the sum of the winding phase difference values between two of the four phase points is obtained as q,
if the q value is 0, the phase point ψm,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
3. The phase unwrapping method according to claim 1, wherein the calculating the phase quality map from the wrapped phase map of the image includes:
the quality value of the phase point (x, y) is:
Qx,ymass value of phase point (x, y), k is the wrapThe k value of the k x k matrix around the phase map, (x, y) is the coordinate value of the phase point at k x k matrix, where
Corrected phase for phase point (x, y), psix,yIs the winding phase of the phase point (x, y).
4. The phase unwrapping method as recited in claim 1, wherein the step of unwrapping the high quality point includes:
dividing the high-quality points into a plurality of pairs of points by taking two adjacent high-quality points as a pair, and calculating the quality value of each pair of points;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the high-quality point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
5. The phase unwrapping method according to claim 1, wherein the step of obtaining the true phase of the residual point by local polynomial surface fitting comprises:
the true phase of the residual point is
Wherein X(x0，y0)Is the polynomial basis of the residual point (x0, y0), R (-) represents a rounding function,
is a column vector of fitting coefficients,. phix,yIs the winding phase of the phase point (x, y),
wherein the column vector is composed of fitting coefficients
The value of (d) is obtained by:
where Φ is a column vector consisting of the true phases of p unwrapped high-quality points, the p unwrapped high-quality points being high-quality points in a v × v window formed centered on a point (X0, y0), X being a matrix of p × (M +1) (N +1) consisting of the polynomial basis of the unwrapped high-quality points;
true phase of p unwrapped high quality points
Is derived from a polynomial function, wherein,
in the above formula, Cm,nRepresenting the coefficients of a polynomial function, M and N representing the order of the polynomial function in the x and y directions, respectively, ex,yIs the approximation error of the polynomial function.
6. The phase unwrapping method according to claim 1, wherein the step of unwrapping the residual points according to the true phase includes:
dividing the residual error points into a plurality of point pairs by taking two adjacent residual error points as a pair, and calculating the quality value of each point pair;
sorting the points according to the quality values;
taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points, and adding the unwound pair of points into a first group;
before the Nth point is unwound, whether the residual error point in the Nth point is unwound or not is judged, N is more than or equal to 2,
if the residual error points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one residual error point in the Nth point pair is unwound, adding the unwound Nth point pair into the group of the unwound residual error points,
if the two residual points of the Nth point are unwound and the two residual points p and q of the Nth point belong to the residual points of the p-th group and the q-th group respectively, if the number of the residual points of the p-th group and the q-th group is the same, combining the p-th group and the q-th group to form a new ith group, if the number of the residual points of the p-th group and the q-th group is different, adding 2k pi to the phase of each residual point in the p-th group with the smaller number of the residual points, and combining the p-th group and the q-th group to form a new ith group;
and repeating the step until all residual error points are unwound.
7. A phase unwrapping device, comprising:
the residual point distribution module is used for calculating to obtain a residual point distribution diagram according to the winding phase diagram of the image;
the quality map module is used for calculating a phase quality map according to the winding phase map of the image;
the branch tangent line module is used for connecting the residual points in the residual point distribution graph by using branch tangent lines and reducing the quality of the residual points by N times;
the high-quality point module is used for setting the phase point outside the branch tangent line as a high-quality point;
the first unwinding module is used for unwinding the high-quality point;
the real phase module is used for obtaining the real phase of the residual point by utilizing local polynomial surface fitting;
and the second unwrapping module is used for unwrapping the residual error points according to the real phase.
8. The phase unwrapping device as recited in claim 7, wherein the residual point distribution module includes:
a square submodule for forming a square by connecting four phase points of the winding phase diagram, the winding phases of the four phase points are psim,n，ψm,n+1，ψm+1,n，ψm+1,n+1；
A difference submodule for obtaining a winding phase difference between two of the four phase points in the square by the following formula, wherein gamma is an integer constant coefficient,
Δ1＝γ{ψm,n+1-ψm,n},
Δ2＝γ{ψm+1,n+1-ψm,n+1},
Δ3＝γ{ψm+1,n-ψm+1,n+1},
Δ4＝γ{ψm,n-ψm+1,n}.；
a summation submodule for summing the winding phase differences between two of the four phase points to q,
a judgment sub-module, if the q value is 0, the phase point psim,nNot a residual point; if the q value is not 0, the phase point ψm,nAre the residual points.
9. The phase unwrapping device of claim 7, wherein the first unwrapping module includes:
the first quality submodule is used for dividing the high-quality points into a plurality of point pairs by taking two adjacent high-quality points as a pair and calculating the quality value of each point pair;
the first sequencing submodule is used for sequencing a plurality of points according to the quality values;
the first primary unwinding submodule is used for taking the pair of points with the highest mass value as a first pair of points, unwinding the first pair of points and adding the unwound pair of points into a first group;
the first deep unwinding submodule is used for judging whether the high-quality point in the Nth point is unwound or not before unwinding the Nth point, N is more than or equal to 2,
if the high-quality points in the Nth point pair are not unwound, adding the unwound Nth point pair into a new N-th group,
if one high-quality point in the Nth pair of points is unwound, adding the unwound Nth pair of points into the group of the unwound high-quality point,
if the two high-quality points of the Nth point pair are both unwound and the two high-quality points p and q of the Nth point pair belong to the high-quality points of the p-th group and the q-th group respectively, if the high-quality points of the p-th group and the q-th group are the same in number, combining the p-th group and the q-th group to form a new ith group, if the high-quality points of the p-th group and the q-th group are different in number, adding 2k pi to the phase of each high-quality point in the p-th group with the smaller number of high-quality points, and then combining the p-th group and the q-th group to form a new ith group,
the steps are repeated until all the high-quality points are unwound.
10. A readable storage medium having stored thereon a phase unwrapping program that, when executed by a processor, implements the steps of the phase unwrapping method as recited in any one of claims 1-6.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104316922A (en) * | 2014-10-11 | 2015-01-28 | 南京邮电大学 | Regional division based multi-strategy InSAR (Interferometric synthetic aperture) radar phase unwrapping method |
| CN105158761A (en) * | 2015-08-31 | 2015-12-16 | 西安电子科技大学 | Radar synthetic phase unwrapping method based on branch-cut method and surface fitting |
| CN108986120A (en) * | 2018-07-13 | 2018-12-11 | 长春师范大学 | A kind of quick and reliable phase unwrapping algorithm |
| CN110109106A (en) * | 2019-04-23 | 2019-08-09 | 中国电力科学研究院有限公司 | A kind of InSAR interferometric phase unwrapping method in region with a varied topography |
| CN113126092A (en) * | 2020-01-15 | 2021-07-16 | 重庆三峡学院 | Phase unwrapping method for radar interference image based on artificial intelligence technology |
-
2021
- 2021-08-17 CN CN202110946224.1A patent/CN113495241B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104316922A (en) * | 2014-10-11 | 2015-01-28 | 南京邮电大学 | Regional division based multi-strategy InSAR (Interferometric synthetic aperture) radar phase unwrapping method |
| CN105158761A (en) * | 2015-08-31 | 2015-12-16 | 西安电子科技大学 | Radar synthetic phase unwrapping method based on branch-cut method and surface fitting |
| CN108986120A (en) * | 2018-07-13 | 2018-12-11 | 长春师范大学 | A kind of quick and reliable phase unwrapping algorithm |
| CN110109106A (en) * | 2019-04-23 | 2019-08-09 | 中国电力科学研究院有限公司 | A kind of InSAR interferometric phase unwrapping method in region with a varied topography |
| CN113126092A (en) * | 2020-01-15 | 2021-07-16 | 重庆三峡学院 | Phase unwrapping method for radar interference image based on artificial intelligence technology |
Non-Patent Citations (6)
| Title |
|---|
| 张妍: "干涉合成孔径雷达相位解缠技术的研究" * |
| 张妍;冯大政;曲小宁;: "枝切法与曲面拟合结合的InSAR相位展开算法" * |
| 李军: "基于质量图分割的InSAR相位解缠方法" * |
| 蒋锐;朱岱寅;朱兆达;: "一种基于等效残差点的InSAR相位解缠绕方法" * |
| 蔡洋: "基于路径跟踪的InSAR相位解缠技术研究" * |
| 马靓婷;卢小平;余振宝;: "相位分块与拟合法结合的InSAR相位解缠算法" * |
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