CN113040825A - Rapid three-dimensional echocardiography speckle tracking method with sub-pixel precision - Google Patents
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Abstract
The invention relates to a sub-pixel precision rapid three-dimensional echocardiography speckle tracking method, which comprises the following steps: selecting a tracking point by an operating doctor, and setting initial parameters such as block size, search area size and the like; performing 1/16 sub-pixel precision block matching tracking after aligning the reference block pixel values in alternate frames (odd frames); and (3) obtaining the even frame tracking point coordinates through spline interpolation calculation, and automatically marking the myocardial tissue interested region on the 3D echocardiography sequence image by a computer. The invention realizes a high-precision fast 3D echocardiography speckle tracking method, and the method has good self-adaptive characteristic and robustness. The method is suitable for the 3D STE imaging technology aiming at realizing accurate evaluation and quantitative diagnosis and treatment of the cardiac function. The 2D variant of the method of the invention is a fast 2D echocardiography speckle tracking method of sub-pixel accuracy.
Description
Technical Field
The invention relates to a three-dimensional (3D) echocardiography Speckle tracking method, in particular to a fast 3D echocardiography Speckle tracking method with sub-pixel precision, which belongs to the technical field of medical ultrasonic image processing and aims to realize 3D STE imaging technology (3D speed tracking echo diagnosis) of accurate heart function evaluation and quantitative diagnosis and treatment.
Background
Heart failure is the last stage in the development of cardiovascular diseases such as coronary heart disease, hypertension, congenital heart disease, valvular heart disease, cardiomyopathy, etc., is the leading cause of death in patients with cardiovascular diseases and the last battlefield of clinical treatment, and is considered to be the biggest challenge facing the cardiovascular world in the 21 st century. The method has the advantages that the quantitative evaluation of the heart function is carried out in the early stage for high-risk people who are easy to suffer from heart failure, the abnormal systolic and diastolic functions are recognized as early as possible, effective intervention is carried out, the occurrence and development of the heart failure are favorably prevented and delayed, and the service life of patients suffering from cardiovascular diseases is prolonged and prognosis is improved. The Speckle tracking three-dimensional echocardiography (3D STE) is an emerging ultrasound imaging technology which aims at realizing accurate evaluation and quantitative diagnosis and treatment of cardiac function, and can accurately realize velocity vector imaging, strain and strain rate imaging of myocardial tissue and measurement and visualization of motion parameters such as left ventricular torsional angular displacement, torsional moment, torsional angular velocity and the like through tracking and motion analysis of 3D echocardiography Speckle (Speckle) or Speckle pattern (Speckle pattern), thereby providing quantitative analysis basis for a clinician to objectively evaluate the whole and local functions of the myocardium and the contraction and relaxation functions of the ventricle, and providing technical means for the clinician to quantitatively research the biological elasticity mechanical properties of the myocardial tissue.
In echocardiographic speckle tracking methods, the speckle or speckle pattern to be tracked and analyzed is, in image processing practice, a number of regions of interest (ROIs) located within the myocardial tissue, i.e., blocks or kernels of conventional Block matching processing (Block/Kernel). The echocardiography speckle tracking methods reported in the literatures mainly have two types: a speckle tracking method of block matching and a speckle tracking method of an optical flow field. The speckle tracking method (Optical flow based specific tracking) of the Optical flow field can realize high-precision myocardial tissue motion tracking, but has strict requirements on image quality and poor clinical practicability. The speckle tracking method (Block matching based speckle tracking) of Block matching has good clinical practicability and is a mainstream method in the technical field of 3D STE imaging, but the traditional Block matching method is difficult to realize high-precision myocardial tissue motion tracking. In addition, the conventional methods generally have poor clinical application performance such as computational processing efficiency, adaptive characteristics, robustness and the like.
Disclosure of Invention
Aiming at the defects that the conventional method is low in tracking precision or poor in clinical practicability and generally cannot meet the requirements of accurate cardiac function evaluation and quantitative diagnosis and treatment clinical application, the invention provides the rapid 3D echocardiogram speckle tracking method which has good self-adaptive characteristic and robustness and 1/16 sub-pixel precision and is based on the technical principles of good performance and clinical practicality.
Interpretation of terms:
1. cubic Spline Interpolation, where a Spline refers to a smooth curve passing through a series of shape points, is a mathematical method of computing such a curve.
2. The Full search algorithm, Full search, a strategy for implementing block matching operations in image processing, obtains matching blocks by evaluating all candidate points within a search area.
3. SAD, Sum of absolute differences.
4. Imaging system 3D image space, a technical term in the field of 3D medical imaging, refers in the present invention to the cartesian space where the 3D echocardiographic sequence images are located, as shown in fig. 3, three dimensions refers to X, Y, Z coordinate three dimensions of the cartesian space.
The technical scheme of the invention is as follows:
a speckle tracking method for 3D echocardiography is realized by a computer workstation configured with accurate heart function evaluation and quantitative diagnosis and treatment functions. Let 3D echocardiography sequence images consist of n frames of images, denoted as I k1,2, n, wherein IkFor the k frame image of a 3D echocardiographic sequence image, I1For an initial frame, InIs a last frame, I1,I3,...,InIs an odd number of frames anda sequence image composed of the last frame; the reference block used for block matching of the t-th frame image is denoted as RtThe reference block after pixel value calibration used for block matching of the t-th frame image is denoted as "1, 3,5The best matching block obtained on the t-th frame image is denoted as MtThe position of the tracking point obtained on the t-th frame image in the 3D image space of the imaging system is recorded as rt(xt,yt,zt) Wherein (x)t,yt,zt) Representing the coordinates of the tracking point in 3D image space, the steps of the method are as follows:
s1) by the clinician at the initial frame I1Manually selecting a tracking point;
in the initial frame I of the 3D echocardiographic sequence image1The tracking point is manually selected by a clinician, and the position of the tracking point in the 3D image space of the imaging system is r1(x1,y1,z1);
S2) setting initial parameters;
setting the size n of the myocardial tissue region of interest centered on the tracking point of each framex×ny×nzWherein n isx、ny、nzThe sizes along the directions of x, y and z axes in the 3D image space of the imaging system respectively; setting the size of a search area; setting a factor m for reference block pixel value calibration; making the current frame serial number j equal to 1; setting an initial reference block size by rj(xj,yj,zj) Forming an initial reference block R centered on a pointj(ii) a Order toRjRefers to a reference block used for block matching in the jth frame image,refers to a reference block, M, after pixel value calibration, used for block matching of the jth frame imagejMeans the best matching block obtained on the j frame image;
s3) reference block pixel value calibration;
j is increased by 2; let Rj=Mj-2;
For reference block RjThe pixel value of the reference block is calibrated to obtain a reference block which is used by the jth frame image for block matching and is calibrated by the pixel value
S4) carrying out block matching calculation with 1/16 sub-pixel precision to obtain the coordinate r of the position of the tracking point of the current frame in the 3D image space of the imaging systemj(xj,yj,zj);
S5) if IjIf the frame is the last frame, executing S6, otherwise executing S3;
s6) calculating the position of the even frame tracking point in the imaging system 3D image space
Respectively taking the coordinates of the odd frame and the last frame of tracking points in the 3D image space of the imaging system, and calculating the coordinates of the even frame of tracking points in the x axis, the y axis and the z axis of the imaging system through cubic spline interpolation to obtain the positions of the even frame of tracking points in the 3D image space of the imaging system and further obtain the positions of all the frame of tracking points in the 3D image space of the imaging system;
s7) forming and recording the myocardial tissue region of interest of all frames
Forming and recording the size of each frame as n by taking the tracking point of all frames as the centerx×ny×nzTo realize speckle tracking of 3D echocardiography.
According to the invention, preferably, for reference block RjIs calibrated, as shown in equation (i):
in the formula (I), 0<m,p,q<1,m+p+q=1,p=0.9(1-m)/(n-3)2·(j-3)2,q=1-m-p。
According to the invention, preferably, inFor reference blocks, 1/16 sub-pixel precision block matching calculation is performed, which is implemented as follows:
s41) at IjUp to rj-2(xj-2,yj-2,zj-2) Carrying out cubic spline interpolation for the first time in the search region with the point as the center, so that 3 equally-spaced inner points among 2 adjacent nodes are interpolated to obtain 1/4 search regions with sub-pixel precision S11;
s42), adopting a full search algorithm and an SAD (sum of absolute differences) matching criterion, using an SAD iterative computation early termination strategy, carrying out primary matching in a search area S11, and recording a point corresponding to the minimum SAD value as a primary 1/4 sub-pixel precision tracking point R11;
s43) with the first 1/4 sub-pixel precision tracking point R11 as the center point, performing a second cubic spline interpolation on the surrounding 8 1/4 voxel blocks, and then interpolating 3 equally spaced interior points between 2 adjacent nodes to obtain a 1/16 sub-pixel precision search region S12.
S44) performs compression processing on the search region S12 by calculating 1/8 sub-pixel precision tracking points:
calculating SAD values of center points B1, B2, B3, B4, B5, B6, B7 and B8 of 8 1/4 voxel blocks, and dividing 1/4 voxel blocks into secondary search areas S13 by taking points (taking B5 as an example) corresponding to the minimum SAD value as centers;
s44) adopting full search algorithm and SAD matching criterion, and using SAD iterative computation to terminate strategy in advance for secondary matching, wherein the point corresponding to minimum SAD value is the tracking point r of 1/16 sub-pixel precision of current frame (j frame)j(xj,yj,zj) The block centered at this point is the best matching block M on the current frame (jth frame)j。
Preferably, in step S42) and step S44), the implementation process is as follows:
let CAmaxAs a full search candidateTotal number of blocks, LmaxFor full search candidate block z-axis direction layer number, SADminFor the current minimum SAD value, r represents the current calculated r-th candidate block, SADrsRepresenting the sum of the previous s-layer errors, SAD, of the r-th candidate blocksRepresenting the sum of the error of the s layer, the specific calculation flow is as follows:
s421) calculating an initial candidate block SAD as SADminLet r be 1;
s422) judging whether the block is the last candidate block, namely r>CAmaxIf true, then the current SADminFor minimum SAD, the calculation ends, otherwise r is increased by 1, s is equal to 1, SADrs0, and performing step S423);
s423) judging whether the candidate block is the last layer of the current candidate block, namely judging S>LmaxIf yes, then recording the current SADrsIs SADminGo to step S422), otherwise, calculate the S-th layer SAD error SADsParallel SADrs=SADrs+SADsAnd step S424) is performed;
s424) judging the previous S-layer error and SADrsWhether it is greater than SADminIf yes, go to step S422), otherwise, S is incremented by 1, go to step S423).
The invention has the beneficial effects that:
the invention adopts a frame separation block matching processing frame; adaptively calibrating pixel values of a reference block in conjunction with medical knowledge of cardiac motion to avoid propagation and accumulation of tracking errors; 1/16 sub-pixel tracking precision is obtained by cubic spline interpolation of the search area; and the calculation efficiency of the block matching processing is improved by adopting the strategies of compressing the search area, terminating SAD iterative calculation in advance and the like. The high-precision fast 3D echocardiography speckle tracking method is realized, and the method has good self-adaptive characteristic and robustness. The method is suitable for the 3D STE imaging technology (3D speed tracking echocardiography) aiming at realizing accurate evaluation and quantitative diagnosis and treatment of the heart function. The method is beneficial to improving the clinical diagnosis and treatment level of quantitative evaluation of the cardiac function of common cardiovascular diseases such as coronary heart disease, hypertension and the like in China.
Drawings
FIG. 1(a) is a schematic diagram of the obtained 1/4 sub-pixel precision tracking point R11 and 8 1/4 voxel blocks around the tracking point;
FIG. 1(b) is a schematic diagram of 1/16 search region S12 with sub-pixel accuracy;
FIG. 1(c) is a schematic diagram of the center points B1, B2, B3, B4, B5, B6, B7 and B8 of 8 1/4 voxel blocks;
fig. 1(d) is a schematic diagram of the secondary search area S13;
FIG. 2 is a schematic flow diagram of a method of 3D echocardiography speckle tracking;
fig. 3 is a schematic diagram of a 3D image space coordinate system of the imaging system.
Detailed Description
The invention is further defined in the following, but not limited to, the figures and examples in the description.
Example 1
In the embodiment, a home-made heart ultrasonic diagnostic apparatus and a computer workstation are configured in an ultrasonic examination room of a cardiology department of a certain hospital. The main function of the workstation is to implement a 3D STE imaging technique based on the method of the invention. Namely, the method of the invention is used for carrying out speckle tracking on 3D echocardiography image data, and realizing the speed vector imaging, strain and strain rate imaging of myocardial tissues, the measurement and the imaging of motion parameters such as left ventricle torsional angular displacement, torsional moment, torsional angular velocity and the like. Through a USB flash disk and other mobile storage media, a clinician transfers and stores 3D echocardiogram image data acquired by an ultrasonic diagnostic apparatus to a workstation, and 3D echocardiogram sequence images are set to be composed of n frames of images and are respectively marked as Ik1,2, n, wherein IkFor the k frame image of a 3D echocardiographic sequence image, I1For an initial frame, InIs a last frame, I1,I3,...,InThe sequence image is formed by odd frames and last frames; the reference block used for block matching of the t-th frame image is denoted as RtThe reference block after pixel value calibration used for block matching of the t-th frame image is denoted as "1, 3,5The best matching block obtained on the t-th frame image is denoted as MtThe position of the tracking point obtained on the t-th frame image in the 3D image space of the imaging system is recorded as rt(xt,yt,zt) Wherein (x)t,yt,zt) Representing the coordinates of the tracking point in 3D image space (as shown in fig. 3), as shown in fig. 2, the steps of the method are as follows:
s1) by the clinician at the initial frame I1Manually selecting a tracking point;
in the initial frame I of the 3D echocardiographic sequence image1The tracking point is manually selected by a clinician, and the position of the tracking point in the 3D image space of the imaging system is r1(x1,y1,z1);
S2) setting initial parameters;
setting the size n of the myocardial tissue region of interest centered on the tracking point of each framex×ny×nzWherein n isx、ny、nzThe sizes along the directions of x, y and z axes in the 3D image space of the imaging system respectively; setting the size of a search area; setting a factor m for reference block pixel value calibration; making the current frame serial number j equal to 1; setting an initial reference block size by rj(xj,yj,zj) Forming an initial reference block R centered on a pointj(ii) a Order toRjRefers to a reference block used for block matching in the jth frame image,refers to a reference block, M, after pixel value calibration, used for block matching of the jth frame imagejMeans the best matching block obtained on the j frame image;
s3) reference block pixel value calibration;
j is increased by 2; let Rj=Mj-2;
For reference blockRjThe pixel value of the reference block is calibrated to obtain a reference block which is used by the jth frame image for block matching and is calibrated by the pixel value
S4) carrying out block matching calculation with 1/16 sub-pixel precision to obtain the coordinate r of the position of the tracking point of the current frame in the 3D image space of the imaging systemj(xj,yj,zj);
S5) if IjIf the frame is the last frame, executing S6, otherwise executing S3;
s6) calculating the position of the even frame tracking point in the imaging system 3D image space
Respectively taking the coordinates of the odd frame and the last frame of tracking points in the 3D image space of the imaging system, and calculating the coordinates of the even frame of tracking points in the x axis, the y axis and the z axis of the imaging system through cubic spline interpolation to obtain the positions of the even frame of tracking points in the 3D image space of the imaging system and further obtain the positions of all the frame of tracking points in the 3D image space of the imaging system;
s7) forming and recording the myocardial tissue region of interest of all frames
Forming and recording the size of each frame as n by taking the tracking point of all frames as the centerx×ny×nzTo realize speckle tracking of 3D echocardiography.
By using the recorded region of interest, the workstation software reliably, conveniently and efficiently assists clinicians in accurately evaluating the cardiac function of a patient and quantitatively diagnosing and treating the cardiac function of the patient through modes or means such as velocity vector imaging, strain and strain rate imaging of myocardial tissues, left ventricle torsional motion parameter measurement and imaging and the like.
Example 2
A method of 3D echocardiographic speckle tracking according to embodiment 1, which differs in that:
for reference block RjIs calibrated, as shown in equation (i):
in the formula (I), 0<m,p,q<1,m+p+q=1,p=0.9(1-m)/(n-3)2·(j-3)2,q=1-m-p。
Example 3
A method of 3D echocardiographic speckle tracking according to embodiment 1, which differs in that:
to be provided withFor reference blocks, 1/16 sub-pixel precision block matching calculation is performed, which is implemented as follows:
s41) at IjUp to rj-2(xj-2,yj-2,zj-2) Carrying out cubic spline interpolation for the first time in the search region with the point as the center, so that 3 equally-spaced inner points among 2 adjacent nodes are interpolated to obtain 1/4 search regions with sub-pixel precision S11;
s42), adopting a full search algorithm and an SAD (sum of absolute differences) matching criterion, using an SAD iterative computation early termination strategy, carrying out primary matching in a search area S11, and recording a point corresponding to the minimum SAD value as a primary 1/4 sub-pixel precision tracking point R11;
s43) with the first 1/4 sub-pixel precision tracking point R11 as the center point, performing a second cubic spline interpolation on the surrounding 8 1/4 voxel blocks (such as the region with a1-a8 as the vertex in fig. 1 (a)), and then interpolating 3 equally spaced interior points between 2 adjacent nodes to obtain a 1/16 sub-pixel precision search region S12 (such as fig. 1 (b)).
S44) performs compression processing on the search region S12 by calculating 1/8 sub-pixel precision tracking points:
calculating SAD values of center points B1, B2, B3, B4, B5, B6, B7 and B8 (as shown in fig. 1(C)) of 8 1/4 voxel blocks, and taking a point (for example, B5) corresponding to the minimum SAD value as a center to define 1/4 voxel blocks as a secondary search region S13 (as shown in fig. 1(d), regions with C1-C7 and R11 as vertexes);
s44) adopting a full search algorithm and SAD matching criteria, anUsing SAD iterative computation early termination strategy to carry out secondary matching, wherein the point corresponding to the minimum SAD value is the tracking point r of the current frame (jth frame) 1/16 with sub-pixel precisionj(xj,yj,zj) The block centered at this point is the best matching block M on the current frame (jth frame)j。
The 2D variant of the method is a fast 2D echocardiogram speckle tracking method with sub-pixel precision, namely the method is also suitable for carrying out speckle tracking on the 2D echocardiogram.
Example 4
A method of 3D echocardiographic speckle tracking according to embodiment 1, which differs in that:
step S42) and step S44), the specific implementation process is as follows:
let CAmaxTotal number of candidate blocks for full search, LmaxFor full search candidate block z-axis direction layer number, SADminFor the current minimum SAD value, r represents the current calculated r-th candidate block, SADrsRepresenting the sum of the previous s-layer errors, SAD, of the r-th candidate blocksRepresenting the sum of the error of the s layer, the specific calculation flow is as follows:
s421) calculating an initial candidate block SAD as SADminLet r be 1;
s422) judging whether the block is the last candidate block, namely r>CAmaxIf true, then the current SADminFor minimum SAD, the calculation ends, otherwise r is increased by 1, s is equal to 1, SADrs0, and performing step S423);
s423) judging whether the candidate block is the last layer of the current candidate block, namely judging S>LmaxIf yes, then recording the current SADrsIs SADminGo to step S422), otherwise, calculate the S-th layer SAD error SADsParallel SADrs=SADrs+SADsAnd step S424) is performed;
s424) judging the previous S-layer error and SADrsWhether it is greater than SADminIf yes, go to step S422), otherwise, S is incremented by 1, go to step S423).
Claims (4)
1. A3D echocardiogram speckle tracking method is characterized in that a 3D echocardiogram sequence image is composed of n frames of images which are respectively marked as Ik1,2, n, wherein IkFor the k frame image of a 3D echocardiographic sequence image, I1For an initial frame, InIs a last frame, I1,I3,...,InThe sequence image is formed by odd frames and last frames; the reference block used for block matching of the t-th frame image is denoted as RtThe reference block after pixel value calibration used for block matching of the t-th frame image is denoted as "1, 3,5The best matching block obtained on the t-th frame image is denoted as MtThe position of the tracking point obtained on the t-th frame image in the 3D image space of the imaging system is recorded as rt(xt,yt,zt) Wherein (x)t,yt,zt) Representing the coordinates of the tracking point in 3D image space, the steps of the method are as follows:
s1) in the initial frame I1Manually selecting a tracking point;
in the initial frame I of the 3D echocardiographic sequence image1The tracking point is selected manually, and the position of the tracking point in the 3D image space of the imaging system is r1(x1,y1,z1);
S2) setting initial parameters;
setting the size n of the myocardial tissue region of interest centered on the tracking point of each framex×ny×nzWherein n isx、ny、nzThe sizes along the directions of x, y and z axes in the 3D image space of the imaging system respectively; setting the size of a search area; setting a factor m for reference block pixel value calibration; making the current frame serial number j equal to 1; setting an initial reference block size by rj(xj,yj,zj) Forming an initial reference block R centered on a pointj(ii) a Order toRjRefers to a reference block used for block matching in the jth frame image,refers to a reference block, M, after pixel value calibration, used for block matching of the jth frame imagejMeans the best matching block obtained on the j frame image;
s3) reference block pixel value calibration;
j is increased by 2; let Rj=Mj-2;
For reference block RjThe pixel value of the reference block is calibrated to obtain a reference block which is used by the jth frame image for block matching and is calibrated by the pixel value
S4) carrying out block matching calculation with 1/16 sub-pixel precision to obtain the coordinate r of the position of the tracking point of the current frame in the 3D image space of the imaging systemj(xj,yj,zj);
S5) if IjIf the frame is the last frame, executing S6, otherwise executing S3;
s6) calculating the position of the even frame tracking point in the imaging system 3D image space
Respectively taking the coordinates of the odd frame and the last frame of tracking points in the 3D image space of the imaging system, and calculating the coordinates of the even frame of tracking points in the x axis, the y axis and the z axis of the imaging system through cubic spline interpolation to obtain the positions of the even frame of tracking points in the 3D image space of the imaging system and further obtain the positions of all the frame of tracking points in the 3D image space of the imaging system;
s7) forming and recording the myocardial tissue region of interest of all frames
Forming and recording the size of each frame as n by taking the tracking point of all frames as the centerx×ny×nzTo realize speckle tracking of 3D echocardiography.
3. The method of 3D echocardiography speckle tracking according to claim 1, further comprising performing a speckle reduction on the image to obtain a speckle reduction imageFor reference blocks, 1/16 sub-pixel precision block matching calculation is performed, which is implemented as follows:
s41) at IjUp to rj-2(xj-2,yj-2,zj-2) Carrying out first cubic spline interpolation on the search region with the point as the center to obtain 1/4 search regions with sub-pixel precision S11;
s42) adopting a full search algorithm and an SAD matching criterion, using an SAD iterative computation early termination strategy, carrying out primary matching in a search region S11, and recording a point corresponding to the minimum SAD value as a primary 1/4 sub-pixel precision tracking point R11;
s43) taking the first 1/4 sub-pixel precision tracking point R11 as a central point, carrying out second cubic spline interpolation on 8 surrounding 1/4 pixel blocks to obtain a search area S12 with 1/16 sub-pixel precision;
s44) performs compression processing on the search region S12 by calculating 1/8 sub-pixel precision tracking points:
calculating SAD values of center points B1, B2, B3, B4, B5, B6, B7 and B8 of 8 1/4 voxel blocks, and taking a point corresponding to the minimum SAD value as a center to demarcate 1/4 voxel blocks as a secondary search area S13;
s44) using the full search algorithm and the SAD matching criterion, and using SAD iterationCalculating a termination strategy in advance, performing secondary matching, wherein the point corresponding to the minimum SAD value is the tracking point r of the current frame 1/16 with sub-pixel precisionj(xj,yj,zj) The block centered at this point is the best matching block M on the current framej。
4. The method for speckle tracking of 3D echocardiography according to claim 3, wherein the steps S42) and S44) are implemented as follows:
let CAmaxTotal number of candidate blocks for full search, LmaxFor full search candidate block z-axis direction layer number, SADminFor the current minimum SAD value, r represents the current calculated r-th candidate block, SADrsRepresenting the sum of the previous s-layer errors, SAD, of the r-th candidate blocksRepresenting the sum of the error of the s layer, the specific calculation flow is as follows:
s421) calculating an initial candidate block SAD as SADminLet r be 1;
s422) judging whether the block is the last candidate block, namely r>CAmaxIf true, then the current SADminFor minimum SAD, the calculation ends, otherwise r is increased by 1, s is equal to 1, SADrs0, and performing step S423);
s423) judging whether the candidate block is the last layer of the current candidate block, namely judging S>LmaxIf yes, then recording the current SADrsIs SADminGo to step S422), otherwise, calculate the S-th layer SAD error SADsParallel SADrs=SADrs+SADsAnd step S424) is performed;
s424) judging the previous S-layer error and SADrsWhether it is greater than SADminIf yes, go to step S422), otherwise, S is incremented by 1, go to step S423).
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