CN112882041B - High-precision arctangent fitting system and ultrasonic imaging device - Google Patents

High-precision arctangent fitting system and ultrasonic imaging device Download PDF

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CN112882041B
CN112882041B CN202110095896.6A CN202110095896A CN112882041B CN 112882041 B CN112882041 B CN 112882041B CN 202110095896 A CN202110095896 A CN 202110095896A CN 112882041 B CN112882041 B CN 112882041B
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fitting
arctangent
nonlinear model
coefficient
module
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CN112882041A (en
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肖梦楠
覃朝辉
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Jurong Medical Technology Hangzhou Co ltd
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Jurong Medical Technology Hangzhou Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88—Sonar systems specially adapted for specific applications
    • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F1/00—Details not covered by groups G06F3/00 - G06F13/00 and G06F21/00
    • G06F1/02—Digital function generators
    • G06F1/03—Digital function generators working, at least partly, by table look-up

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  • Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
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  • General Engineering & Computer Science (AREA)
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Abstract

The invention discloses a high-precision arctangent fitting system and an ultrasonic imaging device, wherein the system comprises: the lookup table construction module is used for constructing an angle lookup table in the nonlinear model; the parameter calculation module is used for calculating nonlinear model parameters; the basic coefficient calculation module is used for calculating basic coefficients; the fitting coefficient calculation module is used for calculating fitting coefficients of the nonlinear model according to the basic coefficients; and the fitting module is used for fitting the arctangent value based on the nonlinear model. Compared with the prior art, the invention has the advantages that: 1. compared with the existing polynomial fitting method lower than 3 steps, the method can obtain higher calculation accuracy; 2. compared with the existing polynomial fitting method lower than 3 th order, the method has the advantages that the calculation complexity is not remarkably increased, in addition, the model fitting coefficient of the method can be calculated in advance, and the calculation efficiency is further improved.

Description

High-precision arctangent fitting system and ultrasonic imaging device
Technical Field
The invention belongs to the technical field of ultrasonic signal processing, and particularly relates to a high-precision arctangent fitting system and an ultrasonic imaging device.
Background
The fast and accurate arctangent method is widely applied to the fields of embedded systems, signal processing, radars and the like. The existing arctangent approximation method mainly comprises three types of a CORDIC algorithm, a lookup table and a polynomial.
The main disadvantage of CORDIC algorithms is that the accuracy of the computation is highly dependent on the number of iterations, which entails an increase in computation time and consumption of memory resources. The main disadvantage of the look-up table is that it is difficult to solve the constraint between accuracy and efficiency. Related studies based on polynomials are more numerous, reference: rajanS, wang S, inkol R, et al Effectent approximations for the arctangent function [ J]IEEE SignalProcessingMagazine,2006,23 (3): 108-111, sreeramann Rajan et al, which have a comparison summary of this type of method, however the methods mentioned in the literature have a calculation accuracy of only 10 -3 For some scenes with higher precision requirements, the method is difficult to meet the performance requirements.
And whatever the above method, the arctan is used in (-pi, pi)]Is to be converted between the point and tanConversion of arctan's calculation toIs carried out.
Thus, a method is provided forThe high-precision arctan fitting method within is highly desirable.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a high-precision arctangent fitting system and an ultrasonic imaging device, which can obtain higher calculation precision and further improve the calculation efficiency.
The invention adopts the following technical scheme: a high precision arctangent fit system, comprising:
the lookup table construction module is used for constructing an angle lookup table in the nonlinear model;
the parameter calculation module is used for calculating nonlinear model parameters;
the basic coefficient calculation module is used for calculating basic coefficients;
the fitting coefficient calculation module is used for calculating fitting coefficients of the nonlinear model according to the basic coefficients;
and the fitting module is used for fitting the arctangent value based on the nonlinear model.
As a preferred solution, the construction angle lookup table in the lookup table construction module specifically includes: will beTangent value [0,1 ]]Equally dividing into two sections and constructing an angle lookup table LUT= [0,0.4636, 07854]。
As a preferred solution, the calculating nonlinear model parameters in the parameter calculating module specifically include: calculation ofIndex ind=round (2*x), t= (2*x-ind)/(2+ind x), where round represents rounding, x, tFor intermediate variables, Q represents the imaginary part and I represents the real part.
As a preferred solution, the calculating base coefficient in the base coefficient calculating module specifically includes:
the basic coefficient a is calculated as follows:
a＝2*tan(0.245/2)；
the base coefficient b is calculated as follows:
b＝2*tan(0.245/2) 3 /3。
as a preferred solution, the fitting coefficient of the nonlinear model calculated according to the basic coefficient in the fitting coefficient calculation module is specifically:
the fitting coefficient A is calculated as follows:
A＝4*a+12*b；
the fitting coefficient B is calculated as follows:
B＝256*b。
as a preferable scheme, the fitting of the arctangent value based on the nonlinear model in the fitting module specifically comprises: nonlinear model pair-basedThe arctangent values within are fitted and the following formula is used:
arctan＝LUT(ind)+A*t-B*t 3
correspondingly, a high-precision arctangent ultrasonic imaging device is also provided, and the high-precision arctangent ultrasonic imaging device comprises a high-precision arctangent fitting system.
The beneficial effects of the invention are as follows:
1. compared with the existing polynomial fitting method lower than 3 th order, the method can obtain higher calculation accuracy.
2. Compared with the existing polynomial fitting method lower than 3 th order, the method has the advantages that the calculation complexity is not remarkably increased, in addition, the model fitting coefficient of the method can be calculated in advance, and the calculation efficiency is further improved.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of a high accuracy arctangent fit system provided in accordance with a first embodiment;
FIG. 2 is a graph comparing error curves of the fitting method of the present invention with those of the prior art;
fig. 3 is a flowchart of a high-precision arctangent fitting method according to the second embodiment.
Detailed Description
The following specific examples are presented to illustrate the present invention, and those skilled in the art will readily appreciate the additional advantages and capabilities of the present invention as disclosed herein. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
Embodiment one:
referring to fig. 1, the present embodiment provides a high-precision arctangent fitting system, comprising:
the lookup table construction module is used for constructing an angle lookup table in the nonlinear model;
the parameter calculation module is used for calculating nonlinear model parameters;
the basic coefficient calculation module is used for calculating basic coefficients;
the fitting coefficient calculation module is used for calculating fitting coefficients of the nonlinear model according to the basic coefficients;
and the fitting module is used for fitting the arctangent value based on the nonlinear model.
Specific:
construct in the lookup table construction moduleThe angle building lookup table specifically comprises: will beTangent value [0,1 ]]Equally dividing into two sections and constructing an angle lookup table LUT= [0,0.4636, 07854]。
The parameters of the nonlinear model calculated in the parameter calculation module are specifically as follows: calculation ofThe embodiment is toI.e. angle +.>For illustration, the indices ind=round (2*x) =2, t= (2*x-ind)/(2+ind x) =0, where round represents rounding, x, t are intermediate variables, Q represents the imaginary part, and I represents the real part.
The basic coefficient calculation module calculates basic coefficients specifically as follows:
the basic coefficient a is calculated as follows:
a＝2*tan(0.245/2)＝0.2462；
the base coefficient b is calculated as follows:
b＝2*tan(0.245/2) 3 /3＝0.0012。
the fitting coefficient of the nonlinear model obtained by calculation according to the basic coefficient in the fitting coefficient calculation module is specifically:
the fitting coefficient A is calculated as follows:
A＝4*a+12*b＝0.9992；
the fitting coefficient B is calculated as follows:
B＝256*b＝0.3072。
the fitting of the arctangent value based on the nonlinear model in the fitting module is specifically as follows: nonlinear model pair-basedIn the inner partThe arctangent values were fitted and the following formula was used:
arctan＝LUT(ind)+A*t-B*t 3 ＝0.7854。
and after specific experiments, the method for calculating the arctangent in this example was carried out as described in the literature (Rajan S, wang S, inkol R, et al efficiency approximations for the arctangent function [ J)]IEEE Signal Processing Magazine,2006,23 (3): 108-111) uses the formula:the final error curve comparison can be seen with reference to fig. 2, by the method of arctangent calculation.
It can be seen that compared with the prior art, this embodiment has the following advantages:
1. compared with the existing polynomial fitting method lower than 3 th order, the method can obtain higher calculation accuracy.
2. Compared with the existing polynomial fitting method lower than 3 th order, the method has the advantages that the calculation complexity is not remarkably increased, in addition, the model fitting coefficient of the method can be calculated in advance, and the calculation efficiency is further improved.
Embodiment two:
referring to fig. 3, the present embodiment provides a high-precision arctangent fitting method, which includes the steps of:
s1, constructing an angle lookup table in a nonlinear model;
s2, calculating nonlinear model parameters;
s3, calculating basic coefficients;
s4, calculating to obtain a fitting coefficient of the nonlinear model according to the basic coefficient;
and S5, fitting the arctangent value based on a nonlinear model.
Specific:
in step S1, the angle lookup table in the nonlinear model is specifically: will beTangent value [0,1 ]]Aliquoting into two sections and constructing cornersDegree lookup table lut= [0,0.4636, 07854]；
In step S2, the calculating the nonlinear model parameter specifically includes the following steps:
s2.1, calculating
S2.2, calculate index ind=round (2*x);
s2.3, calculating t= (2*x-ind)/(2+ind x);
wherein x and t are intermediate variables, Q represents an imaginary part, and I represents a real part.
In step S3, the calculating the base coefficient specifically includes:
s3.1, calculating a basic coefficient a, wherein the formula is as follows:
a＝2*tan(0.245/2)；
s3.2, calculating a basic coefficient b, wherein the formula is as follows:
b＝2*tan(0.245/2) 3 /3；
in step S4, the calculating the fitting coefficient of the nonlinear model according to the basic coefficient specifically includes:
s4.1, calculating a fitting coefficient A, wherein the formula is as follows:
A＝4*a+12*b；
s4.2, calculating a fitting coefficient B, wherein the formula is as follows:
B＝256*b。
in step S5, the fitting of the arctangent value based on the nonlinear model specifically includes: nonlinear model pair-basedThe arctangent values within are fitted and the following formula is used:
arctan＝LUT(ind)+A*t-B*t 3
it should be noted that, the high-precision arctangent fitting method provided in this embodiment is similar to that in the embodiment, and will not be described in detail herein.
Embodiment III:
the present embodiment provides a high-precision arctangent ultrasound imaging device implemented based on a high-precision arctangent fitting system of the first embodiment.
The embodiment is described with specific application of the above arc tangent fitting method in elastography:
the method comprises the following steps:
1. signal acquisition
Performing quadrature demodulation on the ultrasonic echo to obtain an input signal x of elastography:
x＝I+j·Q
in the formula, I is an in-phase component; q is the quadrature component.
2. Cross-correlation computation
The cross-correlation corrx is obtained by calculating the input signals x of two adjacent moments at the same position, and the formula is as follows:
corrx (τ) is the cross-correlation based on the delay τ, and the subscript of x indicates the acquisition instant of the input signal, i.e., x n-1 For the input signal at the previous moment, x n Is the input signal at the current moment; m is the total number of points of the input signal x. Superscript denotes complex conjugate.
3. Angle calculation
The maximum cross-correlation value corrxmax can be calculated according to the cross-correlation values of all delays, and the angle can be further calculated based on corrxmax, and the formula is as follows:
corrx max＝I'+j·Q'
angle＝arctan(Q'/I')
i 'and Q' are the in-phase and quadrature components of corrxmax, respectively, and arctan represents an arctan operation.
4. Strain calculation
Strain is calculated based on angle as follows:
strain＝f(angle)
f is a mapping transformation function of angle, which may be a linear or a non-linear mapping function.
The above examples are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the protection scope of the present invention without departing from the design spirit of the present invention.

Claims (2)

1. A high precision arctangent fit system, comprising:
the lookup table construction module is used for constructing an angle lookup table in the nonlinear model;
the parameter calculation module is used for calculating nonlinear model parameters;
the basic coefficient calculation module is used for calculating basic coefficients;
the fitting coefficient calculation module is used for calculating fitting coefficients of the nonlinear model according to the basic coefficients;
the fitting module is used for fitting the arctangent value based on the nonlinear model;
the construction angle lookup table in the lookup table construction module specifically comprises: will beTangent value [0,1 ]]Equally dividing into two sections and constructing an angle lookup table LUT= [0,0.4636,0.7854 ]]；
The parameters of the nonlinear model calculated in the parameter calculation module are specifically as follows: calculation ofIndex ind=round (2*x), t= (2*x-ind)/(2+ind x), where round represents rounding, x, t are intermediate variables, Q represents the imaginary part, I represents the real part;
the basic coefficient calculation module calculates basic coefficients specifically as follows:
the basic coefficient a is calculated as follows:
a＝2*tan(0.245/2)；
the base coefficient b is calculated as follows:
b＝2*tan(0.245/2) 3 /3；
the fitting coefficient of the nonlinear model obtained by calculation according to the basic coefficient in the fitting coefficient calculation module is specifically:
the fitting coefficient A is calculated as follows:
A＝4*a+12*b；
the fitting coefficient B is calculated as follows:
B＝256*b；
the fitting of the arctangent value based on the nonlinear model in the fitting module is specifically as follows: nonlinear model pair-basedThe arctangent values within are fitted and the following formula is used:
arctan＝LUT(ind)+A*t-B*t 3 。
2. a high-precision arctangent ultrasound imaging device, comprising a high-precision arctangent fitting system as defined in claim 1.
CN202110095896.6A 2021-01-25 2021-01-25 High-precision arctangent fitting system and ultrasonic imaging device Active CN112882041B (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5910117A (en) * 1997-02-20 1999-06-08 Basoglu; Christopher H. Real time color doppler ultrasound imaging
CN101972153A (en) * 2010-11-10 2011-02-16 中国医学科学院生物医学工程研究所 Color ultrasonic Doppler blood flow speed estimation arc tangent optimization algorithm
CN102404263A (en) * 2010-09-19 2012-04-04 中兴通讯股份有限公司 Method and device for processing digital pre-distortion
CN105659941B (en) * 2009-05-31 2012-04-04 北京理工大学 A kind of be applied to AFH/MSK communication system Real-time Channel method of estimation

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5910117A (en) * 1997-02-20 1999-06-08 Basoglu; Christopher H. Real time color doppler ultrasound imaging
CN105659941B (en) * 2009-05-31 2012-04-04 北京理工大学 A kind of be applied to AFH/MSK communication system Real-time Channel method of estimation
CN102404263A (en) * 2010-09-19 2012-04-04 中兴通讯股份有限公司 Method and device for processing digital pre-distortion
CN101972153A (en) * 2010-11-10 2011-02-16 中国医学科学院生物医学工程研究所 Color ultrasonic Doppler blood flow speed estimation arc tangent optimization algorithm

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