CN103714560A - Image reconstruction method and system based on Katsevich algorithm - Google Patents
Image reconstruction method and system based on Katsevich algorithm Download PDFInfo
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Abstract
The invention provides an image reconstruction method based on the Katsevich algorithm. By optimizing errors of all operation modules in the Katsevich reconstruction algorithm, influence of error artifacts on a reconstructed image can be effectively reduced and true information of an original CT image can be kept. As is shown in repeated simulation practice, the method is easy to implement and can effectively reduce error artifacts in the CT image; influence of metal artifacts on the reconstructed image obtained through the method can be reduced, and detail information of regions which a user is interested in can be kept as well.
Description
Technical field
The invention belongs to the image processing field of medical image, be specifically related to a kind of method and system based on Katsevich algorithm image reconstruction.
Background technology
In the reconstruction image of exact reconstruction algorithm katsevich, there will be various difform artifacts, these artifacts have affected the accuracy of algorithm imaging.Because the data for projection in process of reconstruction carries out the artifact that discretize produces, be wherein the most important a kind of source of artifact.Directly causing changing the reason that artifact produces is mainly that Katsevich algorithm itself is a kind of exact reconstruction algorithm, but in actual application or scarce data for projection be discrete, follow-up operation is all that discrete data has been carried out to corresponding approximate operation, thereby has caused containing in final imaging a large amount of artifacts.In order to obtain high-quality CT, rebuild image, need to reduce the error artifact that the discrete operations of data for projection is brought as far as possible, conventionally the method that the method pre-service adopting is optimized, cardinal principle is to be optimized adopting different differentiate algorithms to carry out differentiate module to data for projection in image reconstruction process, thereby reaches the effect that reduces artifact.
From exact reconstruction algorithm Katsevich, rebuild the mechanism that image artifacts produces, multiple CT artifact pre-service removing method is suggested in succession.Pretreated method mainly comprises and adopts the higher Method of Seeking Derivative of a kind of precision to carry out differentiate etc.Adopt single method to carry out differentiate, easily cause the result of differentiate to lose, thereby can produce new error, effect improved obvious not to the reconstruction of image like this.
Summary of the invention
In order to solve the deficiencies in the prior art, the invention provides a kind of simple to operate, reconstructed image quality is high and rebuild fireballing image rebuilding method and system based on Katsevich algorithm.
The present invention is achieved through the following technical solutions:
An image rebuilding method based on Katsevich algorithm, comprises the following steps:
(1) obtain and rebuild the needed data for projection of image;
(2) described data for projection is carried out to the mixing differentiate based on three point method and Richardson extrapolation, be specially: the differentiate of at least two data for projection that start most and last of each row, column of data for projection, frame is adopted to three point method differentiate; Data for projection for other adopts Richardson extrapolation to carry out differentiate, in concrete operations, this module is carried out to fixed point processing in addition;
(3) data for projection of described step (2) being processed carries out length weighted correction;
(4) data for projection of described step (3) being processed carries out the interpolation operation before filtering; data for projection is carried out to coordinate system transformation; in this step; the nearest neighbour interpolation that data for projection is adopted and the married operation of cubic convolution interpolation carry out fixed point processing to this module in addition in concrete operations;
(5) data for projection of described step (4) being processed carries out Hilbert transform, then adds the operation of respective window function;
(6) data for projection of described step (5) being processed carries out interpolation, and data for projection is carried out to coordinate system transformation again, recovers the coordinate system of data for projection, in concrete operations, this module is carried out to fixed point processing in addition;
(7) data for projection of described step (6) being processed carries out back projection and produces reconstruction image, when data for projection is added up in this step, adopt and mix the method that difference is chosen data for projection, in concrete operations, this module is carried out to fixed point processing in addition.
Further, when the data for projection obtaining contains noise, described step (1) also comprises carries out filtering processing to resulting data for projection, to reduce noise impact on artifact in reconstruction image in subsequent operation.
Further, when described step (2) is carried out differentiate to data for projection, the method adopting is the method for mixing differentiate, that is: difference coefficient, three point method or the five-spot differentiate for data acquisition of edge, for center difference coefficient, Richardson extrapolation or fitting process differentiate for middle data acquisition.
Further, described step (5) adopts Fast Fourier Transform (FFT) FFT to complete Hilbert transform.Only need to carry out a FFT computing, and the interim storage of operation result is used for to subsequent calculations.
Further, to adopt interpolation method be the hybrid interpolation method of nearest neighbour interpolation and cubic convolution interpolation to described step (6).
Further, the mixing difference in described step (7) is chosen the method for data for projection, is specially: when coordinate (u*, w*) is positioned at the outermost of detecting plate, adopt the most contiguous difference to choose the data for projection that participates in integration; In the time of on coordinate (u*, w*) is arranged on detecting plate except the rib of upper step and the intersection point of rib, employing be that bilinear interpolation method is chosen data for projection; When coordinate (u*, w*) is arranged on detecting plate except on the rib of above-mentioned two steps time, employing be that the method for neighbor interpolation is chosen data for projection; When coordinate (u*, w*) is positioned on detecting plate the region except above-mentioned three steps, adopt the method for neighbor interpolation to choose data for projection.
Further, while obtaining back projection in described step (7), during required integrating range [sb, st], need to, to completing solving of nonlinear equation, while solving, adopt interative computation or Newton iteration method or the Secant Method based on dichotomy.
Further, the method of carrying out fixed point processing in described step (2), (4), (6), (7), be specially: adopt cordic algorithm to solve transcendental function linearization in specific implementation, for cordic algorithm, realize and in pipeline organization, adopt 14 grades of flowing water progression, can meet the accuracy requirement of medical image, in addition, in fixed point, the algorithm that surface analysis has designed based on affine form is realized; Precision analysis has designed the realization that combines of algorithm based on quantization error propagation model and simulation self-adaptation annealing algorithm; Meanwhile, according to different constraint condition, obtaining respectively error range is 2-4,2-8, the result of tri-groups of precision analysis of 2-13.
Another aspect of the present invention; a kind of system of carrying out the image rebuilding method based on Katsevich algorithm of the present invention is provided, has it is characterized in that: this system has comprised the X ray bulb of CT machine, image reconstruction workstation, high-definition image display device, CT machine, the detecting plate in CT machine; Its working method is: the X-ray tube in CT machine and the relative position of detecting plate are constant, they irradiate rebuilding object along 360 ° of rotations of scanning gantry, the data for projection obtaining is transferred in image reconstruction workstation one by one by PCI-E bus, in image reconstruction workstation, utilize the image rebuilding method based on Katsevich algorithm of the present invention to carry out accurate Fast Reconstruction, the reconstruction image obtaining shows by high-definition image display device.
The invention has the beneficial effects as follows: the present invention is by being optimized the error of modules in Katsevich reconstruction algorithm, can effectively reduce error artifact to rebuilding the impact of image, correlation module has been carried out to fixed point simultaneously and processed the speed of having accelerated reconstruction, and can keep the information of original true CT image.Through simulation practice repeatedly, prove, method of the present invention is simple to operate, can effectively reduce the error artifact in CT image, the reconstruction image obtaining by method of the present invention not only can reduce the impact of metal artifacts on image, and can keep the detailed information of area-of-interest.
Accompanying drawing explanation
Fig. 1 is the image rebuilding method process flow diagram based on Katsevich algorithm of the present invention;
Fig. 2 is the method flow diagram that fixed point is processed;
Fig. 3 is the detailed annotation figure that mixes differentiate operation;
Fig. 4 is the interpolation schematic diagram of individual frames data for projection;
The middle hybrid interpolation schematic diagram of Tu5Shi back projection operation;
Fig. 6 carries out the system of the inventive method in Y-direction cross sectional representation;
Fig. 7 (a) is the Shepp-Logan body mould of standard, is used as the ideal body mould of CT image reconstruction;
Fig. 7 (b) is the image of inventing the Katsevich method for reconstructing reconstruction of optimizing;
Fig. 7 (c) carries out the image that the rear Katsevich method for reconstructing based on the present invention's optimization is rebuild;
In figure, each implication indicating is: the X ray bulb of 1-CT machine, 2-image reconstruction workstation, 3-high-definition image display device, 4-CT machine, the detecting plate in 5-CT machine.
Embodiment
Below in conjunction with accompanying drawing explanation and embodiment, the present invention is further described.
The image rebuilding method based on Katsevich algorithm as shown in Figure 1, in turn includes the following steps:
(1) obtain CT machine systematic parameter and rebuild the needed data for projection of image.When the data for projection obtaining contains noise, need to carry out filtering processing to resulting data for projection, to reduce noise impact on artifact in reconstruction image in subsequent operation.
(2) data for projection step (1) being obtained carries out the mixing differentiate based on three point method and Richardson extrapolation, concrete embodiment as shown in Figure 3, adopts three point method differentiate to the differentiate of later last at least two data for projection (marginal date) that start most of each row, column of data for projection, frame; Data for projection for other adopts Richardson extrapolation to carry out differentiate.The main object that adopts three point method is the derivative that obtains marginal date that it can degree of precision, thereby avoids occurring the not obtainable situation of data for projection derivative; And the object that adopts Richardson extrapolation to carry out differentiate is to utilize advantage that Richardson extrapolation changes along with the variation differentiate precision of extrapolation number of times can requirement as the case may be to adopt Richard's Senn process of different extrapolation situations, meet to greatest extent the accuracy requirement of differentiate.Operation by above just can obtain the data for projection after the differentiate equal with original projection data volume, improve to greatest extent on the one hand the differentiate precision of data, eliminated on the other hand the loss of data after differentiate in order to improve the reconstruction efficiency of reconstruction algorithm, the optimisation strategy of this module having been carried out to fixed point streamline is optimized this module.
(3) data for projection of step (2) being processed carries out length weighted correction;
(4) data for projection of step (3) being processed carries out the interpolation operation before filtering, data for projection is carried out to coordinate system transformation, in this step, the nearest neighbour interpolation that data for projection is adopted and the married operation of cubic convolution interpolation, as shown in Figure 4, what be that edge data acquisition uses is nearest neighbour interpolation, and what for non-marginal date, adopt is cubic convolution interpolation.Because the precision of nearest neighbour interpolation is too low, make to rebuild image effect very poor, but can producing the effect of low-pass filter, simple to operate, bilinear interpolation makes to rebuild image ratio fuzzyyer, and cubic convolution interpolation can both improve precision and also can avoid the fuzzy of image simultaneously, therefore improved the computational accuracy of interpolating module, cubic convolution interpolation makes computing quantitative change large simultaneously.In order to improve the reconstruction efficiency of reconstruction algorithm, the optimisation strategy of this module having been carried out to fixed point streamline is optimized this module, can so that this module carry out hardware while realizing the area of whole hardware circuit less, speed is faster, power consumption is lower.
(5) data of step (4) being processed are carried out Hilbert transform, conventionally data for projection completes Hilbert transform by convolution operation, in the present invention, the Fast Fourier Transform (FFT) (FFT) adopting completes Hilbert transform, completed after Hilbert transform, the data for projection of processing has been added to the operation of respective window function.
(6) data for projection of step (5) being processed carries out interpolation, and data for projection is carried out to coordinate system transformation again, recovers the coordinate system of data for projection, the married operation that remains nearest neighbour interpolation and cubic convolution interpolation adopting in this step.Use the streamline of fixed point to be optimized module simultaneously.
(7) data for projection step (6) being produced carries out back projection and produces reconstruction image, when data for projection is added up in this step, what the present invention adopted is a kind of method that difference is chosen data for projection of mixing, as shown in Figure 5: as coordinate (u*, while w*) being positioned at the outermost of detecting plate, the present invention adopts the most contiguous difference to choose the data for projection that participates in integration; In the time of on coordinate (u*, w*) is arranged on detecting plate except the rib of upper step and the intersection point of rib, employing be that bilinear interpolation method is chosen data for projection; When coordinate (u*, w*) is arranged on detecting plate except on the rib of above-mentioned two steps time, employing be that the method for neighbor interpolation is chosen data for projection; When coordinate (u*, w*) is positioned on detecting plate the region except above-mentioned three steps, adopts the method for neighbor interpolation to choose data for projection, thereby make when choosing data for projection reconstruction point is upgraded precision higher.Speed in order to accelerate to rebuild in addition, the present invention has carried out the optimization of fixed point streamline to this module, thus it is higher to make to rebuild efficiency, and power consumption is lower.
When the data for projection that step (2) is obtained step (1) carries out differentiate, adopt the method for mixing differentiate: the data of edge can adopt difference coefficient, three point method or five-spot etc., for middle data, can adopt the Method of Seeking Derivative that precision is higher, the method of center difference coefficient, Richardson extrapolation or fitting derivative for example, thereby make being consistent before data volume after differentiate and differentiate, avoid data loss and so error.
When step (5) is carried out FFT computing to the data in step (4), owing to need to repeatedly using the FFT operation result of Hilbert core, in process of reconstruction, in order to accelerate computing, only need to carry out once-through operation to it, and the interim storage of its operation result is used for to subsequent calculations.
The method that fixed point is processed as shown in Figure 2, be specially: adopt cordic algorithm to solve transcendental function linearization in specific implementation, for cordic algorithm, realize and in pipeline organization, adopt 14 grades of flowing water progression, can meet the accuracy requirement of medical image, in addition, in fixed point, the algorithm that surface analysis has designed based on affine form is realized; Precision analysis has designed the realization that combines of algorithm based on quantization error propagation model and simulation self-adaptation annealing algorithm; Meanwhile, according to different constraint condition, obtaining respectively error range is 2-4,2-8, the result of tri-groups of precision analysis of 2-13
As shown in Figure 6, be the system of carrying out the image rebuilding method based on Katsevich algorithm of the present invention, this system comprises the X ray bulb of CT machine, image reconstruction workstation, high-definition image display device, CT machine, the detecting plate in CT machine; Its working method is: the X-ray tube in CT machine and the relative position of detecting plate are constant, they irradiate rebuilding object along 360 ° of rotations of scanning gantry, the data for projection obtaining is transferred in image reconstruction workstation one by one by PCI-E bus, in image reconstruction workstation, utilize the image rebuilding method based on Katsevich algorithm of the present invention to carry out accurate Fast Reconstruction, the reconstruction image obtaining shows by high-definition image display device.
As shown in Figure 7, Fig. 7-a is the Shepp-Logan body mould of standard, be used as the ideal body mould of CT image reconstruction, Fig. 7-b is the image of inventing the Katsevich method for reconstructing reconstruction of optimizing, Fig. 7-c carries out the image that the rear Katsevich method for reconstructing based on the present invention's optimization is rebuild, right by the mean square deviation of image and histogram are carried out, the image mean-squared deviation after optimization has had significantly and has declined, and histogrammic high frequency noise is also significantly improved simultaneously.
Above content is in conjunction with concrete preferred implementation further description made for the present invention, can not assert that specific embodiment of the invention is confined to these explanations.For general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.
Claims (10)
1. the image rebuilding method based on Katsevich algorithm, is characterized in that, said method comprising the steps of:
(1) obtain and rebuild the needed data for projection of image;
(2) described data for projection is carried out to the mixing differentiate based on three point method and Richardson extrapolation, be specially: the differentiate of at least two data for projection that start most and last of each row, column of data for projection, frame is adopted to three point method differentiate; Data for projection for other adopts Richardson extrapolation to carry out differentiate, in concrete operations, to this step, adopts fixed point to process;
(3) data for projection of described step (2) being processed carries out length weighted correction;
(4) data for projection of described step (3) being processed carries out the interpolation operation before filtering; data for projection is carried out to coordinate system transformation; in this step, the nearest neighbour interpolation that data for projection is adopted and the married operation of cubic convolution interpolation adopt fixed point processing to this step in concrete operations;
(5) data for projection of described step (4) being processed carries out Hilbert transform, then adds the operation of respective window function;
(6) data for projection of described step (5) being processed carries out interpolation, and data for projection is carried out to coordinate system transformation again, recovers the coordinate system of data for projection, in concrete operations, to this step, adopts fixed point to process;
(7) data for projection of described step (6) being processed carries out back projection and produces reconstruction image, when data for projection is added up in this step, adopts and mixes the method that difference is chosen data for projection, in concrete operations, to this step, adopts fixed point to process.
2. method according to claim 1, it is characterized in that: when the data for projection obtaining contains noise, described step (1) also comprises carries out filtering processing to resulting data for projection, to reduce noise impact on artifact in reconstruction image in subsequent operation.
3. method according to claim 1, it is characterized in that: when described step (2) is carried out differentiate to data for projection, the method adopting is the method for mixing differentiate, that is: difference coefficient, three point method or the five-spot differentiate for data acquisition of edge, for center difference coefficient, Richardson extrapolation or fitting process differentiate for middle data acquisition.
4. method according to claim 1, is characterized in that: described step (5) adopts Fast Fourier Transform (FFT) FFT to complete Hilbert transform.
5. method according to claim 4, is characterized in that: only need to carry out a FFT computing, and the interim storage of operation result is used for to subsequent calculations.
6. method according to claim 1, is characterized in that: it is the hybrid interpolation method of nearest neighbour interpolation and cubic convolution interpolation that described step (6) adopts interpolation method.
7. method according to claim 1, it is characterized in that: the mixing difference in described step (7) is chosen the method for data for projection, be specially: when coordinate (u*, w*) is positioned at the outermost of detecting plate, adopt the most contiguous difference to choose the data for projection that participates in integration; In the time of on coordinate (u*, w*) is arranged on detecting plate except the rib of upper step and the intersection point of rib, employing be that bilinear interpolation method is chosen data for projection; When coordinate (u*, w*) is arranged on detecting plate except on the rib of above-mentioned two steps time, employing be that the method for neighbor interpolation is chosen data for projection; When coordinate (u*, w*) is positioned on detecting plate the region except above-mentioned three steps, adopt the method for neighbor interpolation to choose data for projection.
8. method according to claim 1, it is characterized in that: required integrating range [sb while obtaining back projection in described step (7), st] time, need to, to completing solving of nonlinear equation, while solving, adopt interative computation or Newton iteration method or the Secant Method based on dichotomy.
9. method according to claim 1, it is characterized in that: the method for carrying out fixed point processing in described step (2), (4), (6), (7), be specially: adopt cordic algorithm to solve transcendental function linearization in specific implementation, for cordic algorithm, realize and in pipeline organization, adopt 14 grades of flowing water progression, can meet the accuracy requirement of medical image, in addition, in fixed point, the algorithm that surface analysis has designed based on affine form is realized; Precision analysis has designed the realization that combines of algorithm based on quantization error propagation model and simulation self-adaptation annealing algorithm; Meanwhile, according to different constraint condition, obtaining respectively error range is 2-4,2-8, the result of tri-groups of precision analysis of 2-13.
10. a system for the image rebuilding method based on Katsevich algorithm of execution as described in claim 1-8, is characterized in that: this system comprises the X ray bulb of CT machine, image reconstruction workstation, high-definition image display device, CT machine, the detecting plate in CT machine; Its working method is: the X-ray tube in CT machine and the relative position of detecting plate are constant, they irradiate rebuilding object along 360 ° of rotations of scanning gantry, the data for projection obtaining is transferred in image reconstruction workstation one by one by PCI-E bus, in image reconstruction workstation, utilize the image rebuilding method based on Katsevich algorithm as described in claim 1-8 to carry out accurate Fast Reconstruction, the reconstruction image obtaining shows by high-definition image display device.
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