CN111789623A - Full-band compressed sensing method of PET (positron emission tomography) signal - Google Patents
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Abstract
The invention provides a full-band compressed sensing method of PET signals, which comprises the steps of acquiring a complete PET signal database output by a radiation source with different energy by using a detector; carrying out full-band quantization on the complete PET signal database obtained in the step 1 to obtain the standard energy of the PET signal; carrying out full-band compression quantization on the complete PET signal database obtained in the step 1, and estimating the energy of the PET signal on the basis of the prior information of the PET signal; determining the corresponding relation between the standard energy and the estimated energy in the step 3 by taking the standard energy in the step 2 as a standard; and correcting the estimated energy of the step 3 by using the corresponding relation obtained in the step 4. The method uses the standard energy of the PET signal as the correction standard of the estimated energy after the full-band compression and quantization of the PET signal, avoids the error caused by inaccurate model and feature description of the PET signal, and effectively improves the accuracy of the energy estimation of the PET signal.
Description
Technical Field
The invention relates to the field of ionizing radiation detection and medical imaging, in particular to a full-band compressed sensing method of a PET signal.
Background
One of the basic information obtained by detectors in the field of detection of ionizing radiation is the energy of the PET signal, which is mainly used for: distinguishing the types of rays used in the field of ionizing radiation detection; judging whether rays and substances used in the field of medical imaging are scattered or not; the position of the deposition of the radiation in the optoelectronic position sensitive device is determined. In the field of ionizing radiation detection, the amplitude of the PET signal output by the same detector generally increases with the energy deposited by the rays in the detector, and the rise time and the fall time are always consistent. The ray energies used in the field of ionizing radiation are usually represented by the result of amplitude integration of the PET signal on the time axis.
The traditional method for acquiring the energy of the PET signal has two types: firstly, an integrating circuit is used for collecting charges carried by a PET signal, then a high-speed Analog-to-Digital Converter (ADC) is used for sampling the collected maximum charge amount, and the sampling result represents the energy of the PET signal; secondly, the PET signals are integrated into PET signals with a relatively low speed, then the integrated result is sampled by a low-speed ADC, and then the sampling result is subjected to numerical integration, and the numerical integration result represents the energy of the PET signals. Because the traditional method has a limiting effect on the counting rate in the process of numerical integration, and the shaping circuit is also easily interfered by external factors (temperature, pressure and the like) to influence the performance, and meanwhile, the parameters of the shaping circuit also need to be adjusted along with different application requirements, the correction and maintenance of the whole system are very difficult. Although the problem can be solved by using the high-speed ADC, the problem is solved while the cost and power consumption are increased, and in addition, the high-speed ADC has higher requirements on the processing speed and transmission bandwidth of subsequent data, which greatly increases the design difficulty of subsequent circuits.
In order to solve the problem of limitation of high counting rate in the process of acquiring the PET signal energy, scholars propose an energy acquisition method based on prior information for PET signal full-band compressed sensing. The full band is a region where all data of the PET signal is covered by the processing object when the PET signal is processed. The method needs to use prior information of the PET signal, such as a physical model, characteristics and the like of the PET signal, and since the PET signal output by the detector has sparsity (compressibility), all data of the PET signal can be compressed at a frequency far lower than the Nyquist sampling rate to obtain a small amount of compressed data, and then fitting and maximum likelihood solving of the PET signal are realized by using a statistical method to obtain the energy of the PET signal.
In the prior information-based PET signal full-band compressed sensing energy acquisition system, the accuracy of signal models and feature descriptions can affect the accuracy of PET signal information. In practical research work, the model and characterization of the PET signal is not only related to the detector, but also to the parameters in its generation circuit. Therefore, it is very difficult to realize accurate signal model and feature description. When the ideal model and characteristics of the PET signal are different from those in the actual study, the final estimated energy will be biased.
Therefore, it is necessary to provide a full-band compressive sensing method for PET signals to overcome the above-mentioned problem of deviation of estimated energy due to inaccurate model and feature description of PET signals.
Disclosure of Invention
In view of the above, the present invention provides a full-band compressive sensing method for PET signals, so as to improve the accuracy of energy estimation of PET signals.
In order to achieve the above object, the present invention provides a full-band compressed sensing method for PET signals, which includes the following steps:
step S1: acquiring a complete PET signal database output by the radiation source with different energies by using a detector;
step S2: carrying out full-band quantization on the complete PET signal database obtained in the step S1 to obtain standard energy of the PET signal;
step S3: carrying out full-band compression quantization on the complete PET signal database obtained in the step S1, and estimating the energy of the PET signal on the basis of the prior information of the PET signal;
step S4: determining the corresponding relation between the standard energy and the estimated energy of S3 by taking the standard energy of S2 as a standard;
step S5: the estimated energy of S3 is corrected by the correspondence obtained at S4.
Further, in step S1, the database may be collected by simulation or direct test or a combination of simulation and direct test.
Further, in step S1, the specific process of collecting the database by using the simulation mode is as follows:
(1) repeatedly irradiating the detector by using the same radiation source, and acquiring data output by the detector by using the ADC;
(2) and averaging the data set, amplifying the data set to different degrees, and simulating a database with certain energy by using an amplification result.
Further, the method for averaging the data set includes: summing data output by the detector every time and considering the data as energy of the test, making an energy spectrum of a PET signal after the test process is repeated for multiple times, selecting a first valley point before and after the peak value of the energy spectrum as an upper boundary and a lower boundary, screening data with energy positioned in the upper and lower boundary intervals, assuming that n groups of data are screened out together, and defining Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, and m is the total number of the sampling points of each group of data, so that the result P after averaging the data setzCan be expressed as:
further, the mode of amplifying the data set after averaging is model amplification.
Further, the model amplification process is as follows: determining an energy response model y ═ f (x) of the detector, and averaging the data PzIs regarded as EzIn practical application, the user can set the upper limit of the energy of the radiation source to be measured to be EaTherefore, the PET signal needs to be amplified by a factor of
Under the condition of (3), amplifying to different degrees, and if the total number of the amplified PET signals is known to be K, corresponding to the amplification result PdCan be composed of
And (4) calculating.
Further, in step S1, the specific process of collecting the database by using the direct test method is as follows: the detector is first illuminated with a source of different energy and then data with a certain energy is directly acquired with the ADC.
Further, in step S1, a database is collected by using a combination of simulation and direct test, and the specific process is as follows:
(1) repeatedly irradiating the detector by using radiation sources with different energies, and respectively acquiring data output by the detector by using an ADC (analog to digital converter) according to the energy and the repetition times of the radiation sources;
(2) averaging the data sets of the same source;
(3) and simulating a database with certain energy by utilizing an interpolation method for the average result.
Further, the method for averaging the data set includes: summing data output by the detector every time and considering the data as energy of the test, making an energy spectrum of a PET signal after the test process is repeated for multiple times, selecting a first valley point before and after the peak value of the energy spectrum as an upper boundary and a lower boundary, screening data with energy positioned in the upper and lower boundary intervals, assuming that n groups of data are screened out together, and defining Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, and m is the total number of the sampling points of each group of data, so that the result P after averaging the data setzCan be expressed as:
further, in step S2, the standard energy of the PET signal can be obtained by directly digitizing the complete data set or by full band compression of the data containing the energy information of the PET signal.
Further, in step S2, the specific process of directly digitizing the complete data set to obtain the standard energy of the PET signal is:
(1) performing full-band quantization on the PET signal by using an ADC;
(2) the result of numerical integration or peak of the quantized data is taken to represent the standard energy of the PET signal.
Further, in step S2, the specific process of directly digitizing the complete data set to obtain the standard energy of the PET signal may also be:
(1) passing the PET signal through a maximum hold circuit;
(2) the data output by the maximum hold circuit is full band quantized to obtain a maximum value representing the standard energy of the PET signal.
Further, in step S2, the method of acquiring the standard energy of the PET signal by performing full band compression on the data containing the energy information of the PET signal is also called a linear discharge method.
Further, in step S3, the method for estimating the PET signal energy is SQL or ADC compression fitting.
Further, in step S3, the specific process of estimating the PET signal energy using the SQL method is as follows:
(1) setting a plurality of excessive voltages with the magnitude within the amplitude range of the PET signal, inputting the excessive voltages into a comparator together with the original PET signal in sequence, enabling the comparator to output a jump signal when the original PET signal is intersected with a constant line with the magnitude equal to the excessive voltage, and recording the corresponding time when the jump occurs;
(2) fitting a PET signal by using all the excessive voltages and the corresponding jump time thereof and a model of the PET signal;
(3) and obtaining the estimated energy of the PET signal by adopting a method of constant integration or numerical integration after secondary full-band compression on the fitting result.
Further, in step S3, the specific process of estimating the signal energy by using the ADC compression fitting method is as follows:
(1) performing full-band compression on the PET signal by using an ADC (analog to digital converter) to obtain a group of compressed data;
(2) fitting a PET signal by using the compressed data and a model of the PET signal;
(3) and obtaining the estimated energy of the PET signal by adopting a method of constant integration or numerical integration after secondary full-band compression on the fitting result.
Further, in step S4, the correspondence between the standard energy and the estimated energy is referred to as an energy mapping function g ═ i (x).
Further, the derivation process of the energy mapping function is as follows: will PET signalThe standard energy after full-band quantization is regarded as E1，iThe estimated energy after full band compression quantization is regarded as E2，i，Wherein i represents the ordinal number of the PET signal, and for the standard energy of each uncompressed PET signal, the mapping relation between the standard energy and the compressed estimated energy can be obtained through calculation:
each x isiThe function obtained by curve fitting is the energy mapping function g ═ i (x).
Further, in step S5, the corrected estimated energy E2，iAnd the standard energy E before correction1，iSatisfies the following conditions: e2，i＝I(E1，i)。
Compared with the prior art, the invention has the beneficial effects that:
because the PET signal model and the characteristic description are independent of the standard energy of the PET signal, the standard energy of the PET signal is used as the correction standard of the estimated energy after the full-band compression quantization of the PET signal, and the error caused by the inaccuracy of the signal model and the characteristic description in the PET signal energy estimation process can be avoided.
Drawings
FIG. 1 is a flow chart of a full band compressed sensing method of PET signals of the present invention;
FIG. 2 is a diagram of the energy spectrum after full-band quantization of the complete PET signal, and the result of Gaussian fitting of the photoelectric peak of the energy spectrum;
FIG. 3 is the averaged data after full-band quantification of the complete PET signal;
FIG. 4 is an energy curve of a PET signal calculated using the SQL method;
fig. 5 is a comparison chart before and after correction of the energy spectrum according to the present invention.
Detailed Description
The present invention will be further described with reference to the following specific examples.
It should be understood that the following examples are illustrative only and are not intended to limit the scope of the present invention.
As shown in FIG. 1, the full-band compressed sensing method for PET signals disclosed by the invention comprises the following steps:
s1: acquiring a complete PET signal database output by the radiation source with different energies by using a detector;
s2: carrying out full-band quantization on the complete PET signal database obtained in the step S1 to obtain standard energy of the PET signal;
s3: carrying out full-band compression quantization on the complete PET signal database obtained in the step S1, and estimating the energy of the PET signal on the basis of the prior information of the PET signal;
s4: determining the corresponding relation between the standard energy and the estimated energy of S3 by taking the standard energy of S2 as a standard;
s5: the estimated energy of S3 is corrected by the correspondence obtained at S4.
The invention will now be further illustrated with reference to specific examples:
example 1:
using F18GDG as radiation source and using scintillation crystal as LYSO crystal detector, the prior information-based PET signal full-band compressed sensing energy acquisition method is SQL.
(1) Using F18The GDG radiation source irradiates the detector, then the signal output by the detector is directly input into the oscilloscope by a direct test method, and the oscilloscope is made to acquire 10000 signals at a sampling rate of 50Gsps, the energy spectrum of the full-band quantized PET signal is counted and normalized to 511keV, and the result is shown by the star in fig. 2. The photoelectric peaks of the energy spectrum are then fitted using gaussian curves, the fitting result being shown as the solid line in fig. 2. All PET signals with energy between the first valley point before and after the energy spectrum are taken out, and n groups of data are selected on the assumption that a total of energy is selected to define Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, m is the total number of the sampling points of each group of data, and the data are sampled according to the formula
Obtain the average pulse PzThe results are shown in FIG. 3.
(2) For the average pulse PzUsing linear energy responseThe model y, x, f, (x) is amplified to different degrees, assuming the average data P obtained in step 1zEnergy E ofz511Kev, the upper energy limit E of the radiation source to be measuredaIs 2Mev, then the mean data PzThe maximum amplification factor V of 3.92 can be obtained
Calculating the corresponding amplification result PdWherein the total number of amplified PET signals K is 5000.
(3) Determining the magnitude of the over-value voltage in the SQL method according to the average data obtained in the step (1), and then amplifying the result P in the step (2)dThe energy of the PET signal was calculated using the SQL method. Fig. 4 shows the energy results calculated in this example.
The specific implementation process for acquiring the PET signal energy by using the SQL method is as follows:
setting 129 over-value voltages in advance, and averaging the over-value voltageszGradually increasing from 0.1 times to 0.8 times of the maximum value, and then combining the set over-voltage with PdSequentially input into a comparator, and assuming that the crossing point of the over-voltage and the rising edge of the PET signal is TlIndicating that the crossing point of the over-voltage and the falling edge of the PET signal is TfIs shown to be
The final 258 compressed data obtained by the SQL method are
And fitting and reconstructing an original PET signal by using 258 compressed data obtained in the previous step. Firstly, a proper PET signal model is selected, in this example, a linear-exponential model of the PET signal is selected for fitting, namely, the fitting equation of the rising edge is yl＝kxl+ b, the fitting equation for the falling edge is
After fitting, two equations are simultaneously established to obtain an intersection point, and then the reconstructed PET signal is subjected toAnd (5) integrating to calculate the energy of the PET signal.
(4) Using PdThe direct accumulation result of the amplitude is mapped with the energy calculated by SQL, the mapping data is fitted to obtain an energy mapping function g ═ i (x), and the energy calculated by SQL is corrected by using the energy mapping function, fig. 5 is an energy spectrum correction result of this embodiment, in which a dotted line represents an energy spectrum before correction, and a solid line represents an energy spectrum after correction.
Example 2
Using F18GDG as radiation source and using scintillation crystal as LYSO crystal detector, the prior information-based PET signal full-band compressed sensing energy acquisition method is SQL.
(1) Using F18The GDG radiation source irradiates the detector, then the signal output by the detector is directly input into the oscilloscope by a direct test method, and the oscilloscope is made to acquire 10000 signals at a sampling rate of 50Gsps, the energy spectrum of the full-band quantized PET signal is counted and normalized to 511keV, and the result is shown by the star in fig. 2. The photoelectric peaks of the energy spectrum are then fitted using gaussian curves, the fitting result being shown as the solid line in fig. 2. All PET signals with energy between the first valley point before and after the energy spectrum are taken out, and n groups of data are selected on the assumption that a total of energy is selected to define Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, m is the total number of the sampling points of each group of data, and the data are sampled according to the formula
Obtain the average pulse PzThe results are shown in FIG. 3.
(2) For the average pulse PzDifferent degrees of amplification were performed using a linear energy response model, y ═ x ═ f (x), assuming the average data P obtained from step 1zEnergy E ofz511Kev, the upper energy limit E of the radiation source to be measuredaIs 2Mev, then the mean data PzThe maximum amplification factor V of 3.92 can be obtained
Calculating the corresponding amplification result PdWherein the total number of amplified PET signals K is 5000.
(3) Determining the magnitude of the over-value voltage in the SQL method according to the average data obtained in the step (1), and then amplifying the result P in the step (2)dThe energy of the PET signal was calculated using the SQL method. Fig. 4 shows the energy results calculated in this example.
The specific implementation process for acquiring the PET signal energy by using the SQL method is as follows:
setting 129 over-value voltages in advance, and averaging the over-value voltageszGradually increasing from 0.1 times to 0.8 times of the maximum value, and then combining the set over-voltage with PdSequentially input into a comparator, and assuming that the crossing point of the over-voltage and the rising edge of the PET signal is TlIndicating that the crossing point of the over-voltage and the falling edge of the PET signal is TfIs shown to be
The final 258 compressed data obtained by the SQL method are
And fitting and reconstructing an original PET signal by using 258 compressed data points obtained in the previous step. Firstly, a proper PET signal model is selected, in this example, a linear-exponential model of the PET signal is selected for fitting, namely, the fitting equation of the rising edge is yl＝kxl+ b, the fitting equation for the falling edge is
And after fitting, simultaneously solving two equations to obtain an intersection point, performing secondary full-band compression on the reconstructed PET signal by adopting a sampling rate of 50Gsps, and summing data obtained after all secondary full-band compression to obtain the energy of the PET signal.
(4) Using PdAnd mapping the direct accumulation result of the amplitude value and the energy calculated by SQL, fitting mapping data to obtain an energy mapping function g ═ I (x), and correcting the energy calculated by SQL by using the energy mapping function.
Example 3
Using F18GDG is used as a radiation source, a scintillation crystal is used as a detector of LYSO crystal, and the PET signal full-band compressed sensing energy acquisition method based on the prior information is an ADC compressed fitting method.
(1) Using F18The GDG radiation source irradiates the detector, then the signal output by the detector is directly input into the oscilloscope by a direct test method, and the oscilloscope is made to acquire 10000 signals at a sampling rate of 50Gsps, the energy spectrum of the full-band quantized PET signal is counted and normalized to 511keV, and the result is shown by the star in fig. 2. The photoelectric peaks of the energy spectrum are then fitted using gaussian curves, the fitting result being shown as the solid line in fig. 2. All PET signals with energy between the first valley point before and after the energy spectrum are taken out, and n groups of data are selected on the assumption that a total of energy is selected to define Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, m is the total number of the sampling points of each group of data, and the data are sampled according to the formula
Obtain the average pulse PzThe results are shown in FIG. 3.
(2) For the average pulse PzDifferent degrees of amplification were performed using a linear energy response model, y ═ x ═ f (x), assuming the average data P obtained from step 1zEnergy E ofz511Kev, the upper energy limit E of the radiation source to be measuredaIs 2Mev, then the mean data PzThe maximum amplification factor V of 3.92 can be obtained
Calculating the corresponding amplification result PdWherein the total number of amplified PET signals K is 5000.
According to the average data obtained in the step (1), the amplification result P in the step (2)dThe energy of the PET signal is calculated using an ADC compression fitting method.
The specific implementation process for acquiring the PET signal energy by using the ADC compression fitting method is as follows:
(iv) full band compression of the PET signals using the ADC and obtaining 258 compressed data points [ (v) on each PET signal[1]，t[1])，…，(v[258]，t[258])]。
And fitting and reconstructing an original PET signal by using 258 compressed data points obtained in the previous step. Firstly, a proper PET signal model is selected, in this example, a linear-exponential model of the PET signal is selected for fitting, namely, the fitting equation of the rising edge is yl＝kxl+ b, the fitting equation for the falling edge is
And after fitting, simultaneously solving two equations to obtain an intersection point, and then performing fixed integration on the reconstructed PET signal to calculate the energy of the PET signal.
(3) Using PdAnd mapping the direct accumulation result of the amplitude value with the energy calculated by the ADC compression fitting method, fitting the mapping data to obtain an energy mapping function g ═ I (x), and correcting the energy calculated by the ADC compression fitting method by using the energy mapping function.
Claims (10)
1. A method for full-band compressed sensing of PET signals, the method comprising the steps of:
step S1: acquiring a complete PET signal database output by the radiation source with different energies by using a detector;
step S2: carrying out full-band quantization on the complete PET signal database obtained in the step S1 to obtain standard energy of the PET signal;
step S3: carrying out full-band compression quantization on the complete PET signal database obtained in the step S1, and estimating the energy of the PET signal on the basis of the prior information of the PET signal;
step S4: determining the corresponding relation between the standard energy and the estimated energy of S3 by taking the standard energy of S2 as a standard;
step S5: the estimated energy of S3 is corrected by the correspondence obtained at S4.
2. The method for full-band compressive sensing of PET signals according to claim I, wherein in step S1, the database can be collected by simulation or direct test or a combination of simulation and direct test.
3. The full-band compressed sensing method of PET signals according to claim 2, wherein in step S1, the specific process of acquiring the database by using the simulation mode is as follows:
(1) repeatedly irradiating the detector by using the same radiation source, and acquiring data output by the detector by using the ADC;
(2) and averaging the data set, amplifying, and simulating a database with certain energy by using an amplification result.
4. The method for full-band compressive sensing of PET signals as claimed in claim 3, wherein the method of averaging the data sets is: summing data output by the detector every time and considering the data as energy of the test, making an energy spectrum of a PET signal after the test process is repeated for multiple times, selecting a first valley point before and after the peak value of the energy spectrum as an upper boundary and a lower boundary, screening data with energy positioned in the upper and lower boundary intervals, assuming that n groups of data are screened out together, and defining Pi，jRepresenting the jth sampling point of the ith group of data, i and j are integers, i is more than 0 and less than or equal to n, j is more than 0 and less than or equal to m, and m is the total number of the sampling points of each group of data, so that the result P after averaging the data setzCan be expressed as:
5. the method for full-band compressive sensing of PET signals according to claim 3, wherein the averaging of the data sets followed by amplification is model amplification.
6. The full-band compressive sensing method of PET signals according to claim 5, wherein the model amplification process is as follows: determining an energy response model y ═ f (x) of the detector, and averaging the energy response model y ═ f (x)Energy of data is regarded as EzThe upper energy limit of the radiation source to be measured is regarded as EaThe amplification factor of the PET signal
Corresponding amplification result
Where K is the total number of amplified signals.
7. The full-band compressive sensing method for PET signals according to claim 2, wherein in step S1, the database is acquired by using a direct test method, which comprises the following steps: the detector is illuminated using sources of different energies and data with a certain energy is then acquired directly by the ADC.
8. The method for full-band compressive sensing of PET signals according to claim 2, wherein in step S1, the database is acquired by combining simulation and direct test, and the method comprises the following specific procedures:
(1) repeatedly irradiating the detector by using radiation sources with different energies, and respectively acquiring data output by the detector by using an ADC (analog to digital converter) according to the energy and the repetition times of the radiation sources;
(2) averaging the data sets of the same source;
(3) and simulating a database with certain energy by utilizing an interpolation method for the average result.
9. The method for full-band compressive sensing of PET signals according to claim 1, wherein in step S4, the correspondence between the standard energy and the estimated energy is referred to as an energy mapping function g ═ i (x).
10. The full-band compressed sensing method of PET signals according to claim 1, characterized in that in step S5, the corrected estimated energy E2，iAnd the standard energy E before correction1，iSatisfies the following conditions: e2，i＝I(E1，i)。
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