CN104077763A - TOF-PET image reconstruction method based on compressed sensing theory - Google Patents

Abstract

The invention provides a TOF-PET image reconstruction method based on the compressed sensing theory. The method includes the steps that firstly, according to the flight time positioning imaging principle, a first image is reconstructed based on a data set obtained through a TOF-PET detector and an initial image through a TOF reconstruction algorithm; secondly, according to the compressed sensing theory, a sparse representation of the first image is solved with lp norm minimality as the purpose, the first image is updated according to the solution result, and then a second image is obtained; thirdly, whether a stop condition is met or not is judged, if yes, the second image is a final image, if not, the initial image is updated to be the second image, and the first step is executed again. By means of the TOF-PET image reconstruction method, given time information can be completely utilized, acquisition time is shortened, and the drug dose is reduced; meanwhile, the image signal to noise ratio can be increased, noise can be remarkably suppressed, and therefore better image quality can be acquired.

Description

TOF-PET image rebuilding method based on compressive sensing theory

Technical field

The disclosure relates to nucleus medical image technical field of imaging, relates in particular to a kind of TOF-PET image rebuilding method based on compressive sensing theory.

Background technology

Positron emission tomography (Positron Emission Tomography, PET) be widely used a kind of without wound nucleus medical image diagnostic techniques clinically, it is by the radiotracer imaging to injection live body, thereby the function informations such as the metabolism of live body are provided, in clinical diagnosis, therapeutic evaluation, basic medical research and new drug development, play an important role.Its cardinal principle is: the radioactive tracer drug injection that is marked with positron radionuclide is entered to be detected in body, there is decay and launch positron in positron radionuclide, with the negatron generation annihilation reaction in detected object body, generation both direction is contrary, energy is the γ photon of 511KeV, detects thereby be placed on detected object scintillation crystal bar around.Meet the processing of detection through electronics, record satisfactory γ photon pair, wherein an annihilation reaction is called as an example.

As shown in Figure 1A and 1B, the line detecting between the crystal bar of two gamma-ray photons of an example is called line of response 12 (Line of Response, LOR).The detector 11 that wherein Figure 1A shows be annular detector, and the detector 11 of Figure 1B displaying is plate detector, and more specifically, plate detector can be divided into static type and rotary-type two kinds, but these detector image-forming principles are all identical.After a large amount of such examples of record, can obtain radioactive tracer medicine activity distribution plan by image reconstruction.

Along with the development of modern PET technology, the each several part performance of PET is being optimized always, and a kind of PET (being TOF-PET) based on flight time (Time-of-Flight, TOF) technology becomes the focus that people pay close attention to gradually.The difference of TOF-PET and conventional P ET maximum is the mistiming that it can fly to two ends crystal bar according to two γ photons, roughly determines that annihilation reaction occurs in the position (being the annihilation point 13 in Figure 1A and Figure 1B) in line of response.Because conventional P ET cannot predict the position that annihilation reaction occurs, thereby can only be by all paths that are assigned to this line of response process of example equal weight corresponding every bar response line, TOF-PET can distribute the counting in line of response according to different weights (being in general Gaussian distribution), for example can be as shown in Figure 2.

In theory, as long as temporal information is enough accurate, the mistiming that TOF-PET just can incide two ends crystal bar according to γ photon is determined fall into oblivion the position of putting 13 places completely.But because the temporal resolution of moment detector is limited, time measurement has certain uncertainty, still needs to obtain by image reconstruction the image of increased radioactivity.However, the conventional P of comparing ET, TOF-PET still has huge advantage: due to back projection has been limited to certain limit, TOF-PET can significantly improve signal noise ratio (snr) of image and contrast coefficient of restitution, thereby improves the recall rate of small lesion.Meanwhile, TOF-PET can be in keeping picture quality, reduces drug dose and reduce acquisition time, thereby reduce the person of being detected and the suffered radiation risk of operator.

That application number is that the Chinese patent application of CN200780027583 discloses is a kind of " for improvement of the method and system rebuild of TOF-PET " technical scheme, this scheme comprises the following steps: the position of estimating the first positron annihilation event based on very first time resolution; Estimate the position of the second positron annihilation event based on the second temporal resolution; Utilize estimated position to rebuild the image of positron annihilation event.

Application number is that the Chinese patent application of CN201080030171 discloses one " the flight time PET (positron emission tomography) of utilization based on the flight time information picture material that event generates one by one rebuild " technical scheme, this scheme falls into oblivion point to form synthetic image according to the flight time information location-independent of each example, and synthetic image is suitably used as to the initial pictures of iterative approximation.

In prior art, also have some other other image rebuilding methods based on flying time technology, do not enumerate at this.In all these algorithms, all verified conventional P ET that is compared to, TOF-PET has sizable advantage.

But said method still has room for improvement.For example, although TOF-PET of the prior art can significantly improve signal noise ratio (snr) of image, however simple limited to the improvement of noise.

Summary of the invention

For some or all of problem of the prior art, the disclosure provides a kind of TOF-PET image rebuilding method based on compressive sensing theory, rebuilds the quality of image for further promoting TOF-PET.

Other characteristics of the present disclosure and advantage will become obviously by detailed description below, or the partly acquistion by practice of the present disclosure.

According to an aspect of the present disclosure, a kind of TOF-PET image rebuilding method based on compressive sensing theory, comprising:

S1. according to flight time positioning and imaging principle, the data set obtaining based on TOF-PET detector by TOF reconstruction algorithm and an initial image reconstruction go out the first image;

S2. according to compressive sensing theory, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving, and upgrades described the first image according to solving result, obtains the second image;

S3. judge whether to reach stop condition: if so, taking described the second image as result images; If not, described initial pictures is updated to described the second image, and goes to step S1.

In a kind of example embodiment of the present disclosure, the data layout of the data set that described TOF-PET detector obtains comprises List Mode data layout or Sinogram data layout.

In a kind of example embodiment of the present disclosure, described TOF reconstruction algorithm is the iterative algorithm based on the flight time; The iterations of the described iterative algorithm based on the flight time is for once or repeatedly.。

In a kind of example embodiment of the present disclosure, the whole set of data being obtained by TOF-PET detector by TOF reconstruction algorithm in described step S1 or the subset of whole set of data reconstruct the first image.

In a kind of example embodiment of the present disclosure, in the time carrying out described step S1 for the first time, described initial pictures is set to a certain initial value, or the data set that described initial pictures is obtained by described TOF-PET detector carries out analytic reconstruction acquisition.

In a kind of example embodiment of the present disclosure, described sparse expression mode comprises gradient conversion, discrete cosine transform, Fourier conversion, wavelet transform and the sparse conversion based on redundant dictionary etc.

In a kind of example embodiment of the present disclosure, in described step S2, utilize gradient descent method, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving.

In a kind of example embodiment of the present disclosure, to a sparse expression mode of described the first image with l _pit is an iterative process that Norm minimum turns to object solving, and its iterations is for once or repeatedly.

In a kind of example embodiment of the present disclosure, also comprise

One relaxation factor is set;

When difference degree between described the second image and the first image is greater than default size, reduce the difference between described the second image and the first image according to described relaxation factor.

In a kind of example embodiment of the present disclosure, described stop condition is:

The number of run of described step S1-S3 reaches a preset times; Or,

In described step S2, before and after upgrading, the difference degree between described the first image is less than a predetermined threshold value.

In the TOF-PET image rebuilding method based on compressive sensing theory that example embodiment of the present disclosure provides, based on compressive sensing theory, image is reduced, thereby can utilize more fully the temporal information providing, reduce acquisition time, reduce drug dose; Meanwhile, by the method, not only can improve signal noise ratio (snr) of image, and noise is had to significant inhibiting effect, therefore can obtain more excellent picture quality.

Brief description of the drawings

By describe its example embodiment in detail with reference to accompanying drawing, above-mentioned and further feature of the present disclosure and advantage will become more obvious.

Figure 1A is two γ photons of a ring-like detector and example line of response between crystal bar;

Figure 1B is two γ photons of a plate detector and example line of response between crystal bar;

Fig. 2 is the principle schematic of TOF-PET;

A kind of schematic flow sheet of the TOF-PET image rebuilding method based on compressive sensing theory in Fig. 3 disclosure example embodiment;

Fig. 4 is flight time positioning and imaging principle schematic;

Fig. 5 A, 5B are the image schematic diagram before and after gradient conversion;

Fig. 6 is the TOF-PET detector schematic diagram of GATE software simulation;

Fig. 7, Fig. 8 are the Phantom object schematic diagram that simulation obtains;

Fig. 9 A is the image reconstruction result of TOF-PET method in prior art;

Fig. 9 B is the image reconstruction result of method in disclosure example embodiment;

Figure 10 is the contrast noise ratio contrast schematic diagram of the image reconstruction result of method in the image reconstruction result of TOF-PET method in prior art and disclosure example embodiment.

Description of reference numerals:

11: detector

12: line of response

13: fall into oblivion point

S1-S3: step

Embodiment

Referring now to accompanying drawing, example embodiment is more fully described.But example embodiment can be implemented in a variety of forms, and should not be understood to be limited to embodiment set forth herein; On the contrary, provide these embodiments to make the disclosure by comprehensive and complete, and the design of example embodiment is conveyed to those skilled in the art all sidedly.Identical in the drawings Reference numeral represents same or similar structure, thereby will omit their detailed description.

In addition, described feature, structure or characteristic can be combined in one or more example embodiment in any suitable manner.In the following description, thus provide many details to provide fully understanding example embodiment of the present disclosure.But, one of skill in the art will appreciate that and can put into practice technical scheme of the present disclosure and there is no one or more in described specific detail, or can adopt other method, material, constituent element etc.In other cases, be not shown specifically or describe known features or operation to avoid fuzzy each side of the present disclosure.

First a kind of TOF-PET image rebuilding method based on compressive sensing theory is provided in this example embodiment.As shown in Figure 3, should in the TOF-PET image rebuilding method based on compressive sensing theory, mainly comprise:

Step S1. is according to flight time positioning and imaging principle, and the data set obtaining based on TOF-PET detector by TOF reconstruction algorithm and an initial image reconstruction go out the first image; In the time carrying out this step for the first time, described initial pictures can be set as a certain initial value (for example, can be 0 or 1 etc.), and the data set that also can be obtained by TOF-PET detector carries out analytic reconstruction acquisition.

Wherein, flight time positioning and imaging principle refers to the method that incides definite position of falling into oblivion some place of mistiming of two ends crystal bar according to two γ photons.As shown in thick line in Fig. 4, the position of wherein falling into oblivion point 13 has certain uncertain region.In this uncertain region, the probability distribution that falls into oblivion point 13 positions should be the product of system matrix probability model and standard probability model.Wherein, system matrix has been described the detection process of detector to detected material, and it has connected image space and projector space.In general, system matrix has reacted the content of two aspects: the one, and the coupling location between pixel and line of response, is also whether the photon that some pixels are sent is detected by a certain bar response line; The 2nd, the degree of coupling between pixel and line of response, is also the probability that photon that some pixels are sent is detected by a certain bar response line.Conventional system matrix probability model has Point and Line Model, line integral model, area sub-model, solid angle model and point spread function model based on system matrix method; Conventional standard probability model is Gauss model.

The most probable position of annihilation reaction can be obtained by following formula:

$\mathrm{\Δx}=\frac{c}{2}\mathrm{\Δt}$

In formula, Δ x falls into oblivion point to depart from the distance at line of response center, and Δ t is the differential time of flight of two γ photons, and c is the light velocity.

The data layout of the data set that described TOF-PET detector obtains comprises List Mode data layout or Sinogram data layout.Wherein, List Mode data layout is the information of the annihilation reaction example detecting to be recorded successively according to the form of data stream and a kind of data file layout of forming; Sinogram data layout is that the example occurring on every bar response line is merged to storage and a kind of data file layout of formation.

Above-mentioned TOF reconstruction algorithm is the iterative algorithm based on the flight time.In the iterative algorithm based on the flight time, the whole set of data being obtained by TOF-PET detector by TOF reconstruction algorithm in described step S1 or the subset of whole set of data reconstruct the first image.In addition, the described iterative algorithm based on the flight time can iteration once, also can iteration repeatedly.

Statistics iterative reconstruction algorithm is as example to expect maximum (Maximum Likelihood Expectation Maximization, MLEM) taking the maximum likelihood based on List Mode data layout, and its formula is:

$f^{\left(k\right)}\left(i\right)=\frac{f^{(k-1)}\left(i\right)}{\underset{j\∈s_n}{\mathrm{\Σ}}{p}^{\mathrm{TOF}}(i,j)}\underset{j\∈s_n}{\mathrm{\Σ}}{{\mathrm{\η}}_j}^{\mathrm{att}}{p}^{\mathrm{TOF}}\frac{1/{\mathrm{\η}}^{\mathrm{multi}}}{\underset{i^{\′}}{\mathrm{\Σ}}{{\mathrm{\η}}_j}^{\mathrm{att}}{p}^{\mathrm{TOF}}(i^{\′},f)f^{(k-1)}\left(i^{\′}\right)+S+R}$

Wherein η ^multi=η ^det_geomη ^decayη ^deadtime, represent respectively Near field, decay factor and the dead time factor how much, η ^attfor the correction for attenuation factor, p ^tOFfor the system matrix of temporal extension function constraint, S is scatter correction data, and R is accidental coincidence correction data.

S2. according to compressive sensing theory, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving, and upgrades described the first image according to solving result, obtains the second image.

Wherein, compressive sensing theory is a kind of signal Renew theory, and this theory points out to suppose that signal is sparse or can rarefaction representation, can go out original signal by less sampled value precise restoration.Rebuild image sparse and represent to be that original signal is sparse or approximate sparse in certain transform domain, original signal by sparse conversion after, most conversion coefficients are 0 or close to 0.As long as meeting above-mentioned reconstruction image sparse, above-mentioned sparse expression mode expresses, more specifically, above-mentioned sparse expression mode can be changed for gradient variable, discrete cosine transform, Fourier conversion, wavelet transform and the sparse conversion based on redundant dictionary etc., can be also the combination of multiple sparse expression mode.

In medical image, be very effective way using gradient conversion as the sparse conversion of image, the formula of gradient conversion is:

$\left|\stackrel{\→}{\▿}{f}_{s,t}\right|=\sqrt{{(f_{s,t}-f_{s-1,t})}^2+{(f_{s,t}-f_{s,t-1})}^2}$

To be taking Shepp-Logan standard picture as example in Fig. 5 A, it is done to a gradient conversion, the image obtaining is as shown in Figure 5 B.

L _pnorm formula is as follows:

||x|| _p＝(|x ₁| ^p+|x ₂| ^p+...+|x _n| ^p) ^1/p

With l ₁norm is example, the l of gradient conversion ₁norm can be approximated to be total variation (TV) conversion:

${\left|\right|\stackrel{\→}{f}\left|\right|}_{\mathrm{TV}}={\mathrm{\Σ}}_{m,n}{({({\stackrel{\→}{f}}_{m+1,n}-{\stackrel{\→}{f}}_{m,n})}^2+{({\stackrel{\→}{f}}_{m,n+1}-{\stackrel{\→}{f}}_{m,n})}^2)}^{1/2}\≈{\left|\right|\▿\stackrel{\→}{f}\left|\right|}_{l_1}$

In this step, can utilize gradient descent method or other related algorithms, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving.Taking gradient descent method as example, it can be described as:

$x^{(k+1)}=x^{\left(k\right)}-{\mathrm{\α}}_k\▿\mathrm{\Ψ}\left(x^{\left(k\right)}\right)$

In formula, Ψ (x ^(k)) be objective function, α _kfor step-size in search.Be applied in this example embodiment, be objective function, it asked to local derviation, have:

$\begin{array}{c}{v}_{s,t}=\frac{\∂{\left|\right|\stackrel{\→}{f}\left|\right|}_{\mathrm{TV}}}{{\∂f}_{s,t}}\≈\frac{(f_{s,t}-f_{s-1,t})+(f_{s,t}-f_{s,t-1})}{\sqrt{\mathrm{\ϵ}+{(f_{s,t}-f_{s-1,t})}^2+{(f_{s,t}-f_{s,t-1})}^2}}\\ -\frac{(f_{s+1,t}-f_{s,t})}{\sqrt{\mathrm{\ϵ}+{(f_{s+1,t}-f_{s,t})}^2+{(f_{s+1,t}-f_{s+1,t-1})}^2}}\\ -\frac{(f_{s,t+1}-f_{s,t})}{\sqrt{\mathrm{\ϵ}+{(f_{s,t+1}-f_{s,t})}^2+{(f_{s,t+1}-f_{s-1,t+1})}^2}}\end{array}$

In formula, ε is a minimum positive number, and step-size in search can have multiple definite mode, can be even 1.An example embodiment of step-size in search is:

α _k＝||f ⁽⁰⁾-f ^(k)|| ₂

According to above-mentioned example embodiment, this step can be described as:

${\stackrel{\→}{f}}^k={\stackrel{\→}{f}}^{k-1}-a{\mathrm{\α}}_k\frac{{\stackrel{\→}{v}}^{k-1}}{\left|{\stackrel{\→}{v}}^{k-1}\right|}$

Wherein:

α _k＝||f ⁽⁰⁾-f ^(k)|| ₂

${\stackrel{\→}{v}}^k={\frac{\∂{\left|\right|\stackrel{\→}{f}\left|\right|}_{\mathrm{TV}}}{\∂f}|}_{f={\stackrel{\→}{f}}^k}$

The value of a can be set voluntarily.As from the foregoing, to a sparse expression mode of described the first image with l _pit is an iterative process that Norm minimum turns to object solving, and its iterations is for once or repeatedly.

S3. judge whether to reach stop condition:

If so, taking the second image of obtaining in described step S2 as result images;

If not, described initial pictures is updated to described the second image, and goes to step S1, the initial image reconstruction after the data set obtaining based on TOF-PET detector by TOF reconstruction algorithm and renewal goes out the first image, then performs step S2, S3.

In the loop iteration process of step S1-S2, may occur that the difference degree between the second image and the first image is excessive, and cause dispersing of nonlinear iteration process.Therefore, in this example embodiment, also comprise: a relaxation factor is set; When difference degree between described the second image and the first image is greater than default size, reduce the difference between described the second image and the first image according to this relaxation factor, thereby avoid the result that ensures loop iteration between each step to be unlikely to have big difference.

For example, described stop condition can be, the number of run of described step S1-S3 reaches a preset times, after preset times, stops having circulated.Described stop condition can be also, and in described step S2, before and after upgrading, the difference degree between described the first image is less than a predetermined threshold value, and before and after upgrading, the image of gained there is no obvious difference, can stop.

For above-mentioned example embodiment is carried out to result verification, in this example embodiment, also simulate with monte carlo method the human body PET system that Chinese Academy of Sciences's study of high energy physics is researched and developed.At this, the concrete simulation softward using is GATE software, GATE software is a kind of Monte Carlo simulation platform that is specifically designed to simulation radial imaging, has higher correctness and reliability, has become research institution and image company and has carried out the requisite a kind of instrument of radial imaging instrument development.

As shown in Figure 6, the design parameter of TOF-PET detector and collection is as shown in table 1 for GATE software simulation TOF-PET detector out.

Table 1

Detector rings internal diameter (diameter)	887mm
		Module sum	64

Block composition	4*1
		Block size (mm 2)	39.6*39.6
Crystal composition	11*11
		Crystalline size (mm 3)	3.5*3.5*25
Scintillator crystal materials	LYSO
		Crystal gap material	High-reflecting film
Gap size (mm)	0.1
		Crystal number	30976
Monocycle crystal number	704
		Seam between the Block of transversal section	3.57mm
Axially seam between Block	0.4mm
		Energy resolution	0.21
Can window	361keV～661keV
		Temporal resolution	500ps
Time window	6ns

Copy the picture quality Phantom in NEMA (National Electrical Manufactures Association, national electrical manufacturers association) standard to design a Phantom object (as shown in Figure 7).This Phantom object is cylindrical, and radius is 147mm, and length is 214mm, and material is filled to water, and activity density is 0.14uCi/CC.Wherein insert six beads that vary in size (as shown in Figure 8), diameter is respectively 37,28,22,17,13,10mm, and wherein two maximum beads are low-temperature receiver, and all the other beads are thermal source, activity density is back end 8 times.Bead connects with kapillary, and the pipe thickness of kapillary and bead is 1mm.In addition, also inserting diameter in cylindrical center is 50mm, and the cylinder low-temperature receiver that length is 214mm is filled lung's material.

Get the data that effective tale is 12M, be divided into 10 subsets, carry out image reconstruction respectively by TOF-PET method in prior art and method of the present invention, total iterations is 10 times, rebuilds image respectively as shown in Fig. 9 A and Fig. 9 B.

Comparing 9A figure by Fig. 9 B can find out, the method that the present invention proposes has further suppressed picture noise on the basis of TOF-PET method in the prior art, increases substantially for the identification degree of focus especially small lesion.In addition,, to this two width image calculation contrast noise ratio (Contrast-to-noise ratio, CNR), result as shown in Figure 10.From result, the image that reconstructs of algorithm that the present invention proposes is compared with the image that in prior art, TOF-PET method reconstructs, and contrast noise ratio has had and significantly improves.Because contrast noise ratio is to weigh an important indicator of Lesion Detection rate, thereby this method can significantly improve the recall rate of focus (especially small lesion).

The disclosure is described by above-mentioned associated exemplary embodiment, but above-mentioned example embodiment is only for implementing example of the present disclosure.Must be pointed out that, the example embodiment having disclosed does not limit the scope of the present disclosure.On the contrary, not departing from change and the retouching done in spirit and scope of the present disclosure, all belong to scope of patent protection of the present disclosure.

Claims (10)

1. the TOF-PET image rebuilding method based on compressive sensing theory, is characterized in that, comprising:

S1. according to flight time positioning and imaging principle, the data set obtaining based on TOF-PET detector by TOF reconstruction algorithm and an initial image reconstruction go out the first image;

S2. according to compressive sensing theory, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving, and upgrades described the first image according to solving result, obtains the second image;

S3. judge whether to reach stop condition: if so, taking described the second image as result images; If not, described initial pictures is updated to described the second image, and goes to step S1.

2. method according to claim 1, is characterized in that, the data layout of the data set that described TOF-PET detector obtains comprises List Mode data layout or Sinogram data layout.

3. method according to claim 2, is characterized in that, described TOF reconstruction algorithm is the iterative algorithm based on the flight time; The iterations of the described iterative algorithm based on the flight time is for once or repeatedly.

4. method according to claim 1, is characterized in that, in the time carrying out described step S1 for the first time, described initial pictures is set to a certain initial value, or the data set that described initial pictures is obtained by described TOF-PET detector carries out analytic reconstruction acquisition.

5. method according to claim 1, is characterized in that, the whole set of data being obtained by TOF-PET detector by TOF reconstruction algorithm in described step S1 or the subset of whole set of data reconstruct the first image.

6. method according to claim 1, is characterized in that, described sparse expression mode comprises gradient conversion, discrete cosine transform, Fourier conversion, wavelet transform and the sparse conversion based on redundant dictionary.

7. method according to claim 1, is characterized in that, in described step S2, utilizes gradient descent method, to a sparse expression mode of described the first image with l _pnorm minimum turns to object solving.

8. method according to claim 1, is characterized in that, to a sparse expression mode of described the first image with l _pit is an iterative process that Norm minimum turns to object solving, and its iterations is for once or repeatedly.

9. method according to claim 1, is characterized in that, also comprises:

One relaxation factor is set;

When difference degree between described the second image and the first image is greater than default size, reduce the difference between described the second image and the first image according to described relaxation factor.

10. method according to claim 1, is characterized in that, described stop condition is:

The number of run of described step S1-S3 reaches a preset times; Or,

In described step S2, before and after upgrading, the difference degree between described the first image is less than a predetermined threshold value.