CA2070879A1 - Gamma camera images having reduced artifacts - Google Patents

Abstract

Abstract of the Disclosure A system for recording fewer of the events that are caused either by Compton scatter photons or by gamma radiation interacting with lead. The system locally determines the energy spectrum and fits the determined energy spectrum with a trial function composed of a photopeak component of known energy shape, but unknown magnitude and a Compton scatter component having a theoretically derived energy shape and an unknown magnitude for each pixel of the image.
The trial function is locally fitted to the measured energy spectrum to obtain the values of both the Compton Coefficient and the gamma radiation interacting with lead. This enables removal of Compton contamination and also the contamination caused by interaction of the gamma photons with lead components.

Description

P~95 ~7~7~

Field of th Q _Ivention This invention is concerned with gamma camera imaging and, more particularly, with methods and systems for obtaining images having reduced artifacls du~ -to multiple photopeak and unwanted events.
An event is herein defined as a pho-ton strikins. the gamma camera detector and causing a scintillation that is ac~luired as data for use in constructing an image. This is an improvement to the invention entitled "Compton-Free Gamma Camera lmages" filed in Israel on June 11, ~990, and which received ~erial No. 094691.

Back~round of_tle Invention In passin~ thro-lgh the human body, gamma pholons have a certain probability o~ scattering due to the Compl-~n effect. Such scattering changes the direc-tion and energy o~ e photons. When a photon that has been scattered is detect:ed by Ihe gamma camera, false position informa-tion is derived from the ~.ca-ttered photons.
Thus, the scattered pho-tons cause events tha-t a-e unwarl-ted for use in cons-tructing the ima~e. ~lther unwantecl ~vents exist. For example, the radiation emitted from -the patient -ften excites lead (K~ X-rays from the collimator and other lead narts. These X-rays also impinge on the detector and may be regi!-lered as events.
These X-ray photons constitute an additionill source of image blurrin~.

-~ 2 ~

The problem Or X-I ay induce(i ~v~nts arises esr~ ially for radio isotopes emitting photons in the energy rang~ of ~8-1~0 KEV. In -this range, tlle lead X-ray e~cita-t;orl probabilil-~ is high and the spectrum of these photons coincides with a relevant part of -the isotopes spec-trum, by partially o~erlapping the pho-topeak. Thus, the unwanted part of the spectruln in each pixel has two terms: one made up of -the Conlp-ton scatterecl phol:ons, and t~ other made up of the lead X-ray photons.

In principle the events caused by unwan-ted photons should be discarded. Howeve.r, it is not easy to arrive at ,~.riteria that are e.fficient ancl efEective for discarding such events. For example, an energy level criterion i5 not efEective because although the photon loses par-t of its ellergy in the scatlering process, the energy resolulion of the -typical .gamllla camera jr such that there is a large amount o~ overlap betueen the energ~ oE unscatterecl and scattered photons.

The invention of the previously mentioned ~-atent application provided methods and means ~o~ qualitativel~ and quantitatively improving the recorded images by signiEica~ ly reducing the contribution of Compton scattered photons to the final image to thereby provicling a practically Comp-ton-free .image within seconds after acquisiticn. The invention accomplishes ~he task oE reducing the number of` events caused by Compton scaltered photons by locally determining the energy spectrum and fi-tling -the determined

2 ~ 7 ~

energy spectrum wi-th a "trial" function comr~3sed of a photopeak component of known energy shape but unknown magnitude and a Compton scatter component having a theore~ically derived energy shape and an unknown magnitude for each pixel o[ -the image.

The true physical charac-teris-tics of the Comp-ton process are used in the previously mentioned Patent Applicatiol)-to derive Compton multi-sca-tter functions which are subsequently llsed -to cons-truct the Compton sca-tter component energy spectra. Ihus, the previous Patent Application uses the following inputs to determine the unknowns; (i.e., the magnjtude of -the photopeak component and the magni-tude of -the Gompton multi-scat-ter componenl:s):

1. -the measured energy spectrum E)er piY~I. This includes counts due -to sca-tterecl and unscattere-:l pho-tons, and the measured system energy spread function for -the isoto~3e centerline which provide the photopeak energy shape.

The shape of -the ~ompton Gomponent of tl~ trial function is analytically derived in the prior application hy conver-ting the Nishina-Klein Eguation that describes -the physical relativistic scattering of photons wi-th electrons int-o a probability distribution for a photon to scat-ter from a given energy -to a lower energy in a single in-teraction with an electron. Repeated r; ~ $

convolutions arc llsed to obtai~l Ihe probabil.it:y distribution for the higher order scatter terms.

By locally fit-ting -the -trial function to t.he measured energy spectrum of acquired data the values of the multi-scattered Compton co-ef~i.cients and the ~hotopeak magnilllde were obtalned.
This enables the removal of Compton contalllination from the acquired data.

The prior invention however assumed a single photopeak. In certain isotopes -there is more than one photopeak. If a single peak is assumed when more -than one pealc a~ ually exists the removal of scat-tered events ftom -the image will t!e incomplete.

Accordingly the invention of this Applica-tion is an improvement over the invention of -the pri.or mentioned ~pl~lications in tha-t among other -thin~s it takes in-to account radi(~ isotopes having more than one peak and also takes in-to account all unwanted events due to Compton sca~tered photons and photons de~rived from such phenomena as X-rays caused t~y gamma radiatioll interacting with lead components.

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Brief De~ t.ion_of the Inverltioll The present invention represents an improvement over -the inventi.on oE -the Israel Paten-t Application, Serial No. 09~1691. The present invention reduces events caused by unwanted pho-t:ons including, but not limited to, Compton scat-ter photons and also -takes in-to account multiple photopeaks, such as are )I>tained when using certain radio isotopes. Thus, -the image provided by utilization of the present invention improves over -the image o~ the invention of the prior mentioned Patent Application.

In accordance with the present invention, thele is provided a method of reducing the contribution of unwanted photons to an image produced by a gamma ray imaging system, said method including the s-teps of:

detecting photons impinging on a ga.mma ray detector as event counts, measuring the energy of said ;mpingin~ phot-~rls and an X, Y
location for each photon according to the location of the impingement of the photons on the detector, grouping each detected photon according to the measured energy and the X, Y location, accumulating counts of said ~hotons at ea~ X, Y location according to the determined energy level of the photons, constructing a rneasured energy spectrum a-t each X, Y location using the accumulated counts oE -the determined erlergy levels, said measured energy spectrum including counts oE wanted and unwanted photons, calculating the energy distributions of unwanted photons, determining the energy spread ~unction of the f~amma ray imaging system bein~ used, .
o~taining a sys-tem dependent energy distribution of the unwanted photons per location by using the energy distribution of the unwanted photons and the energy spread function of the system, constructin~ a trial function compri~ing -the system dependent energy spread function mult;p];e~l by an unkno~1n coefficient of wanted photons plLIs unknown ,-oeflicients ol: unwanted photons convolved with the system's energy spread function.

solving Eor the unknown coeff.icient of the wanted photons by locally fitting the measured energy distrihlltion to the trial energy distribution of photons, and P495 ~ 7 ~

using the cOIJnt of -the wanted pi~otons -to produce an image prac-tically free of unwanted photons.

According to a feature of the inverltion, the unwanted photons include Gompton scattered photons origina-ting from single or mul-tiple radio iso-tope photopeaks.

According -to another feature of the invention, the unwanted photons further include photons such as those due to lead X-rays.

Brief ~escript on of the ~ a in~s The a~ove men-tioned obiec-ts and features of the present invention along with addi-tional obiec-ts and ~eatu.res will be best understood when considered in -the light of the following description made in con~unction wi~.h t}-~e accompanying clrawings; wherein:

Fig. 1 is a block diagram showing of a gamma radiation imaging system for providing improved images by elimir)ating blurs caused in the pas-t by multiple pho-topeak isotopes and Ihe inclusion of unwanted even-ts genera-ted by Comp-ton scattered photons and other unwanted photons, and Fig. 2 represents details of the preparatiorls, compu-tations and operations used in the system shown in Fig. 1.

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General Descri~tion Fig. 1 at 11 generally shows in block diagram form the inventive gamma camer~a system for producing improve-l images. Fig.
comprises a measured energy spectrum s-tage 12, a -trial function preparation stage 14 and a curve fi-tting or compu-tation stage 15 which provides an unwanted pho-ton-Eree image (~ I) 16.

The measured energy spectrum stage 12 comprises a gamma radiation detector 17. The gamma radiation de-tector 17 provides electrical signals responsive to events; i.e., photons imp;nging on the Eac.e thereof, such as indicated a-t 1~. When an event occurs, electrical signals are provided on conductors 19, 21 and 22. These conductors 19, 21 and 22 are directed immediately -t:o a coordinate computer 23 which determines X and Y loca-tion of tlle impingelllent of the pho-ton 18 onto the detector 17.

Conductors 22 and ~4 carry an electrical rel!resentation of the energy oE the photon. The electrlcal represerlt~tion of the energy is provided to an energy (Z) correction Cil~CUit ~5. An energy processing circuit 26 divides -the range of energy de-tected into a number of energy windows prede-termined by the s~stem operator.

When the energy is within certain limits, the energy correction circuit sends an enable signal over conductor ~ which enables the coordinate computer to determine the X and Y coordinate location~

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of the event. This informa-tion is direc-ted -to an image corrector and digitizer circuit 31 which correc-ts and digi-tizes the X Y
coordinates of the event. The information on tlle number o~ events is placed into a plurality of matrices ~2 clependent on the photon s energy. Each of the matrices is a memory that retains the counts of even-ts per X Y location for a partic~llar energy window such as for example a window tha-t extends frolll 22 KEV to 25 KEV
for window No. 1 and ~5 KEV to ~8 KEV for window No. 2 etc. The windows are shown as W1 W.2 W3 e~tending -to Wn where n is the predetermined number of energy windows.

The matrices are thus divided into X Y locations that correspond to the co-ordinate loca-tion of the event on the cle-tector. The X Y
locations also correspond to pixels in the final image. An imaging preprocessor 33 receives the clata pixel-by-pixe.l from each of -the winclows and computes a measured or an acquired energy spectru~ N~
per pixel as shown in block 34. This acquiled energy spectrum includes both the counts due to unwanted photons and wanted pho-tons. The unwanted photons include Compton scat-ter photons and other or additional unwanted photons. No-te -tha-t the energy spectrum may include more than one energy peal~ as shown in block 34.

The trial function s-tage 14 of Fig. 1 prepares a -theoretical or a trial energy distribu-tion n(X Y ~) including wanted and unwanted events herein:

~(XlY~)=Np(X~Y)~ m (x~y)Jd~F~ )~m(~ ~(X ~Y) R(~) (1) m=1 here:

~ = E/m~C2 the photon ener~y in units of electron rest energy, m~C~, u) P(~)=,EWlP(~ ); it is -the sys-tem energy spread Eunction at ~ 2...; (P(~) can also be measured in an envil~onment free of all unwanted photons).

(k) is a superscript denoting the number of discrete energy lines in the source, m is a subscript indicating -the numbe:r of the C.ompton scat-ter order, and M is a script indicating the chQsen number of Compton scatter orders included in the computa-tion.

~m(~ ) iS -the energy distri~ution of events caused by photons scattered m times from original energies ~ ith known relative intensities W~ to intermediate energy ~' (i.e., the shape of the energy probability distribution of pho-tons scattered m times), ~m(~ Wl~ ) with ~[~, for m~ being calculated recursively, ' :

- 12 - 2B7~7a~
P~95 W1 are the known relative intensities of ~ Wi=1.

N~tX,Y) is the spa-tial distribu-tion (counts/pixel) of events caused by unscattered photons.

Qn.rX,Y) is the spatial dis-tribution (counts/pixel) of events caused by photons scattered m times, is the original energies of the pho-tons emitted from a radioactive source, is -the measured energy of the photon, ~' is an intermediate energy of a photoll, R(~) is the measured energy spectrum of aclditional unwanted photons such as by way of example photons from lead X-rays. tNote R(~) can also be calculated using published tables and convolvi.ng with -the system spread function).

Ko(X~Y) is the spatial distribution tcounts/pixel) of the events caused by the addi-tonal unwanted radiation.

~n important purpose of the invention is -to determine the spatial distribution of the wanted events N~ (X, Y).

-- ~ ~ 7 ~ 3 1 Y~i95 To determi.ne -tlle coun-t of events per pixel, block 15 fits the measured value6 that i8 the measurecl energy spectrum per pixel and the system energy spread function with unknowns; i.e., the magnitude of the photopeaks and the shape and magnitude of the unwan-ted photon spectrum -to the values of the trial distribution n(X,Y,~). 'rlle fit provides the wanl:ed spa-tial dis-tribution N~ (X, Y). With the knowledgè of the spatial distribution of the wanted photon, the scattered and other unwan-ted photon-free image is pr~cluced as indicated at 1~.

Details of the computations that oscur a-t -the trial function preparation sectiorl 14 of Fig. 1 are inclicated ln Fig. ~. More particularly, as shown in l~ig. 2, values based on the system energy spread Eunction shown in block ~,1 of Fig. 1 and Fig. 2, are entered into bloclcs 36 Figs. 1 and 2. In addition, values based on acldlti.onal unwanted (photons) racliation such as, for example, lead X~rays are determined (either by measurement or by compu-tation) as 6hown in block 40 oE Figs. 1 and 2.

The energy spread function of the system i6 a.~.sumed to be known.
It is measured once and ls kep-t in -the memory of -the sy~tem. The measurement is easily accomplished by providin~ sources of gamma radia-tion oE known energy and detecting the racliation with -the equipmen-t 11 oE Fig. 1, for example. The de-tecl:ion is made without any Compton scatter media or X-ray providing lead between the energy 50urce and the detector. This provides an energy spread function for a monoenergy source or a multi-energy force due to the detector energy resolution without unwanted photons as shown in block 41. The preparation block 36 comE~u-tes ~m i.e., the energy distribution of the unwanted photons including Compton photons, for example, and further including Compton photons for eac.h scattering order. This is done by using the Nishina-Klein equation to derive -the differen-t orders of scat-tered unpolarised photons; i.e.:

-~-rl (c~ t ~

; elsewhere ~ ) is the weighted com~ination of the fil~st order Comp-ton energy distribution for each oE tt-e k photopeaks, or ~t~ W~ a) i=l The higher orders of sca-tters are derived recursively by repeated convolution usin~ the equa-tion:

,,~ 6~ (3 ~

~ ~ ; elsewhere Where ~ is the maximum of all ~ ... k).

Note that -the equations are solved recursivel~ in that each hi~her order equation requires knowledge oE the lower prior orders.

The energy distribution of Compton scatter photons provide a curve independent of the system for each order of the scatter. However, -this system independent curve is acted upon by the system energy spread function to provide -the system clependent Compton multi-scattered energy distributions denoted by ~m(~). The shapes of the C~ ) dis-tributions are obtained by convolving ~m with the system ~nergy spread function P(~ ); i.e.:

(k) ~ (k) C~ (~)=) d~'~m (~')P(~ ) (4) This set of equations provides the shape of the Compton energy distributions for each order of scatter af-ter bein~ operated on by the system energy spread function.

Fig. 2 indicates the computations resulting in the ~m values using the Nishina-Klein equa-tion in blocks 42, 4~ and 44 for ~. and ~) consequently ~2 . . . m.

The shapes of ~kl ~2 and ~ in blocks 42, 43 and 44 are shown as being convolvecl with the sys-tem energy spread furlction of block 41 in blocks 46, 47 and 48 respectively, thereby providing the shapes C1~ C2, etc . The computations to determine ~ 2, e-tc., are P495 2~7~

indicated as being recursive by the arrows going from ~ to ~2, etc.

Hereafter the superscript (k) denoting the number of discrete energy lines in the source is omit-ted from the Cs.

A method for drastically reducing the number of computations is useful in this system. The reduction in the number of computations is accomplished by orthonormalization of the se-t Cm(~). The orthonormiaization is provided by constructing an orthonormal function (vector) set ~ using the Graham-Schmidt procedure:

~, = Cl/ J~C12>

(~2 = ( C2 ~ C2 > ~ < C2~2 > - < ~ l ~ C2 > 2 ~) M ¦ ~ M ~
= (C - E ~C >~D/I<c - ~<~- C ~2 (5) M-~1 M+l ~=1 M+1 ~ Y M+1 ~ =1 M-~1 Where for convenlenc,e C~ ) is defined as being identical to R(~).

Where sums (integrals) over energy are defined by:

E F(E) - ~F~
E

P~.95 Note that -the array set C~} obeys:

(~,i=j < ~ = ~ ~ J
o,i=i .

The or-thonormalization is accomplished in computer 49 and the results; i.e., ~ 2.. .~m-~l are shown in blocks 51, 52 53, for example.

The Compton sum (EQ(4)) can be rewritten using the ~k'S:

QmCn~ = ~ am~ < Cm~31c ~.~)1': ( ) E t ~ < Gm ~ ~)k > Qm ) ~ ~)k ( 6 ) =~ qle ~ ~k where:
.
q~ < Cm ~)k > am and: m = 1,2...M+1 k = 1,2...M+1.

*[with an orthonormal base ~"~} any vector v can be represented as a superposition of an array oE ~m' 2~7~8~

v = ~<v~m>~m.] (7) The trial distribution now reads:

n(X,Y;E) = Np(X,Y) P(Eo~ C(X,Y;Eo,E) ~8) where:

C(X,Y;Eo,E) = Lq~(X,Y)~k(EO,E) (9) Hereafter the known energy spread function, P is normalized such that <P> = 1.

In a preferred implementation, a least squares fit is used. More par-ticularly, with the trial function n(X,Y;~) of equation (1) and the multi--window acquisition resul-ts N~(X,Y) from block 34, a solution is sought for -the number of counts caused by unscattered photons N~(X,Y) that will minimize the sum of the squares of differences for each pixel ~(X,Y):

~ (X,Y) = ~n(X,Y;E) - N~(X,Y]2> (10) More particularly, in the block 15 the followin~ "fit" operation is performed, i.e., - = o, and (11) N~

~
= O, where k = 1,2,....................... (12) It can be shown that the solution of these equations is:

N~(X,Y) = <N~(X,Y) J(E)> (13) qk(X,Y~ = ~N~(X,Y) G~(E)> (14) where:

P(Eo,E) - <P-Q.c>.Qk(E~,E) J(E) - - (15) ~ p2> -- ~ p~ Q~e >2 k Gk(E) = ~k(E~,E) - <P-Ok> ~J~f ~ (16) Note that since J(E) and Gk(E) are data independent, they can be apriori derived as indicated in Fig. 2 by block 54 which shows computing J(E) using ~ ,02 ....Q~c and P. The "per-pixel"
operations entail only the evaluation of the scalar product Np = <N~ ~J(E) ~ . (17) - 20 ~ r P4~5 The fit, therefore, determines the per pixel Compton scatter free count N~.

To compensate ior low statistics per pixel per energy window, the relative constancy of scatter distributions over large spatial domains is put to advanta~e by use of a "quasi-local" solution.
More particularly, an expanded or "large" pixel is preferably used. Thus, if the top pixel is (XOIYO) the spatial window W is defined as:

(XO-W)~X~(XO~W) ; (YO-W)~Y~(YO+W) (18) of area s = (2Wtl)~

When the Compton component of the entire window s, C~ is computed, the "per-pixel" Comp-ton ac-tivi-ty, C~ can be approximated by its average:

C ~ - C~/s . ( 1 9 ) The measured activity in the spatial window 5 ( symmetric around the coordinates (X,Y)) is deno-ted as N~(X,Y), and the (X,Y)-pixel activity is denoted as N~(X,Y). A single parameter fit is done to find the local pho-topeak count. It can be shown that this i5 Oiven by:

P~195 S s Np>(X,Y) = <N~X,Y) A,~ + Nr~(X,Y) .A,E> (20) where:

A~ = P(E)/<P2s (21) s Al = [J(E) - Al ]/s (22) Solving for N~X,Y) gives the count/pixel of the Compton free image.

An alternative fitting method is the Maximum Likelihood Me-thod.
Given the measured ac-tivities {Nl } the ioin-t Poi5son probability with respect to the parameters of the -trial function n(E) are maximized; i.e., find n(E) such that = ~ Çn(E) -n(E~
~= maximum (23) Nl! J

or, since ~ is positive:

ln ~ = <N~ ln n(E) - n~E) - ln N~!> - maximum (24) t can be shown that for the maximum likelihood solution:
<n(E)> - ~N~>
which enables eliminating N~ from the n(E) function.

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(llereaf-ter (X,Y) are implicit, e.g., n(X,Y;E) = n(E). Thus from equations (8) and (9) it follows tha-t:

n~E) = < N~>P ~qk(~C - ~k>~P) (25) Calculating the derivative~ of ln ~ wi-th respec-t to q,~ and settlng the resulting equation -to o as required b~ -the maximum condition, the following equations are obtained:

N~
< (~ <~.c~P)> = ~ ; k = 1,2,.. t26) n(E) This is a set of non-linear coupled equations and canno-t be solved in closed form. IJsing the mul-ti-gradient method, an iterative solution Eor the q,cs can be obtained. Denoting oq,c as the difEerence between q.c before and q',~ after the i-teration oq~ = q k - q.~ . ( 27 The coupled set of equations is linearized and soluble ~Mi~oq. = Ul (28) N~
M1J = < (~)1 <01>P) (~ -<~ ~P) > (29) nZ(E) 2 ~ 7 `~

N~
U = < ( ~ - < ~ P ) > ~ 3Q ) n(E) Af-ter proper convergence of the solution for the array q,c has been attained, the Compton free activity Nv can be obtained from:

N~ - <Ni> - ~qk<~l~> (31) 1~

Yet another alternative fit is the partial Maximum Likelihood Solution. Suppose that the least square solution provides the approximate functional structure of the Compton component.
However, it is desired to in-troduce the Poisson statistics by changing the ratio of the photopeak to Comp-ton events Eraction in order to optimize the ioint distribution. The trial func-tion, n(E), then is n( E) = <NOE ? t f~.P + (1-f~)C] (32) where:

N~ .
f~ = is the photopeak fraction (33) ~N~>

and C is the least square Compton solution, normalized to t;
i.e.:

C = C /<C? (34) - ~4 -P495 '~ ~ 7 ~

Now, the Maximum Likelihood ~qua-tion is maximized with respect -to a single parameter, the photopeak fraction, f~. Once f~ is calcula-ted, the scatter-free event distribution N~ can be found using the equation:

N~ = fv,~N~> (3~) The optimization equation resulting from the differentiation with respect to fF, reads:

N~tp-~) ~_ ) = O (~) ~fF~(P-) It is soluble by an iterative New-ton-Raphson method:

<N~.~>
f F~ = fF~ (37) <N~ .~2 where:

P-C
_ (38) C+f~(P-C) Yet another related me-thod of obtaining the value of NF~ involves the semi-local Maximum Likelihood Fi-t Solution. As for the quasi-local solution, this is implemented here as follows: First a solution is ob-tained for the square called S surrounding the pixel XO~Yo~ i.e.:

- .

- ~5 -P4~ $ ~ ~

5=(XO-W)~X~(XO~w), (Y~-W)~Yc(YO~w) = (2w+l)2 t39) Once the Compton free component of the entire window has been o~tained, el-ther by the full or by the partial Maximum Likelihood method; i.e., N~(X,Y) is known, the slow Compton spatial variance is used by assumlng:

Cl = C~/s (40) -to obtain the (X,Y)-pixel Compton free activity-N,~ N
N ' = -- ~ <N ' - `~
p s E s (41 ) If it i5 desired to eliminate the events caused by additional unwanted photons then block 40 is used to include such additional unwanted photons ori~inated events in the "trial" equation.

In operation, the inventive system locally analyzes the energy spectrum which may comprise mu].tiple energies and fits it with a trial function comprising a combination of the unscattered pho-topeak function and a function, representing the Compton scattered spectrum, and a function representing other unwan-ted photons. The function representin~ the Compton scattered spectrum is derived usinO the Nishina-Klein formula. The Compton sca-tter spectrum shape, therefore, inherently reflects the true -P495 ~ Q'~8~

rela-tivistic distributions of the Compton sca-tter, unlike the previously used arbitrary polynomlals. The function representing other unwanted photons can either be measured or computed. If measured, the system spread function is automatically included in -the result. If computed, the result must be convolved with the system spread function.

The Nishina-Klein formula is recursively used to generate the multi-scat-tered Compton distribution ~c. Then each ~(~)is convolved with the system energy spread function to obtain C~m~ the system dependent Compton scatter distributions. The convolved functions are averaged or integrated for discrete windows to obtain discrete arrays required for the calculations. The set of discrete ~u~
functions Ci is then preferably orthonormalized to reduce the number of computations necessary and to assure that the inventive system can provide practically Compton free ima~es within seconds after acquisition. The coefficients of the orthonormalized functions are parameters that provide the scattered counts per pixel. The parameters are determined by fitting between the final trial function comprised of the photopeak component or components, the scatter component and on other unwanted photon components to the measured ener~y distribution which includes both the scattered, unscattered photons and other unwanted photons. Local (and quasi-local) fitting can be used to expedite obtaining the coefficients of the fit functions.

- ~7 -P4~5 ~7~8~9 A unique approach of the invention is tha-t the parame-ters -to be determined are coefficients of the physical Compton scatter functions. The said func-tions have the correct high energy threshold behavior ensuring correct fit at every point.

The inventive method also preferably improves the statistics for the calculations for the Compton fit by a me-thod that takes advantage of the smoothness of the Compton distribution (quasi-local method). That is, the data in a preferred embodiment is summed over (2n ~ 1) square pixels for the fit where n is an integer. The values are then a-ttributed only to the central pixel of the square. Similar calculations are done for each pixel.

Preferably a leas-t square fit is used to solve the unknown c.oefficients, i.e., the amount per pixel of the unscattered events (and if desired for the amount per pixel of the scattered events).
However, several variations employing the maximum likelihood fit are also described and are within the scope of this invention.

While the invention has been described with regard to specific embodiments, it should be understood that the description is made by way of example only and not as a limi-tation of the scope of the invention which is defined by the accompanying claims.

Claims (40)

What is claimed is:

1. A method of improving images from a gamma camera system by considering isotopes having k photopeaks and by reducing the contribution of unwanted photons on an image produced by a gamma ray imaging system, said method including the steps of:

detecting photons impinging on a gamma ray detector in an X,Y
coordinate location according to the location of the impingement on the detector.

determining the energy of each detected photon, grouping each detected photon according to the determined energy in the X, Y coordinate location, accumulating counts of said grouped photons according to the determined energy level of the photons at each X, Y coordinate location, constructing an energy spectrum of each X, Y location using the accumulated counts, determining an energy distribution of unwanted photons, determining the energy spread function of the gamma camera system for the known energy of the wanted photon and for the determined energies of the unwanted photons, using the determined energy distribution of unwanted photons and the energy spread function of the system to obtain a system dependent energy distribution of the unwanted photons per X,Y
coordinate location, constructing a trial function comprising the system energy spread function multiplied by an unknown coefficient of wanted photons plus the system dependent energy distribution of unwanted photons multiplied by unknown coefficients of unwanted photons, locally fitting, the trial function to the constructed energy spectrum to obtain the count of the wanted photons by solving for the unknown coefficient of the wanted photons, and using the count of the wanted photons to produce an image practically free of unwanted photons.

2. The method of improving images from gamma camera systems of Claim 1 wherein unwanted photons include Compton scattered photons.

3. The method of improving images from gamma camera systems of Claim 2 wherein said unwanted photons include other unwanted photons.

4. The method of Claim 2 wherein said unwanted photons include lead X-ray photons.

5. The method of Claim 3 wherein k=1.

6. The method of Claim 3 wherein k>1.

7. The method of Claim 1 wherein the step used to obtain the system dependent energy distribution of unwanted photons includes the step of calculating the energy distribution of unwanted photons for each value of k.

8. The method of Claim 7 wherein the step of using the determined energy distribution of unwanted photons and the energy spread function of the gamma ray imaging system includes convolving the energy distribution of unwanted photons with the energy spread function of the gamma ray imaging system.

9. The method of Claim 7 wherein the step of using the determined energy distribution of unwanted photons and the energy spread function of the system includes the step of measuring at least one energy distribution of unwanted photons with the system whereby the measured distribution inherently includes the energy spread function of the system.

10. The method of Claim 8 wherein said step of constructing a trial function comprises:

summing the convolved system dependent energy distribution of the determined energy distribution of unwanted photons including the system energy distribution of Compton scattered photons and additional unwanted photons both with unknown X,Y coefficients, and locally fitting the trial function to the constructed energy spectrum to solve for the unknown X,Y coefficients and thus for determining the counts of the unscattered photons.

11. The method of Claim 10 wherein said step of determining the energy distribution of unwanted photons comprises the step of:

analytically determining the energy distribution of Compton scattered photons.

12. The method of Claim 11 wherein the step of analytically determining the energy distribution of Compton scattered photons includes the steps of:

converting a Nishina-Klein equation to an m order photon scatter probability distribution to determine the energy distribution of the m order scattered photons where m=1,2...M, and convolving the energy distribution of the m-order scatter photons with the energy spread function of the system to obtain probability distributions of m+1 order scatter photons.

13. The method of Claim 12 including the step of obtaining a set of discrete functions from the energy distribution of the m-order Compton scatter photons by averaging the calculated Compton energy distributions for each grouping.

14. The method of Claim 13, including the step of reducing the number of calculations.

15. The method of Claim 14 wherein the step of reducing the number of calculations comprises converting discrete functions into an orthonormal set of functions.

16. The method of Claim 15 wherein the fitting step includes:

using quasi-local pixels to obtain local counts of the scattered photons, and doing a single parameter fit to determine the local counts at each of the k photopeaks.

17. The method of Claim 16 wherein the step of using quasi-local pixels comprises:

using large pixels comprising a (2n +l)X(2m +1) rectangle of pixels where both n and m are positive integers and the value of the large pixel is divided by the number of pixels in the large pixel and attributed to the center pixel, and evaluating all pixels in this method.

18. The method of Claim 1 wherein the step of locally fitting the trial function to the constructed energy spectrum is accomplished using a maximum likelihood fit.

19. The method of Claim 1 wherein the step of locally fitting the trial function to the constructed energy spectrum is accomplished using a partial maximum likelihood fit.

20. The method of Claim 1 wherein the step of locally fitting the trial function to the constructed energy spectrum is accomplished using a combined least square and maximum likelihood fit.

21. A method of producing practically unwanted photon free images of a patient with a gamma ray imaging system, said method comprising the steps of:

determining a trial function, said step of determining a trial function comprising the steps of:

multiplying a known system energy spread function by an unknown count number due to unscattered photons, convolving an energy distribution of m-order scatter photons derived from the probability of physical interaction of the photons in the known system and a system energy spread function to provide a system dependent set of Compton fit functions, multiplying the system dependent Compton fit functions by unknown numbers corresponding to counts of scattered photons, locally measuring an energy spectrum of the patient that includes total counts due to wanted photons from k energy lines in a radio isotope ingested by the patient, where k=1, and due to unwanted photons including scattered and additional unwanted photons, locally fitting the trial function to the locally measured energy spectrum to determine the unknown count due to unscattered photons, and using the count number due to the unscattered photons to produce the practically Compton free image.

22. The method of Claim 20 wherein the step of measuring the energy function includes the steps of:

determining an X,Y location and energy of photons impinging on a system photon detector, using a plurality of matrices having X,Y pixels corresponding to impinging locations to accumulate counts of impinging photons, each of said matrices corresponding to one of a plurality of energy windows spanning an energy range, and constructing the measured energy spectrum from the accumulated counts in the matrices.

23 A system for improving images from a gamma camera system by considering isotopes having k photopeaks and by reducing the contribution of unwanted photons on an image produced by a gamma ray imaging system, said system comprising:

a gamma camera detector for detecting gamma photons impinging thereon at an X,Y coordinate location, means for determining the energy of each detected photon, means for grouping each detected photon according to the determined energy in the X, Y coordinate location, means for accumulating counts of said grouped photons according to the determined energy level of the photons at each X, Y coordinate location, means for constructing an energy spectrum of each X, Y location using the accumulated counts, means for determining an energy distribution of unwanted photons, means for determining the energy spread function of the gamma camera system for the known energy of the wanted photon and for the determined energies of the unwanted photons, means for using the determined energy distribution of unwanted photons and the energy spread function of the system to obtain a system dependent energy distribution of the unwanted photons per X,Y coordinate location, means for constructing a trial function comprising the system energy spread function multiplied by an unknown coefficient of wanted photons plus the system dependent energy distribution of unwanted photons multiplied by unknown coefficients of unwanted photons, means for locally fitting the trial function to the constructed energy spectrum to obtain the count of the wanted photons by solving for the unknown coefficient of the wanted photons, and means for using the count of the wanted photons to produce an image practically free of unwanted photons.

24. The system for improving images from gamma camera systems of Claim 23 wherein unwanted photons include Compton scattered photons.

25, The system for improving images from gamma camera systems of Claim 24 wherein said unwanted photons include other unwanted photons.

26. The system of Claim 24 wherein said unwanted photons include lead X-ray photons.

27 The system of Claim 25 wherein k=1.

28. The system of Claim 25 wherein k>1.

29. The system of Claim 23 wherein the means to obtain the system dependent energy distribution of unwanted photons includes means for of calculating the energy distribution of unwanted photons for each value of k.

30. The system of Claim 29 wherein the means for using the determined energy distribution of unwanted photons and the energy spread function of the gamma ray imaging system includes means for convolving the energy distribution of unwanted photons with the energy spread function of the gamma ray imaging system.

31. The system of Claim 30 wherein the means for using the determined energy distribution of unwanted photons and the energy spread function of the system includes means for measuring at least one energy distribution of unwanted photons with the system whereby the measured distribution inherently includes the energy spread function of the system.

32. The system of Claim 30 wherein said means for constructing a trial function comprises:

means for summing the convolved system dependent energy distribution of the determined energy distribution of unwanted photons including the system energy distribution of Compton scattered photons and additional unwanted photons both with unknown X,Y coefficients, and means for locally fitting the trial function to the constructed energy spectrum to solve for the unknown X,Y coefficients and thus for determining the counts of the unscattered photons.

33. The system of Claim 32 wherein said means for determining the energy distribution of unwanted photons comprises:

means for analytically determining the energy distribution of Compton scattered photons.

34. The system of Claim 33 wherein the means for analytically determining the energy distribution of Compton scattered photons includes:

means for converting a Nishina-Klein equation to an m order photon scatter probability distribution to determine the energy distribution of the m order scattered photons where m=1,2...M, and means for convolving the energy distribution of the m-order scatter photons with the energy spread function of the system to obtain probability distributions of m+1 order scatter photons.

The system of Claim 34 including means for obtaining a set of discrete functions from the energy distribution of the m-order Compton scatter photons and means for averaging the calculated Compton energy distributions for each grouping.

36. The system of Claim 35, including means for reducing the number of calculations.

37. The system of Claim 36 wherein the means for reducing the number of calculations comprises means for converting discrete functions into an orthonormal set of functions.

38. The system of Claim 36 wherein the means for fitting includes:

quasi-local pixel means for obtaining local counts of the scattered photons, and means for doing a single parameter fit to determine the local counts at each of the k photopeaks.

39. The system of Claim 38 wherein the quasi-local pixel means comprises:

large pixels comprising a (2n +1)X(2m +1) rectangle of pixels where both n and m are positive integers and the value of the large pixel is divided by the number of pixels in the large pixel and attributed to the center pixel, and means for evaluating all pixels in this method.

40. The method of Claim 1 wherein the step of locally fitting the trial function to the constructed energy spectrum is accomplished using least square fitting.