JP3660998B2 - SPECT tomographic image correction method, system, and program - Google Patents

Description

【００１１】
即ち、吸収補正の際に減弱計数μとして理想値（例えば１６０ｋｅＶのガンマ線に対する水の場合で約０．１４６ｃｍ^-1）を採用すると、散乱線による不要な計数の分まで計数値を補ってしまい補正が過剰にかかってしまうので、あたかも吸収が少なかったかのようにみなし、減弱係数μを理想値より若干減らして、断層画像を真の計数値に近づけるものとする。
【００１２】
しかし、この断層画像を別施設において利用しようとしても、有用な読影が困難である。というのも、断層画像再構成時に減少させた減弱係数μの値が上記のように経験的に決定されることから、当該別施設において採用されている減弱係数μが断層画像取得施設における減弱係数μと異なることが多く、散乱線補正のかかり度合が異なってしまうからである。
【００１３】
従って、異なる減弱係数を採択する施設間や、散乱線補正の有無の異なる施設間において被検者が転院する場合等には、断層画像を取得し直すこととなるが、同様のデータを何度も取得することとなって手間がかかってしまう。そこで、他施設において取得された断層画像につき、演算により読影に値するものに変換する技術が必要とされてきている。
【００１４】
このような変換技術の一例として、下記特許文献１に開示された方法が提案されている。この方法では、脳の立体模型データから自施設の条件設定下での断層画像を取得し（解剖学的標準化）、他施設で取得された断層画像に対し、自施設と他施設の解剖学的標準化に係る断層画像の差につき画素毎に係数化したものを用いて補正をかける。
【００１５】
【特許文献１】
特開２００３−１０７１６１公報
【００１６】
【発明が解決しようとする課題】
特許文献１の補正方法では、散乱線補正以外の因子に対する補正も考慮されたものとなってはいるが、他施設の異なる条件毎に脳立体模型データの断層画像に係る測定ないし計算が必要となり、煩わしい。また、脳模型データないし解剖学的標準化では、実際の被検者の脳に存在する形状、吸収や散乱の度合等の個人差が反映されないため、変換の精度自体にも限界がある。
【００１７】
そこで、請求項１，請求項４，請求項７に記載の発明は、どのような施設で取得された断層画像に対しても、実際の散乱現象に近い散乱関数を採用して、散乱線についての補正を事後において（経験に依らず）同程度の（良好な）精度で（個人差に配慮して）施して、広く他施設の利用に供することのできるＳＰＥＣＴ断層画像補正方法，システム，プログラムを提供することを目的としたものである。
【００１８】
【課題を解決するための手段】
上記目的を達成するために、請求項１に記載の発明は、ＳＰＥＣＴ断層画像補正方法にあって、任意の減弱係数における吸収補正がなされたＳＰＥＣＴ断層画像を補正開始画像として、原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得る第１ステップと、

補正開始画像から推定散乱線画像を減じて中間画像を得る第２ステップと、吸収補正時に採用された減弱係数に係る吸収補正因子画像を分母とし、ほぼ理想値の減弱係数に係る吸収補正因子画像を分子とした吸収補正因子画像比を中間画像に乗じて補正画像を得る第３ステップとを含むことを特徴とするものである。
【００２０】
請求項２に記載の発明は、上記目的に加えて、散乱の影響をできるだけ取除いて精度をより高くする目的を達成するため、上記発明において、第１ステップおよび第２ステップに代えて、原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成し、

第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成し、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成し、第ｎ中間画像（ｎ≧２）の何れかを中間画像とすることを特徴とする。
【００２１】
請求項３に記載の発明は、上記目的に加えて、各位置における散乱線率を考慮に入れて精度をより高くする目的を達成するため、上記発明において、第１ステップおよび第２ステップに代えて、原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得、これを補正開始画像から減じて中間画像を作成するにあたり、

または上記散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成するにあたり、または第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成するにあたり、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成するにあたり、吸収補正時に採用された減弱係数に係る吸収補正因子画像からシミュレーションまたは実験を用いて算出される散乱線率画像を、推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）に乗算して調整された推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）を得、補正開始画像から調整された推定散乱線画像または調整された第ｎ推定散乱線画像（ｎ≧１）を減ずることで、中間画像または第ｎ中間画像（ｎ≧１）を得、第ｎ中間画像（ｎ≧２）を得た場合には、第ｎ中間画像（ｎ≧２）の何れかを中間画像とすることを特徴とする。
【００２２】
上記目的を達成するために、請求項４に記載の第２発明は、ＳＰＥＣＴ断層画像補正システムにあって、任意の減弱係数における吸収補正がなされたＳＰＥＣＴ断層画像である補正開始画像の入力を受付ける入力装置と、（１）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得る散乱線演算指令部

（２）補正開始画像から推定散乱線画像を減じて中間画像を得る中間画像演算指令部、および（３）吸収補正時に採用された減弱係数に係る吸収補正因子画像を分母とし、ほぼ理想値の減弱係数に係る吸収補正因子画像を分子とした吸収補正因子画像比を中間画像に乗じて補正画像を得る比乗算指令部の各部を備えるプログラムを実行して補正開始画像から補正画像を得る演算装置と、補正画像を出力する出力装置とを含むことを特徴とするものである。
【００２４】
請求項５に記載の発明は、上記目的に加えて、散乱の影響をできるだけ取除いて精度をより高くする目的を達成するため、上記発明において、（１）および（２）に代えて、プログラムが（４）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成し、

第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成し、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成し、第ｎ中間画像（ｎ≧２）の何れかを中間画像とする繰返し指令部を備えることを特徴とする。
【００２５】
請求項６に記載の発明は、上記目的に加えて、各位置における散乱線率を考慮に入れて精度をより高くする目的を達成するため、上記発明において、（１）および（２）に代えて、プログラムが（５）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得、これを補正開始画像から減じて中間画像を作成するにあたり、

または上記散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成するにあたり、または第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成するにあたり、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成するにあたり、吸収補正時に採用された減弱係数に係る吸収補正因子画像からシミュレーションまたは実験を用いて算出される散乱線率画像を、推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）に乗算して調整された推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）を得、補正開始画像から調整された推定散乱線画像または調整された第ｎ推定散乱線画像（ｎ≧１）を減ずることで、中間画像または第ｎ中間画像（ｎ≧１）を得、第ｎ中間画像（ｎ≧２）を得た場合には、第ｎ中間画像（ｎ≧２）の何れかを中間画像とする散乱線調整指令部を備えることを特徴とする。
【００２６】
上記目的を達成するために、請求項７に記載の第３発明は、ＳＰＥＣＴ断層画像補正プログラムにあって、（１）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得る散乱線演算指令部

（２）補正開始画像から推定散乱線画像を減じて中間画像を得る中間画像演算指令部、および（３）吸収補正時に採用された減弱係数に係る吸収補正因子画像を分母とし、ほぼ理想値の減弱係数に係る吸収補正因子画像を分子とした吸収補正因子画像比を中間画像に乗じて補正画像を得る比乗算指令部の各部を備え、実行により任意の減弱係数における吸収補正がなされたＳＰＥＣＴ断層画像である補正開始画像から補正画像が得られることを特徴とするものである。
【００２８】
請求項８に記載の発明は、上記目的に加えて、散乱の影響をできるだけ取除いて精度をより高くする目的を達成するため、上記発明において、（１）および（２）に代えて、（４）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成し、

第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成し、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成し、第ｎ中間画像（ｎ≧２）の何れかを中間画像とする繰返し指令部を備えることを特徴とする。
【００２９】
請求項９に記載の発明は、上記目的に加えて、各位置における散乱線率を考慮に入れて精度をより高くする目的を達成するため、上記発明において、（１）および（２）に代えて、（５）原点からの距離に依存して単調減少する関数であって次に示す数式の右辺またはその何れかの項で示されるものである散乱関数と補正開始画像とで畳込み積分を行い、推定散乱線画像を得、これを補正開始画像から減じて中間画像を作成するにあたり、

または上記散乱関数と補正開始画像との畳込み積分から第１推定散乱線画像を得、これを補正開始画像から減じて第１中間画像を作成するにあたり、または第１中間画像と上記散乱関数との畳込み積分から第２推定散乱線画像を得、これを補正開始画像から減じて第２中間画像を作成するにあたり、またはこれらを繰返して第ｎ中間画像（ｎ＞２）を作成するにあたり、吸収補正時に採用された減弱係数に係る吸収補正因子画像からシミュレーションまたは実験を用いて算出される散乱線率画像を、推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）に乗算して調整された推定散乱線画像または第ｎ推定散乱線画像（ｎ≧１）を得、補正開始画像から調整された推定散乱線画像または調整された第ｎ推定散乱線画像（ｎ≧１）を減ずることで、中間画像または第ｎ中間画像（ｎ≧１）を得、第ｎ中間画像（ｎ≧２）を得た場合には、第ｎ中間画像（ｎ≧２）の何れかを中間画像とす
る散乱線調整指令部を備えることを特徴とする。
【００３０】
なお「任意の減弱係数」は、断層画像取得施設あるいは吸収補正を施した施設が採用した減弱係数の値に対応し得る。
【００３１】
【発明の実施の形態】
以下、本発明の一実施形態に係るＳＰＥＣＴ断層画像補正方法（本方法）、ＳＰＥＣＴ断層画像補正システム（本システム）、およびＳＰＥＣＴ断層画像補正プログラム（本プログラム）について、次に示す目次の順序に従い、適宜図面に基づいて説明する。
（Ａ）本方法の大要
（Ｂ）本システムの外的側面
（Ｃ）本システムの内的側面ないし本プログラムの構成的側面
（Ｄ）本方法の内容、本システムの動作内容ないし本プログラムの動作内容
（Ｅ）本方法、本システムないし本プログラムが奏する効果
（Ｆ）主に上記実施形態を変更してなる本発明の実施形態の例示
【００３２】
（Ａ）本方法の大要
本方法における主要な目標は、ＴＥＷ法等による散乱線補正なしに再構成された断層画像を、ＴＥＷ法等による散乱線補正後に再構成された断層画像と同程度まで、断層画像の再構成後に演算でもって散乱線補正することである。
【００３３】
本方法における補正対象のＳＰＥＣＴ断層画像（補正開始画像）は、ＴＥＷ法等による散乱線補正なしに再構成された断層画像である。ここで、この断層画像には、吸収補正が施される。吸収補正は、ガンマ線が被験者内で吸収されることで減ってしまう計数値を演算により補うもので、上記［数１］の関係を満たす、ガンマ線の有するエネルギーおよび物質に固有の減弱係数μを用いる。
【００３４】
吸収補正の例としては、断層画像の再構成後に実行され、閾値処理で描出した体輪郭情報に基づき、各画素につき投影方向における減弱距離ｔと減弱係数μとから求めた平均ガンマ線透過率の逆数とした吸収補正因子画像ＡＣＦ_broad を作成し、これを断層画像に対し画素毎に乗算するChang法が知られている。
【００３５】
また、このような吸収補正にあって、擬似的な散乱線補正を行うため、減弱係数μを理想値（例えば上記０．１４６ｃｍ^-1）から若干減らす（例えばある施設では０．０９ｃｍ^-1）ことが施設毎に行われている。減弱係数μを減らした分、［数１］において計数値Ｉから算出される補正値Ｉ_０が少なくなり、散乱線によって増加した計数値Ｉの影響を経験的に減らせる。
【００３６】
なお、吸収補正は、ガンマ線を計数する（断層画像を取得する）施設において、断層画像の再構成直後に行われることが多いが、この施設とは異なる施設において行われても良く、次に示す本方法の主要部の前であればいつ行われるかを問わない。例えば、本方法の主要部に係る演算を行う他施設において、演算の直前に吸収補正を行っても良い。
【００３７】
そして本方法の主要部では、まず、補正開始画像Ｉ_ＡＣ(ｒ)と散乱関数Ｓとで畳込み積分を行い、補正開始画像Ｉ_ＡＣ(ｒ)とは別個の第１推定散乱線画像Ｉ_ｓ ^{< １ >}(ｒ)を得る。ここで、散乱関数Ｓ(Ｒ)は、座標原点からの距離Ｒが増加するほど減少する（Ｒ＝０を頂点としＲに依存して単調減少する）関数で、例えば次に示す［数２］、または［数２］の何れかの項（以下第１項を「モノｅｘｐ項」第２項を「ガウス項」という）が挙げられる。また、畳込み積分は［数３］（フーリエ変換，Fourier Transform，ＦＴ）のように表される。
【００３８】
【数２】

【数３】

【００３９】
このように第１推定散乱線画像Ｉ_ｓ ^{< １ >}(ｒ)を得ると、補正開始画像Ｉ_ＡＣ(ｒ)から第１推定散乱線画像Ｉ_ｓ ^{< １ >}(ｒ)を対応する画素毎に減算し、第１中間画像Ｉ_ＡＣＭＤ ^{< １ >}(ｒ)を得る（［数４］）。そして、第１中間画像Ｉ_ＡＣＭＤ ^{< １ >}(ｒ)を中間画像Ｉ_ＡＣＭＤ(ｒ)とする。中間画像Ｉ_ＡＣＭＤ(ｒ)にあっては、散乱線が大部分除去されたものとなっている。
【００４０】
【数４】

【００４１】
なお、第１中間画像Ｉ_ＡＣＭＤ ^{< １ >}(ｒ)と散乱関数Ｓとから第２推定散乱線画像Ｉ_ｓ ^{< ２ >}(ｒ)を得、補正開始画像Ｉ_ＡＣ(ｒ)から減じて第２中間画像Ｉ_ＡＣＭＤ ^{< ２ >}(ｒ)を得てこれを中間画像Ｉ_ＡＣＭＤ(ｒ)とするか、あるいはこれを繰返して第ｎ中間画像Ｉ_ＡＣＭＤ ^{< ｎ >}(ｒ)から第ｎ＋１散乱線画像Ｉ_ｓ ^{< ｎ＋１ >}(ｒ)を得（［数５］）、補正開始画像Ｉ_ＡＣ(ｒ)から減じて第ｎ＋１中間画像Ｉ_ＡＣＭＤ ^{< ｎ＋１ >}(ｒ)を得て（［数６］）これを中間画像Ｉ_ＡＣＭＤ(ｒ)とすることが好ましく、この場合、計算量との兼合いから、ｎ＝１〜４が好ましい。
【００４２】
【数５】

【数６】

【００４３】
また、上記各推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)と［数７］のような散乱線率画像ＳＦ(ｒ)とを画素毎に乗算して、各推定散乱線画像Ｉ_ｓ(ｒ)を調整し、この調整された推定散乱線画像ＳＦ(ｒ)・Ｉ_ｓ(ｒ)を補正開始画像Ｉ_ＡＣ(ｒ)から減じて中間画像Ｉ_ＡＣＭＤ(ｒ)を得るのがより好ましい（［数８］）。
【００４４】
【数７】

【数８】

【００４５】
以上によって散乱線の影響を十分に緩和できるので、次に、減弱係数μを理想値とした状態で吸収補正をし直し、本方法による補正画像Ｉ_ＡＣＳＣ(ｒ)を得る。即ち、まず、理想値の減弱係数μにおいて、Chang法等により、補正開始画像Ｉ_ＡＣ(ｒ)から吸収補正因子画像ＡＣＦ_narrowを作成する。そして、中間画像について、施設において採用された減弱係数μに基づく吸収補正因子画像ＡＣＦ_broadで対応画素毎に除算し、吸収補正因子画像ＡＣＦ_narrowを対応画素毎に乗算する（中間画像に対する吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad の乗算、［数９］）。
【００４６】
【数９】

【００４７】
このように、本方法にあっては（ａ）ＴＥＷ法等による散乱線補正がなされない断層画像Ｉ_ＡＣ(ｒ)から、散乱関数Ｓとの畳込み積分を用いて推定散乱線画像Ｉ_ｓ(ｒ)を抽出し、これを断層画像Ｉ_ＡＣ(ｒ)から減算し、更に（ｂ）吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad を乗算することで、様々な施設において取得された散乱線補正されない断層画像Ｉ_ＡＣ(ｒ)から、施設間格差の殆ど存在しない、ＴＥＷ法等と同水準の散乱線補正された断層画像Ｉ_ＡＣＳＣ(ｒ)を、放射性医薬品の再投与、ガンマ線の再計数および断層画像の再々構成なしに得ることができる。
【００４８】
（Ｂ）本システムの外的側面
上記のような本方法を実行可能である本システムを図１に示す。本システム１は、本プログラムとしての補正プログラム２や補正開始画像Ｉ_ＡＣ(ｒ)等を格納する記憶装置６と、補正プログラム２を読出して実行する演算装置１０と、演算装置１０に対する入力装置１２および出力装置１４とを備える。
【００４９】
なお、記憶装置６の具体例としてハードディスク、ＲＡＭ、ＲＯＭまたはこれらの組合わせが挙げられ、演算装置１０の具体例としてＲＡＭおよびＣＰＵが挙げられ、入力装置１２の具体例としてキーボード、ポインティングデバイス、通信装置、リムーバブルディスクまたはこれらの組合わせが挙げられ、出力装置１４の具体例としてディスプレイ、プリンタ、通信装置またはこれらの組合わせが挙げられる。
【００５０】
（Ｃ）本システムの内的側面ないし本プログラムの構成的側面
記憶装置６に格納される補正プログラム２は、図２に示すように、Chang法等により補正開始画像Ｉ_ＡＣ(ｒ)から計数施設で採用された減弱係数μを用いて吸収補正因子画像ＡＣＦ_broad を算出し記憶装置６における保存を指令する第１因子演算指令部２０と、Chang法等により補正開始画像Ｉ_ＡＣ(ｒ)から理想値である減弱係数μ（例えばμ＝０．１４６）を用いて吸収補正因子画像ＡＣＦ_narrowを作成する第２因子演算指令部２１と、［数７］の散乱線率画像ＳＦ(ｒ)を吸収補正因子画像ＡＣＦ_broad 等から算出して保存する散乱線率演算指令部２２とを含む。
【００５１】
また、補正プログラム２は、補正開始画像Ｉ_ＡＣ(ｒ)または第ｎ中間画像Ｉ_ＡＣＭＤ ^{< ｎ >}(ｒ)を対象に［数３］の計算を経た第１推定散乱線画像Ｉ_ｓ ^{< １ >}(ｒ)または第ｎ＋１推定散乱線画像Ｉ_ｓ ^{< ｎ＋１ >}(ｒ)の算出および保存を指令する散乱線演算指令部２３（［数３］，［数５］）を含んでいる。
【００５２】
更に、補正プログラム２は、［数８］の最右項のように、第ｎ推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)と散乱線率画像ＳＦ(ｒ)から調整された第ｎ推定散乱線画像ＳＦ(ｒ)・Ｉ_ｓ ^{< ｎ >}(ｒ)を算出し保存する散乱線調整指令部２４と、［数８］のように、第ｎ推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)と散乱線率画像ＳＦ(ｒ)との積を補正開始画像Ｉ_ＡＣ(ｒ)から引いて第ｎ中間画像Ｉ_ＡＣＭＤ ^{< ｎ >}(ｒ)を算出する中間画像演算指令部２５を含む。
【００５３】
また更に、補正プログラム２は、第ｋ中間画像Ｉ_ＡＣＭＤ ^{< ｋ >}(ｒ)の算出までの繰返しを指令する繰返し指令部２６とを含んでいる。なお、繰返し回数ｋは入力装置１２等を介した指示により容易に変更することができる。
【００５４】
加えて、補正プログラム２は、［数９］のように、中間画像Ｉ_ＡＣＭＤ(ｒ)｛＝Ｉ_ＡＣＭＤ ^{< ｋ >}(ｒ)｝に吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad を乗算し補正画像として保存する比乗算指令部３０を含んでいる。
【００５５】
（Ｄ）本方法の内容、本システムの動作内容ないし本プログラムの動作内容
図３に示すように、本システム１の演算装置１０において実行される補正プログラム２によって実施される本方法では、まず、補正開始画像Ｉ_ＡＣ(ｒ)について同施設または異施設から入力装置１２を介して入力する（ステップ５０，例として図４（１），図４につき以下同様）。なおここでは、位置ｒや畳込み積分は全て３次元により計算するものとする。
【００５６】
ここで、補正開始画像Ｉ_ＡＣ(ｒ)には、主に施設毎に固有の減弱係数μに基づきChang法等の吸収補正のみが施される。また、当該減弱係数μの入力を受付け、これに基づく吸収補正因子画像ＡＣＦ_broad を、第１因子演算指令部２０の実行により作成する（ステップ５２，図４（３））。更に、理想的な減弱係数μを参照し、第２因子演算指令部２１の実行により、補正開始画像Ｉ_ＡＣ(ｒ)から吸収補正因子画像ＡＣＦ_narrowを作成する（ステップ５４）。
【００５７】
次に、散乱線率演算指令部２２の実行により、［数７］に基づき吸収補正因子画像ＡＣＦ_broad から散乱線率画像ＳＦ(ｒ)を作成する（ステップ５６）。
【００５８】
なお、定数Ａ，Ｂ，Ｃ，β，γは、モンテカルロ法による計算シミュレーション（例えば Yuuichiro Narita et al, Monte Carlo and experimental evaluation of accuracy and noise properties of two scatter correction methods for SPECT, Phys. Med. Biol. vol.41 (1996) p.2481-2496 参照）等により求め、入力しておく。
【００５９】
続いて、適正な範囲で入力された繰返し回数ｋによる繰返し制御の開始を指令する（ステップ６０）。
【００６０】
繰返し制御内の当初において、散乱線演算指令部２３の実行により、［数８］（ｎは繰返し制御による）に基づいて補正開始画像Ｉ_ＡＣ(ｒ)（ｎ＝１）または第ｎ−１中間画像Ｉ_ＡＣＭＤ ^{< ｎ−１ >}(ｒ)（ｎ≧２）と散乱関数Ｓとを畳込み積分して推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)を得、更に散乱線調整指令部２４の実行により、散乱線率画像ＳＦ(ｒ)を乗算して、調整された推定散乱線画像ＳＦ(ｒ)・Ｉ_ｓ ^{< ｎ >}(ｒ)を得る（ステップ６２，ｎ＝１につき図４（５））。
【００６１】
なお、定数ａ_１，ａ_２，ｂ_１，ｂ_２は、ＴＥＷ法による補正画像も得られる補正開始画像Ｉ_ＡＣ(ｒ)について本発明に係る補正画像を得て、補正画像同士を比較するシミュレーションを１回ないし複数回行うことで定められる。
【００６２】
また、散乱線率画像ＳＦ(ｒ)は、吸収され易い部位ほど散乱もし易いという関連性に着目して、各位置における吸収の度合を示す吸収補正因子画像から算出されるもので、これと第ｎ推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)とを乗算することで第ｎ推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)の影響（畳込み積分の影響）を、各部位の特性に応じて調整することができるものである。
【００６３】
次に、中間画像演算指令部２５の実行により、調整された推定散乱線画像ＳＦ(ｒ)・Ｉ_ｓ ^{< ｎ >}(ｒ)を補正開始画像Ｉ_ＡＣ(ｒ)から減じて第ｎ中間画像Ｉ_ＡＣＭＤ ^{< ｎ >}(ｒ)を作成し（ステップ６４，［数４］，［数６］）、繰返し制御をｎ＝ｋの完了まで行い（ステップ６６）、中間画像Ｉ_ＡＣＭＤ(ｒ)を作成する（図４（６））。
【００６４】
そして、比乗算指令部３０の実行により、作成された中間画像Ｉ_ＡＣＭＤ(ｒ)に吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad （図４（４））を乗算し、補正画像Ｉ_ＡＣＳＣ(ｒ)を取得する（ステップ７０，［数９］，図４（７））。補正画像Ｉ_ＡＣＳＣ(ｒ)は、画素毎の値の大きさに対応した色あるいは濃度等で出力装置１４から出力される。
【００６５】
（Ｅ）本方法、本システムないし本プログラムが奏する効果
以上のように、本方法等では、散乱関数Ｓとの畳込み積分により推定散乱線画像Ｉ_ｓ(ｒ)を得、これを補正開始画像Ｉ_ＡＣ(ｒ)から減じて中間画像Ｉ_ＡＣＭＤ(ｒ)を得、吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad を中間画像Ｉ_ＡＣＭＤ(ｒ)に乗じて補正画像Ｉ_ＡＣＳＣ(ｒ)を得るため、図４，図５に示すように、ＴＥＷ法に係る散乱線補正がなされず、減弱係数μとして任意値が採用された補正開始画像Ｉ_ＡＣ(ｒ)から、ＴＥＷ法に係る補正画像と同等の補正がなされた補正画像Ｉ_ＡＣＳＣ(ｒ)を作成することができる。
【００６６】
特に、図５の例では、矢印で示す部位が、補正開始画像Ｉ_ＡＣ(ｒ)に比べてよりＴＥＷ法による散乱線補正画像に近づいており、本方法等に係る補正画像Ｉ_ＡＣＳＣ(ｒ)の診断における利用価値は高い。
【００６７】
また、次に示す［表１］は、放射性医薬品^９９ｍＴｃ−ＥＣＤ（エチルシステイネートダイマー）を用いたＳＰＥＣＴ撮影により５人の被検者から取得した５種類の各画像（補正開始画像）につき（ｎ＝５）、個別にＴＥＷ法による補正画像および補正画像Ｉ_ＡＣＳＣ(ｒ)を作成し、最上行に示す関心領域の対小脳比を補正開始画像Ｉ_ＡＣ(ｒ)ともども個々に得てこれらの平均を並べ、また統計解析「paired t-test(one-side)」（一標本ｔ検定，パラメトリック法，有意水準の確率ｐは０．０１を基準とする）により、補正開始画像Ｉ_ＡＣ(ｒ)の群または補正画像Ｉ_ＡＣＳＣ(ｒ)の群とＴＥＷ法の群との比較をそれぞれ関心領域毎に行い、有意な差がある場合（ｐ＜０．０１）に印「＊」を付したものである。
【００６８】
【表１】

【００６９】
［表１］によれば、５箇所の関心領域のうち４箇所についてＴＥＷ法による補正画像の群と有意な差の認められた補正開始画像Ｉ_ＡＣ(ｒ)の群から、本発明により補正画像Ｉ_ＡＣＳＣ(ｒ)の群を求め、ＴＥＷ法による補正画像の群と統計解析をしたところ、全ての関心領域において有意な差は認められない。よって［表１］からも、本発明の補正画像Ｉ_ＡＣＳＣ(ｒ)が事後に得られるものでありながら、ＴＥＷ法の水準に達し、本発明の補正が有効なものであることが分る。
【００７０】
そして、本方法等では、散乱関数Ｓに係る畳込み積分により散乱線の除去した上で吸収補正因子画像比ＡＣＦ_narrow／ＡＣＦ_broad を乗ずるので、各施設においてどのような減弱係数μの値が採用されたとしても、同様に高画質の補正画像Ｉ_ＡＣＳＣ(ｒ)を得ることができ、異施設での光子計数や画像再構成を無駄にすることなく、極めて読影し易い補正画像Ｉ_ＡＣＳＣ(ｒ)を診断用に提供することができる。
【００７１】
また、本方法等では、散乱関数Ｓを［数２］またはそのモノｅｘｐ項もしくはガウス項としたため、散乱関数Ｓを実際の散乱現象に近い理想的な分布にすることができ、更なる補正精度の向上を図ることができる。
【００７２】
更に、本方法等では、演算の繰返しにより第ｎ中間画像Ｉ_ＡＣＭＤ ^{< ｎ >}(ｒ)（ｎ＞１）を求めるため、散乱の影響を繰返し取除くことができ、一層の補正精度向上を図ることができる。
【００７３】
加えて、本方法等では、散乱線率画像ＳＦ(ｒ)と第ｎ推定散乱線画像Ｉ_ｓ ^{< ｎ >}(ｒ)（ｎ≧１）とを乗算するため、各位置における散乱のし易さを反映させることができ、精度をより一層高くすることができる。
【００７４】
（Ｆ）主に上記実施形態を変更してなる本発明の実施形態の例示
本発明は、次の［表２］の最左列に示す上記本方法等の要素を、それぞれその右側の何れかに変えて得られるようなバリエーションを有する。
【００７５】
【表２】

【００７６】
即ち、散乱関数として［数２］の各項の何れかとすることができる。なお、散乱関数として、原点を頂点とした他の単調減少関数を採用することもできるし、座標系として２次元を採用することもできる。
【００７７】
また、散乱率を畳込み積分値に乗算しないバリエーションや、一定値を乗ずるバリエーションが存在する。更に、第ｎ中間画像（ｎ≧２）を求めていく反復計算をしなかったり（即ちｎ＝１の場合）、任意の反復計算数としたりすることが可能である。加えて、畳込み積分を、周波数領域で行うＦＴを利用するものの代りに実空間で行う離散フーリエ変換を利用するものにしたり、これらのうちの何れかにおいて２次元における計算を用いるものにしたりする。なお、ＦＴとして、ＦＦＴ（Fast Fourier Transform）を採用することができる。
【００７８】
なお、次に示す状態で求めた本発明に係る補正画像を図６に示す。
（１）散乱関数［数２］，散乱率［数７］，反復計算ｎ＝５，３次元ＦＴ
（２）散乱関数［数２］，散乱率固定，反復計算なし，２次元ＦＴ
（３）散乱関数モノｅｘｐ項，散乱率［数７］，反復計算なし，３次元ＦＴ
（４）散乱関数モノｅｘｐ項，散乱率固定，反復計算ｎ＝５，３次元ＦＴ
（５）散乱関数［数２］，散乱率［数７］，反復計算なし，２次元ＦＴ
【００７９】
加えて、本方法等と同等な他の演算を採用したり、本システムの構成を同等なものに変えたり、本方法等における処理の順序を入替えたりする。特に、吸収補正因子画像比を先に求めておいたり、各数式を適宜一体化した状態で一括計算したりする。また更に、各種定数を、使用する放射性核種に応じて適宜実験により求める。
【００８０】
また、本方法等を心臓を始めとする他の部位についての画像の補正に利用する。更に、本プログラムを、記録媒体に格納して、あるいは通信により配布する。
【００８１】
【発明の効果】
本発明によれば、散乱関数との畳込み積分により推定散乱線画像を得、補正開始画像から減じて中間画像を得、吸収補正因子画像比を中間画像に乗じて補正画像を得、あるいは更に精度を求めて演算を施している。よって、何れの施設において取得された断層画像について事後に高品位に補正し、様々な施設の有効な利用に供させ、施設間の適切な医療情報の授受という時代の要請に応える、という優れた効果を奏する。
【図面の簡単な説明】
【図１】本発明に係るシステムのブロック図である。
【図２】本発明に係るプログラムのブロック図である。
【図３】本発明に係る方法等のフローチャートである。
【図４】補正開始画像、中間画像、補正画像等を示す図である。
【図５】ＴＥＷ法（３ウィンドウ方式）に係る補正画像、補正開始画像、本発明に係る補正画像を示す図である。
【図６】本発明のバリエーションに係る補正画像を示す図である。
【符号の説明】
１・・システム、２・・補正プログラム、６・・記憶装置、１０・・演算装置、１２・・入力装置、１４・・出力装置、２０・・第１因子演算指令部、２１・・第２因子演算指令部、２２・・散乱線率演算指令部、２３・・散乱線演算指令部、２４・・散乱線調整指令部、２５・・中間画像演算指令部、２６・・繰返し指令部、３０・・比乗算指令部。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a correction method, system, and program for a tomographic image once obtained by SPECT (Single Photon Emission Computed Tomography).
[0002]
[Prior art]
In SPECT, a radiopharmaceutical labeled with a radioisotope that emits a gamma ray having a specific energy value is administered to the subject, and a gamma ray is detected on a two-dimensional detection surface, and a detector around the subject is used. The gamma rays emitted from the subject in each direction are counted in association with their energy values, and a tomographic image is reconstructed using the count value distribution on the detection surface in each direction.
[0003]
Here, with respect to gamma rays, absorption by the body tissue (transmitting substance) of the subject and scattering due to the Compton effect and the like occur with a probability depending on the energy and the transmitting substance. Therefore, a general SPECT apparatus that performs gamma ray counting and image reconstruction performs absorption correction that compensates for a decrease in the count value due to absorption, and scattered ray correction that removes unnecessary count values due to scattered radiation. Software or hardware to perform numerical values is provided.
[0004]
In SPECT, a main window is set for counting gamma rays. The main window is a predetermined energy range including the gamma rays of the intrinsic energy value, and is set for the purpose of counting only the gamma rays in this range. The reason why the gamma rays relating to the energy within the range of the main window are counted without counting only those relating to the intrinsic energy values corresponding to the gamma rays is as follows. That is, because of the energy resolution of the detector, even gamma rays related to intrinsic energy values may be detected as gamma rays related to slightly different energy.
[0005]
However, since the main window is set, scattered rays that have lost energy are mixed. In image reconstruction, in principle, all count values are processed as those relating to gamma rays that have traveled straight, so that the count values based on mixed scattered radiation are completely unnecessary.
[0006]
Therefore, as a scattered ray correction, there has been proposed a method for estimating scattered rays in the main window and actively reducing the count value. The value to be reduced is proportional to the count value in the sub-window set to a lower energy range than the main window (two-window method), or estimated from the count value in the sub-window set on both sides of the main window (three-window method) , TEW method). Thereby, although it is not exact | strict, the influence by a scattered radiation can be excluded to such an extent that it can be used for a clinical diagnosis.
[0007]
However, these scattered ray corrections require counting in the gamma ray sub-window. Software or hardware corresponding to such counting or scattered radiation correction is beginning to be installed in recent SPECT apparatuses. Therefore, in a facility that does not have such software or hardware, a tomographic image is reconstructed without correction of scattered radiation from the count values in only the main window.
[0008]
Even in a facility having such software or hardware, the scattered radiation correction may not be performed because a sufficient image can be obtained in the facility by the following device.
[0009]
That is, even with reconstruction using only the main window, a tomographic image that can be interpreted to some extent can be obtained by the device operator's original device in the facility. This contrivance is appropriately performed in conjunction with the absorption correction using the attenuation coefficient in [Equation 1] shown below.
[0010]
[Expression 1]

[0011]
That is, an ideal value (for example, about 0.146 cm in the case of water for 160 keV gamma rays as an attenuation coefficient μ at the time of absorption correction.^-1), The count value is supplemented to the unnecessary count due to scattered radiation, and the correction is excessive. Therefore, it is assumed that the absorption is low, the attenuation coefficient μ is slightly reduced from the ideal value, and the fault Let the image be close to the true count value.
[0012]
However, useful interpretation is difficult even if this tomographic image is to be used in another facility. This is because the value of the attenuation coefficient μ decreased at the time of tomographic image reconstruction is determined empirically as described above, so the attenuation coefficient μ adopted in the other facility is the attenuation coefficient in the tomographic image acquisition facility. This is because it is often different from μ and the degree of scattered ray correction is different.
[0013]
Therefore, when a subject is transferred between facilities that adopt different attenuation coefficients or between facilities that have different corrections for scattered radiation, the tomographic images will be re-acquired. It also takes time and effort. Therefore, there is a need for a technique for converting tomographic images acquired at other facilities into those that are worthy of interpretation by calculation.
[0014]
As an example of such a conversion technique, a method disclosed in Patent Document 1 below has been proposed. In this method, a tomographic image under the condition setting of the institution is acquired from the brain model data (anatomical standardization), and the anatomical data of the institution and the other institution is obtained from the tomographic image acquired in the other institution. Correction is performed using a coefficient obtained for each pixel with respect to a difference in tomographic images related to standardization.
[0015]
[Patent Document 1]
JP 2003-107161 A
[0016]
[Problems to be solved by the invention]
In the correction method of Patent Document 1, correction for factors other than the scattered radiation correction is also considered, but measurement or calculation related to a tomographic image of brain stereo model data is required for each different condition of other facilities. ,troublesome. In addition, brain model data or anatomical standardization does not reflect individual differences such as the shape of the actual subject's brain, the degree of absorption or scattering, and so there is a limit to the conversion accuracy itself.
[0017]
  Therefore, claim 1,Claims 4 and 7The invention described in, for tomographic images acquired at any facility,Adopting a scattering function close to the actual scattering phenomenon,A SPECT tomographic image correction method that can be used for other facilities widely, with subsequent corrections (regardless of experience) with the same (good) accuracy (considering individual differences), The purpose is to provide systems and programs.
[0018]
[Means for Solving the Problems]
  To achieve the above object, the invention according to claim 1 is a SPECT tomographic image correction method, wherein a SPECT tomographic image subjected to absorption correction at an arbitrary attenuation coefficient is used as a correction start image at a distance from the origin. Monotonically decreasing depending onA function that is indicated by the right side of the following formula or any of its termsConvolution integration is performed between the scattering function and the correction start image, and an estimated scattered radiation image is obtained.FirstSteps,

Subtract the estimated scattered radiation image from the correction start image to obtain an intermediate imageSecondThe correction image is obtained by multiplying the intermediate image by the absorption correction factor image ratio using the absorption correction factor image relating to the step and the attenuation coefficient adopted at the time of the absorption correction as the denominator and the numerator of the absorption correction factor image relating to the substantially ideal attenuation coefficient. GetThirdIncluding a step.
[0020]
  Claim 2In order to achieve the purpose of further improving the accuracy by removing the influence of scattering as much as possible in addition to the above object,Instead of the first step and the second step, a scattering function and a correction start image which are functions that monotonously decrease depending on the distance from the origin and are represented by the right side of the following mathematical expression or any term thereof: WhenA first estimated scattered radiation image is obtained from the convolution integral of the above, and this is subtracted from the correction start image to create a first intermediate image,

With the first intermediate imagethe aboveA second estimated scattered radiation image is obtained from the convolution integral with the scattering function, and this is subtracted from the correction start image to create a second intermediate image, or these are repeated to create an nth intermediate image (n> 2). Any one of the nth intermediate images (n ≧ 2) is used as an intermediate image.
[0021]
  Claim 3In addition to the above-mentioned object, the invention described in the above-described invention achieves the object of increasing the accuracy by taking into account the scattered radiation rate at each position.Instead of the first step and the second step, a scattering function and a correction start image which are functions that monotonously decrease depending on the distance from the origin and are represented by the right side of the following mathematical expression or any term thereof: And convolution integration to obtain an estimated scattered radiation image and subtract this from the correction start image to create an intermediate image.

Alternatively, when the first estimated scattered radiation image is obtained from the convolution integral of the scattering function and the correction start image and is subtracted from the correction start image to create the first intermediate image, or the first intermediate image and the scattering function In obtaining the second estimated scattered radiation image from the convolution integral of and subtracting this from the correction start image to create the second intermediate image, or repeating these to create the nth intermediate image (n> 2),Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction An adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1) is obtained, and the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) is subtracted from the correction start image. Thus, an intermediate image or an nth intermediate image (n ≧ 1) is obtained.When the nth intermediate image (n ≧ 2) is obtained, any one of the nth intermediate images (n ≧ 2) is set as the intermediate image.It is characterized by that.
[0022]
  To achieve the above objective,Claim 4A second aspect of the invention is a SPECT tomographic image correction system, wherein the input device receives an input of a correction start image that is a SPECT tomographic image subjected to absorption correction at an arbitrary attenuation coefficient, and (1) a distance from the origin. Monotonically decreasing depending onA function that is indicated by the right side of the following formula or any of its termsScattered ray calculation command unit that obtains an estimated scattered ray image by performing convolution integration with the scattering function and the correction start image

(2) An intermediate image calculation command unit that obtains an intermediate image by subtracting the estimated scattered radiation image from the correction start image, and (3) an absorption correction factor image related to the attenuation coefficient employed at the time of absorption correction is used as a denominator, Arithmetic apparatus for obtaining a corrected image from a correction start image by executing a program including each unit of a ratio multiplication command unit that obtains a corrected image by multiplying an intermediate image by an absorption correction factor image ratio using an absorption correction factor image related to an attenuation coefficient as a numerator And an output device for outputting a corrected image.
[0024]
  Claim 5In order to achieve the purpose of further improving the accuracy by removing the influence of scattering as much as possible in addition to the above object,Instead of (1) and (2),The program is (4)A function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any one of the terms, a correction start image,A first estimated scattered radiation image is obtained from the convolution integral of the above, and this is subtracted from the correction start image to create a first intermediate image,

With the first intermediate imagethe aboveA second estimated scattered radiation image is obtained from the convolution integral with the scattering function, and this is subtracted from the correction start image to create a second intermediate image, or these are repeated to create an nth intermediate image (n> 2). In addition, a repetition command unit that uses any one of the nth intermediate images (n ≧ 2) as an intermediate image is provided.
[0025]
  Claim 6In addition to the above-mentioned object, the invention described in the above-described invention achieves the object of increasing the accuracy by taking into account the scattered radiation rate at each position.Instead of (1) and (2),The program is (5)A function that monotonously decreases depending on the distance from the origin, and is a convolution integral between the scattering function that is shown on the right side of the following formula or one of its terms and the correction start image, and the estimated scattered radiation To obtain an image and subtract this from the correction start image to create an intermediate image,

Alternatively, when the first estimated scattered radiation image is obtained from the convolution integral of the scattering function and the correction start image and is subtracted from the correction start image to create the first intermediate image, or the first intermediate image and the scattering function In obtaining the second estimated scattered radiation image from the convolution integral of and subtracting this from the correction start image to create the second intermediate image, or repeating these to create the nth intermediate image (n> 2),Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction An adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1) is obtained, and the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) is subtracted from the correction start image. Thus, an intermediate image or an nth intermediate image (n ≧ 1) is obtained.When the nth intermediate image (n ≧ 2) is obtained, any one of the nth intermediate images (n ≧ 2) is set as the intermediate image.A scattered radiation adjustment command unit.
[0026]
  To achieve the above objective,Claim 7The third aspect of the invention is a SPECT tomographic image correction program, and (1) monotonously decreases depending on the distance from the origin.A function that is indicated by the right side of the following formula or any of its termsScattered ray calculation command unit that obtains an estimated scattered ray image by performing convolution integration with the scattering function and the correction start image

(2) An intermediate image calculation command unit that obtains an intermediate image by subtracting the estimated scattered radiation image from the correction start image, and (3) an absorption correction factor image related to the attenuation coefficient employed at the time of absorption correction is used as a denominator, SPECT tomography that includes each part of a ratio multiplication command unit that obtains a corrected image by multiplying an intermediate image by an absorption correction factor image ratio using an absorption correction factor image related to the attenuation coefficient as a numerator, and has been subjected to absorption correction at an arbitrary attenuation coefficient by execution A correction image is obtained from a correction start image that is an image.
[0028]
  Claim 8In order to achieve the purpose of further improving the accuracy by removing the influence of scattering as much as possible in addition to the above object,Instead of (1) and (2),(4)A function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any one of the terms, a correction start image,A first estimated scattered radiation image is obtained from the convolution integral of the above, and this is subtracted from the correction start image to create a first intermediate image,

With the first intermediate imagethe aboveA second estimated scattered radiation image is obtained from the convolution integral with the scattering function, and this is subtracted from the correction start image to create a second intermediate image, or these are repeated to create an nth intermediate image (n> 2). In addition, a repetition command unit that uses any one of the nth intermediate images (n ≧ 2) as an intermediate image is provided.
[0029]
  Claim 9In addition to the above-mentioned object, the invention described in the above-described invention achieves the object of increasing the accuracy by taking into account the scattered radiation rate at each position.Instead of (1) and (2),(5)A function that monotonously decreases depending on the distance from the origin, and is a convolution integral between the scattering function that is shown on the right side of the following formula or one of its terms and the correction start image, and the estimated scattered radiation To obtain an image and subtract this from the correction start image to create an intermediate image,

Alternatively, when the first estimated scattered radiation image is obtained from the convolution integral of the scattering function and the correction start image and is subtracted from the correction start image to create the first intermediate image, or the first intermediate image and the scattering function In obtaining the second estimated scattered radiation image from the convolution integral of and subtracting this from the correction start image to create the second intermediate image, or repeating these to create the nth intermediate image (n> 2),Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction An adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1) is obtained, and the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) is subtracted from the correction start image. Thus, an intermediate image or an nth intermediate image (n ≧ 1) is obtained.When the nth intermediate image (n ≧ 2) is obtained, any one of the nth intermediate images (n ≧ 2) is set as the intermediate image.
A scattered radiation adjustment command unit.
[0030]
The “arbitrary attenuation coefficient” can correspond to the value of the attenuation coefficient adopted by the tomographic image acquisition facility or the facility subjected to absorption correction.
[0031]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a SPECT tomographic image correction method (this method), a SPECT tomographic image correction system (this system), and a SPECT tomographic image correction program (this program) according to an embodiment of the present invention are according to the following table of contents. This will be described based on the drawings as appropriate.
(A) Outline of this method
(B) External aspects of this system
(C) Internal aspects of this system or structural aspects of this program
(D) Contents of this method, operation contents of this system or operation contents of this program
(E) Effects of the method, the system or the program
(F) Illustrative embodiment of the present invention, which is mainly modified from the above embodiment
[0032]
(A) Outline of this method
The main goal of this method is that the tomographic image reconstructed without correcting the scattered radiation by the TEW method or the like is the same as the tomographic image reconstructed after the scattered radiation correction by the TEW method or the like after the reconstruction of the tomographic image. It is to correct scattered radiation by calculation.
[0033]
The SPECT tomographic image (correction start image) to be corrected in this method is a tomographic image reconstructed without correcting the scattered radiation by the TEW method or the like. Here, the tomographic image is subjected to absorption correction. Absorption correction compensates for the count value that decreases when gamma rays are absorbed within the subject, and uses an attenuation coefficient μ specific to the energy and substance of gamma rays that satisfies the relationship of [Equation 1]. .
[0034]
As an example of the absorption correction, the reciprocal of the average gamma ray transmittance obtained from the attenuation distance t and the attenuation coefficient μ in the projection direction for each pixel is executed after reconstruction of the tomographic image and based on the body contour information drawn by the threshold processing. Absorption correction factor image ACF_broadThe Chang method is known in which a tomographic image is generated and multiplied by a pixel for a tomographic image.
[0035]
Further, in such absorption correction, in order to perform pseudo scattered ray correction, the attenuation coefficient μ is set to an ideal value (for example, the above 0.146 cm).^-1) Slightly reduced (for example, 0.09cm in some facilities)^-1) Is done for each facility. The correction value I calculated from the count value I in [Formula 1] by the amount by which the attenuation coefficient μ is reduced.₀And the influence of the count value I increased by the scattered radiation can be reduced empirically.
[0036]
Absorption correction is often performed immediately after reconstruction of a tomographic image at a facility that counts gamma rays (acquires a tomographic image), but may be performed at a facility different from this facility. It does not matter when it takes place before the main part of the method. For example, absorption correction may be performed immediately before the calculation in another facility that performs the calculation related to the main part of the present method.
[0037]
The main part of the method starts with the correction start image I._ACConvolution integration is performed between (r) and the scattering function S, and the correction start image I_ACFirst estimated scattered radiation image I separate from (r)_s ^{< 1 >}(r) is obtained. Here, the scattering function S (R) is a function that decreases as the distance R from the coordinate origin increases (R = 0 is a vertex and monotonously decreases depending on R). Or any one of [Equation 2] (hereinafter, the first term is referred to as “mono exp term” and the second term as “Gauss term”). Further, the convolution integral is expressed as [Equation 3] (Fourier transform, Fourier Transform, FT).
[0038]
[Expression 2]

[Equation 3]

[0039]
Thus, the first estimated scattered radiation image I_s ^{< 1 >}When (r) is obtained, the correction start image I_ACFrom (r), the first estimated scattered radiation image I_s ^{< 1 >}(r) is subtracted for each corresponding pixel, and the first intermediate image I_ACMD ^{< 1 >}(r) is obtained ([Equation 4]). The first intermediate image I_ACMD ^{< 1 >}(r) is the intermediate image I_ACMD(r). Intermediate image I_ACMDIn (r), most of the scattered radiation is removed.
[0040]
[Expression 4]

[0041]
The first intermediate image I_ACMD ^{< 1 >}The second estimated scattered radiation image I from (r) and the scattering function S_s ^{< 2 >}(r), correction start image I_ACThe second intermediate image I subtracted from (r)_ACMD ^{< 2 >}(r) is obtained and the intermediate image I_ACMD(r) or this is repeated and the nth intermediate image I_ACMD ^{< n >}From (r), the (n + 1) th scattered radiation image I_s ^{< n + 1 >}(r) is obtained ([Equation 5]), and correction start image I_ACsubtracted from (r), the (n + 1) th intermediate image I_ACMD ^{< n + 1 >}(r) is obtained ([Equation 6])._ACMD(r) is preferable, and in this case, n = 1 to 4 is preferable in consideration of the calculation amount.
[0042]
[Equation 5]

[Formula 6]

[0043]
Further, each estimated scattered radiation image I_s ^{< n >}(r) and the scattered radiation rate image SF (r) as in [Equation 7] are multiplied for each pixel, and each estimated scattered radiation image I_s(r) is adjusted, and this adjusted estimated scattered radiation image SF (r) · I_s(r) is the correction start image I_ACIntermediate image I subtracted from (r)_ACMDIt is more preferable to obtain (r) ([Equation 8]).
[0044]
[Expression 7]

[Equation 8]

[0045]
Since the influence of the scattered radiation can be sufficiently mitigated by the above, the absorption correction is performed again with the attenuation coefficient μ set to an ideal value, and the corrected image I by this method is corrected._ACSC(r) is obtained. That is, first, with the attenuation coefficient μ of the ideal value, the correction start image I is determined by the Chang method or the like._ACFrom (r), the absorption correction factor image ACF_narrowCreate Then, with respect to the intermediate image, the absorption correction factor image ACF based on the attenuation coefficient μ adopted in the facility_broadIs divided for each corresponding pixel, and the absorption correction factor image ACF_narrowFor each corresponding pixel (absorption correction factor image ratio ACF to intermediate image)_narrow/ ACF_broad[Equation 9]).
[0046]
[Equation 9]

[0047]
As described above, in this method, (a) a tomographic image I which is not subjected to scattered ray correction by the TEW method or the like._ACFrom (r), the estimated scattered radiation image I using the convolution integral with the scattering function S_s(r) is extracted and the tomographic image I is extracted._ACSubtract from (r), and (b) Absorption correction factor image ratio ACF_narrow/ ACF_broadTomographic images I obtained at various facilities and not corrected for scattered radiation I_ACFrom (r), the tomographic image I with the same level of scattered radiation correction as that of the TEW method or the like, where there is almost no disparity between facilities._ACSC(r) can be obtained without radiopharmaceutical re-administration, gamma ray recounting and tomographic image re-reconstruction.
[0048]
(B) External aspects of this system
The present system capable of executing the present method as described above is shown in FIG. The system 1 includes a correction program 2 as a main program and a correction start image I._AC(r) and the like, a storage device 6, a calculation device 10 that reads and executes the correction program 2, and an input device 12 and an output device 14 for the calculation device 10.
[0049]
Specific examples of the storage device 6 include a hard disk, a RAM, a ROM, or a combination thereof. Specific examples of the arithmetic device 10 include a RAM and a CPU. Specific examples of the input device 12 include a keyboard, a pointing device, and communication. Examples of the output device 14 include a display, a printer, a communication device, and a combination thereof.
[0050]
(C) Internal aspects of this system or structural aspects of this program
As shown in FIG. 2, the correction program 2 stored in the storage device 6 is a correction start image I by the Chang method or the like._ACThe absorption correction factor image ACF using the attenuation coefficient μ adopted in the counting facility from (r)._broadThe first factor calculation command unit 20 that calculates the value and commands the storage device 6 to store, and the correction start image I by the Chang method or the like_ACAn absorption correction factor image ACF using an ideal attenuation coefficient μ (for example, μ = 0.146) from (r)._narrowA second factor calculation command unit 21 for generating the scattered radiation rate image SF (r) of [Equation 7] as an absorption correction factor image ACF_broadAnd a scattered radiation rate calculation command unit 22 that calculates and stores the same.
[0051]
Further, the correction program 2 reads the correction start image I_AC(r) or the nth intermediate image I_ACMD ^{< n >}First estimated scattered radiation image I that has undergone the calculation of [Equation 3] for (r)._s ^{< 1 >}(r) or the (n + 1) th estimated scattered radiation image I_s ^{< n + 1 >}It includes a scattered radiation calculation command section 23 ([Equation 3], [Equation 5]) that commands the calculation and storage of (r).
[0052]
Further, the correction program 2 calculates the n-th estimated scattered radiation image I as shown in the rightmost term of [Equation 8]._s ^{< n >}n-th estimated scattered radiation image SF (r) · I adjusted from (r) and the scattered radiation rate image SF (r)_s ^{< n >}The scattered radiation adjustment command unit 24 that calculates and stores (r), and the nth estimated scattered radiation image I as shown in [Equation 8]._s ^{< n >}The product of (r) and the scattered radiation image SF (r) is the correction start image I_ACn-th intermediate image I subtracted from (r)_ACMD ^{< n >}An intermediate image calculation command unit 25 for calculating (r) is included.
[0053]
Still further, the correction program 2 executes the k-th intermediate image I._ACMD ^{< k >}and a repeat command unit 26 for commanding repetition until the calculation of (r). Note that the number of repetitions k can be easily changed by an instruction via the input device 12 or the like.
[0054]
In addition, the correction program 2 uses the intermediate image I as shown in [Equation 9]._ACMD(r) {= I_ACMD ^{< k >}(r)} is the absorption correction factor image ratio ACF._narrow/ ACF_broadAnd a ratio multiplication command unit 30 that stores the corrected image as a corrected image.
[0055]
(D) Contents of this method, operation contents of this system or operation contents of this program
As shown in FIG. 3, in the method implemented by the correction program 2 executed in the arithmetic device 10 of the system 1, first, the correction start image I_AC(r) is input from the same facility or a different facility through the input device 12 (step 50, for example, FIG. 4 (1), FIG. 4 and so on). Here, the position r and the convolution integral are all calculated in three dimensions.
[0056]
Here, the correction start image I_ACIn (r), only the absorption correction such as the Chang method is performed mainly based on the attenuation coefficient μ specific to each facility. Also, the input of the attenuation coefficient μ is accepted, and the absorption correction factor image ACF based on the input_broadIs created by executing the first factor calculation command unit 20 (step 52, FIG. 4 (3)). Further, referring to the ideal attenuation coefficient μ, by executing the second factor calculation command unit 21, the correction start image I_ACFrom (r), the absorption correction factor image ACF_narrowIs created (step 54).
[0057]
Next, by executing the scattered radiation rate calculation command unit 22, the absorption correction factor image ACF based on [Equation 7]._broadIs used to create a scattered radiation rate image SF (r) (step 56).
[0058]
The constants A, B, C, β, and γ are calculated by Monte Carlo method simulation (for example, Yuuichiro Narita et al, Monte Carlo and experimental evaluation of accuracy and noise properties of two scatter correction methods for SPECT, Phys. Med. Biol. vol.41 (1996) p.2481-2496), etc.
[0059]
Subsequently, the start of repetitive control based on the number of repetitions k input within an appropriate range is instructed (step 60).
[0060]
At the beginning of the iterative control, the correction start image I is calculated based on [Equation 8] (n is based on the iterative control) by executing the scattered radiation calculation command unit 23._AC(r) (n = 1) or the (n-1) -th intermediate image I_ACMD ^{< n-1 >}(r) The estimated scattered radiation image I is obtained by convolving the scattering function S with (n ≧ 2) and the scattering function S._s ^{< n >}(r) is obtained, and the scattered radiation rate image SF (r) is multiplied by the execution of the scattered radiation adjustment command unit 24, and the adjusted estimated scattered radiation image SF (r) · I is adjusted._s ^{< n >}(r) is obtained (step 62, FIG. 4 (5) per n = 1).
[0061]
The constant a₁, A₂, B₁, B₂Is a correction start image I from which a corrected image by the TEW method can also be obtained._ACWith respect to (r), a correction image according to the present invention is obtained and a simulation for comparing the correction images is performed once or a plurality of times.
[0062]
Further, the scattered radiation rate image SF (r) is calculated from an absorption correction factor image indicating the degree of absorption at each position, paying attention to the relevance that a part that is more easily absorbed is more likely to be scattered. n estimated scattered radiation image I_s ^{< n >}By multiplying by (r), the n-th estimated scattered radiation image I_s ^{< n >}The effect of (r) (the effect of convolution integral) can be adjusted according to the characteristics of each part.
[0063]
Next, the estimated scattered radiation image SF (r) · I adjusted by the execution of the intermediate image calculation command unit 25 is performed._s ^{< n >}(r) is the correction start image I_ACn-th intermediate image I subtracted from (r)_ACMD ^{< n >}(r) is created (step 64, [Equation 4], [Equation 6]), and the repetitive control is performed until n = k is completed (step 66)._ACMD(r) is created (FIG. 4 (6)).
[0064]
Then, the intermediate image I created by the execution of the ratio multiplication command unit 30 is_ACMD(r) is the absorption correction factor image ratio ACF._narrow/ ACF_broad(FIG. 4 (4)) and the corrected image I_ACSC(r) is acquired (step 70, [Equation 9], FIG. 4 (7)). Corrected image I_ACSC(r) is output from the output device 14 in a color or density corresponding to the value of each pixel.
[0065]
(E) Effects of the method, the system or the program
As described above, in this method and the like, the estimated scattered radiation image I is obtained by convolution with the scattering function S._s(r) is obtained, and this is corrected starting image I_ACIntermediate image I subtracted from (r)_ACMD(r), and the absorption correction factor image ratio ACF_narrow/ ACF_broadIntermediate image I_ACMDMultiply (r) to correct image I_ACSCIn order to obtain (r), as shown in FIGS. 4 and 5, the correction start image I in which an arbitrary value is adopted as the attenuation coefficient μ without performing the scattered ray correction according to the TEW method._ACFrom (r), the corrected image I corrected in the same manner as the corrected image according to the TEW method_ACSC(r) can be created.
[0066]
In particular, in the example of FIG. 5, the part indicated by the arrow is the correction start image I._ACCompared to (r), it is closer to the scattered radiation corrected image by the TEW method, and the corrected image I according to the present method etc._ACSCThe utility value in the diagnosis of (r) is high.
[0067]
The following [Table 1] shows the radiopharmaceuticals^99mFor each of five types of images (correction start images) acquired from five subjects by SPECT imaging using Tc-ECD (ethyl cysteinate dimer) (n = 5), individually corrected images by the TEW method and Corrected image I_ACSC(r) is created, and a correction start image I for the cerebellum ratio of the region of interest shown in the top row is created._AC(r) Both are obtained individually and their averages are arranged, and statistical analysis “paired t-test (one-side)” (one-sample t-test, parametric method, probability p of significance level is based on 0.01) ) To start the correction start image I_ACGroup (r) or corrected image I_ACSCThe comparison between the group (r) and the TEW method group is performed for each region of interest, and a mark “*” is given when there is a significant difference (p <0.01).
[0068]
[Table 1]

[0069]
According to [Table 1], correction start images I in which significant differences from the group of correction images by the TEW method are recognized in four of the five regions of interest are recognized._ACFrom the group (r), the corrected image I according to the invention is_ACSCWhen the group (r) is obtained and statistically analyzed with the group of corrected images by the TEW method, no significant difference is recognized in all regions of interest. Therefore, from [Table 1], the corrected image I of the present invention is_ACSCAlthough (r) is obtained after the fact, it reaches the level of the TEW method, and it can be seen that the correction of the present invention is effective.
[0070]
And in this method etc., after removing scattered radiation by the convolution integral concerning the scattering function S, the absorption correction factor image ratio ACF_narrow/ ACF_broadTherefore, no matter what attenuation coefficient μ value is adopted in each facility, the high-quality corrected image I is similarly applied._ACSC(r) can be obtained, and the corrected image I is extremely easy to interpret without wasting photon counting and image reconstruction at different facilities._ACSC(r) can be provided for diagnosis.
[0071]
Further, in this method and the like, since the scattering function S is set to [Equation 2] or its mono-exp term or Gaussian term, the scattering function S can have an ideal distribution close to the actual scattering phenomenon, and further correction accuracy can be obtained. Can be improved.
[0072]
Further, in the present method or the like, the nth intermediate image I is obtained by repeating the calculation._ACMD ^{< n >}Since (r) (n> 1) is obtained, the influence of scattering can be removed repeatedly, and the correction accuracy can be further improved.
[0073]
In addition, in the present method, the scattered radiation rate image SF (r) and the nth estimated scattered radiation image I_s ^{< n >}Since (r) (n ≧ 1) is multiplied, the ease of scattering at each position can be reflected, and the accuracy can be further increased.
[0074]
(F) Illustrative embodiment of the present invention, which is mainly modified from the above embodiment
The present invention has variations that can be obtained by changing the elements of the present method shown in the leftmost column of the following [Table 2] to any one of the right side thereof.
[0075]
[Table 2]

[0076]
In other words, the scattering function can be any one of the terms in [Equation 2]. As the scattering function, another monotonically decreasing function with the origin as a vertex can be adopted, and a two-dimensional coordinate system can be adopted.
[0077]
There are variations in which the scattering rate is not multiplied by the convolution integral value, and variations in which a constant value is multiplied. Furthermore, it is possible not to perform the iterative calculation for obtaining the n-th intermediate image (n ≧ 2) (that is, when n = 1), or to use an arbitrary number of iterative calculations. In addition, the convolution integral is to use discrete Fourier transform performed in real space instead of using FT performed in the frequency domain, or to use two-dimensional calculation in any of these. . In addition, FFT (Fast Fourier Transform) is employable as FT.
[0078]
A corrected image according to the present invention obtained in the following state is shown in FIG.
(1) Scattering function [Equation 2], scattering rate [Equation 7], iterative calculation n = 5, 3D FT
(2) Scattering function [Equation 2], fixed scattering rate, no iterative calculation, two-dimensional FT
(3) Scattering function mono exp term, scattering rate [Equation 7], no iterative calculation, 3D FT
(4) Scatter function mono exp term, fixed scattering rate, iterative calculation n = 5, 3D FT
(5) Scattering function [Equation 2], scattering rate [Equation 7], no iterative calculation, two-dimensional FT
[0079]
In addition, another calculation equivalent to the present method or the like is adopted, the configuration of the present system is changed to an equivalent one, or the processing order in the present method or the like is changed. In particular, the absorption correction factor image ratio is obtained in advance, or the numerical formulas are collectively calculated in a state where the mathematical expressions are appropriately integrated. Furthermore, various constants are obtained by experiments as appropriate according to the radionuclide used.
[0080]
In addition, this method and the like are used for correcting images of other parts including the heart. Further, the program is stored in a recording medium or distributed by communication.
[0081]
【The invention's effect】
According to the present invention, an estimated scattered radiation image is obtained by convolution integration with a scattering function, an intermediate image is obtained by subtracting from the correction start image, a correction image is obtained by multiplying the intermediate image by the absorption correction factor image ratio, or further Arithmetic is performed for accuracy. Therefore, tomographic images acquired at any facility are corrected to high quality after the fact, and are used for effective use of various facilities, meeting the needs of the times of appropriate medical information exchange between facilities. There is an effect.
[Brief description of the drawings]
FIG. 1 is a block diagram of a system according to the present invention.
FIG. 2 is a block diagram of a program according to the present invention.
FIG. 3 is a flowchart of a method and the like according to the present invention.
FIG. 4 is a diagram illustrating a correction start image, an intermediate image, a corrected image, and the like.
FIG. 5 is a diagram illustrating a corrected image, a correction start image, and a corrected image according to the present invention according to the TEW method (3-window method).
FIG. 6 is a diagram illustrating a corrected image according to a variation of the present invention.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... System, 2 ... Correction program, 6 ... Storage device, 10 ... Arithmetic unit, 12 ... Input device, 14 ... Output device, 20 ... First factor calculation command section, 21 ... Second Factor calculation command section, 22 .... scattered ray rate calculation command section, 23 ... scattered ray calculation command section, 24 ... scattered ray adjustment command section, 25 ... intermediate image calculation command section, 26 ... repeat command section, 30 .. Ratio multiplication command section.

Claims (9)

A SPECT tomographic image subjected to absorption correction at an arbitrary attenuation coefficient is used as a correction start image.
A function that monotonously decreases depending on the distance from the origin, and is a convolution integral between the scattering function that is shown on the right side of the following formula or one of its terms and the correction start image, and the estimated scattered radiation A first step of obtaining an image;

A second step of obtaining an intermediate image by subtracting the estimated scattered radiation image from the correction start image;
A correction image is obtained by multiplying the intermediate image by the absorption correction factor image ratio with the absorption correction factor image relating to the attenuation coefficient adopted at the time of absorption correction as the denominator and the absorption correction factor image relating to the attenuation coefficient of almost ideal value as the numerator . And a SPECT tomographic image correction method comprising three steps. Instead of the first step and the second step,
The first estimated scattered radiation from the convolution integral of the scattering function and the correction start image, which is a function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any term thereof: An image is obtained and subtracted from the correction start image to create a first intermediate image,

Obtain a second estimated scatter images from convolution integral between the first intermediate image and the scattering function, which creates a second intermediate image by subtracting from the corrected starting image,
Or, repeat these to create the nth intermediate image (n> 2),
The SPECT tomographic image correction method according to claim 1 , wherein any one of the n-th intermediate images (n ≧ 2) is used as an intermediate image. Instead of the first step and the second step,
A function that monotonously decreases depending on the distance from the origin, and is a convolution integral between the scattering function that is shown on the right side of the following formula or one of its terms and the correction start image, and the estimated scattered radiation To obtain an image and subtract this from the correction start image to create an intermediate image,

Alternatively, the first estimated scattered radiation image is obtained from the convolution integral of the scatter function and the correction start image, and is subtracted from the correction start image to create the first intermediate image.
Alternatively, in obtaining the second estimated scattered radiation image from the convolution integral of the first intermediate image and the scattering function, and subtracting this from the correction start image to create the second intermediate image,
Or when repeating these to create the nth intermediate image (n> 2),
Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction Obtaining an adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1);
By subtracting the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) from the correction start image, an intermediate image or the nth intermediate image (n ≧ 1) is obtained ,
When obtaining the n-th intermediate image (n ≧ 2) is, SPECT tomographic image correction method according to any one of the n intermediate image (n ≧ 2) in claim 1, wherein the intermediate image and to Rukoto . An input device that receives an input of a correction start image that is a SPECT tomographic image subjected to absorption correction at an arbitrary attenuation coefficient;
An arithmetic unit that executes a program including the following units (1) to (3) to obtain a corrected image from a correction start image;
An SPECT tomographic image correction system comprising: an output device that outputs a corrected image.
(1) Perform a convolution integration with a scattering function and a correction start image, which is a function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any term thereof : Scattered ray calculation command unit for obtaining estimated scattered ray images

(2) Intermediate image calculation command unit for obtaining an intermediate image by subtracting the estimated scattered radiation image from the correction start image. (3) An attenuation coefficient that is substantially ideal with the absorption correction factor image related to the attenuation coefficient adopted at the time of absorption correction as the denominator. Ratio multiplication command unit for obtaining a corrected image by multiplying an intermediate image by an absorption correction factor image ratio using the absorption correction factor image according to the numerator 5. The SPECT tomographic image correction system according to claim 4 , wherein the program includes the following part (4) instead of (1) and (2) .
(4) A function that monotonously decreases depending on the distance from the origin and is expressed by a convolution integral between the scattering function and the correction start image, which is indicated by the right side of the following formula or any term thereof . Obtain an estimated scattered radiation image and subtract it from the correction start image to create a first intermediate image,

Obtain a second estimated scatter images from convolution integral between the first intermediate image and the scattering function, which creates a second intermediate image by subtracting from the corrected starting image,
Or, repeat these to create the nth intermediate image (n> 2),
Repetition command unit that uses any one of the nth intermediate images (n ≧ 2) as an intermediate image The SPECT tomographic image correction system according to claim 4 , wherein the program includes the following part (5) instead of (1) and (2) .
(5) Perform a convolution integral with the scattering function and the correction start image, which is a function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any term thereof: In obtaining an estimated scattered radiation image and subtracting this from the correction start image to create an intermediate image,

Alternatively, the first estimated scattered radiation image is obtained from the convolution integral of the scatter function and the correction start image, and is subtracted from the correction start image to create the first intermediate image.
Alternatively, in obtaining the second estimated scattered radiation image from the convolution integral of the first intermediate image and the scattering function, and subtracting this from the correction start image to create the second intermediate image,
Or when repeating these to create the nth intermediate image (n> 2),
Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction Obtaining an adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1);
By subtracting the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) from the correction start image, an intermediate image or the nth intermediate image (n ≧ 1) is obtained ,
When obtaining the n-th intermediate image (n ≧ 2) is the scattered radiation adjustment command unit one of the n intermediate image (n ≧ 2) shall be the intermediate image A SPECT tomographic image correction program comprising the following sections (1) to (3), wherein a corrected image is obtained from a correction start image that is a SPECT tomographic image that has been subjected to absorption correction at an arbitrary attenuation coefficient by execution. .
(1) Perform a convolution integration with a scattering function and a correction start image, which is a function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any term thereof : Scattered ray calculation command unit for obtaining estimated scattered ray images

(2) Intermediate image calculation command unit for obtaining an intermediate image by subtracting the estimated scattered radiation image from the correction start image. (3) An attenuation coefficient that is substantially ideal with the absorption correction factor image related to the attenuation coefficient adopted at the time of absorption correction as the denominator. Ratio multiplication command unit for obtaining a corrected image by multiplying an intermediate image by an absorption correction factor image ratio using the absorption correction factor image according to the numerator 8. The SPECT tomographic image correction program according to claim 7 , further comprising the following (4) instead of (1) and (2) .
(4) A function that monotonously decreases depending on the distance from the origin and is expressed by a convolution integral between the scattering function and the correction start image, which is indicated by the right side of the following formula or any term thereof . Obtain an estimated scattered radiation image and subtract it from the correction start image to create a first intermediate image,

Obtain a second estimated scatter images from convolution integral between the first intermediate image and the scattering function, which creates a second intermediate image by subtracting from the corrected starting image,
Or, repeat these to create the nth intermediate image (n> 2),
Repetition command unit that uses any one of the nth intermediate images (n ≧ 2) as an intermediate image 8. The SPECT tomographic image correction program according to claim 7 , further comprising the following (5) instead of (1) and (2) .
(5) Perform a convolution integral with the scattering function and the correction start image, which is a function that monotonously decreases depending on the distance from the origin and is represented by the right side of the following formula or any term thereof: In obtaining an estimated scattered radiation image and subtracting this from the correction start image to create an intermediate image,

Alternatively, the first estimated scattered radiation image is obtained from the convolution integral of the scatter function and the correction start image, and is subtracted from the correction start image to create the first intermediate image.
Alternatively, in obtaining the second estimated scattered radiation image from the convolution integral of the first intermediate image and the scattering function, and subtracting this from the correction start image to create the second intermediate image,
Or when repeating these to create the nth intermediate image (n> 2),
Multiplying the estimated scattered radiation image or the nth estimated scattered radiation image (n ≧ 1) by the scattered radiation rate image calculated using the simulation or experiment from the absorption correction factor image related to the attenuation coefficient adopted at the time of the absorption correction Obtaining an adjusted estimated scattered radiation image or an nth estimated scattered radiation image (n ≧ 1);
By subtracting the adjusted estimated scattered radiation image or the adjusted nth estimated scattered radiation image (n ≧ 1) from the correction start image, an intermediate image or the nth intermediate image (n ≧ 1) is obtained ,
When obtaining the n-th intermediate image (n ≧ 2) is the scattered radiation adjustment command unit one of the n intermediate image (n ≧ 2) shall be the intermediate image

Images