Prca-based method and system for dynamically re-establishing pet image

A method for dynamically reconstructing positron emission tomography (PET) images based on a robust principal component analysis (PRCA), comprising the following steps:

• (1) using a detector to detect a biological organism injected with a radioactive substance, dynamically collecting n groups of coincidence count vectors of the PET, and correcting the coincidence count vectors, then constructing a coincidence count matrix of the PET;
• n is a natural number greater than 1;
• (2) establishing a measurement equation of the PET based on the principle of the PET imaging;
• (3) adding correction conditions to time and space factors of the measurement equation;
• estimating PET concentration data based on the coincidence count matrix and through following iteration equation:
• (
• X
• k
• +
• 1
• ,
• Z
• k
• +
• 1
• )
• =
• arg
• 
• 
• 
• min
• X
• ,
• Z
• 
• {
• 
• G
• 
• (
• X
• +
• Z
• )
• -
• Y
• -
• A
• k
• 
• 2
• +
• 
• X
• -
• B
• k
• -
• C
• k
• 
• 2
• +
• r
• 
• 
• HZ
• -
• D
• k
• +
• E
• k
• 
• 2
• }
• wherein Xk+1 is a PET concentration distribution matrix after (k+1)-th iteration, Zk+1 is a PET background concentration distribution matrix after (k+1)-th iteration, G is a system matrix, H is a correction matrix, Y is a coincidence count matrix, r is a correction coefficient, Ak is a first correction coefficient matrix after k-th iteration, Bk is a second correction coefficient matrix after k-th iteration, Ck is a third correction coefficient matrix after k-th iteration, Dk is a fourth correction coefficient matrix after k-th iteration, Ek is a fifth correction coefficient matrix after k-th iteration, X and Z are respectively randomized matrix corresponding to Xk+l and Zk+1, k is a natural number;
• (4) separating or decomposing the PET concentration data to obtain n frames of successive PET images.