3PI algorithm for spiral CT

A method of computing exact images derived from spiral computer tomography scan with area detectors, comprising the steps of:

• (a) collecting cone beam (CB) projection data from a detector, which is wider than what is required for a 1PI algorithm;
• the cone beam covering projections of four turns of the spiral that are adjacent to a current source position;
• (b) identifying families of lines on a plane Π intersecting the cone beam projection;
• (c) preprocessing the CB projection data;
• (d) convolution-filtering said preprocessed CB projection data along said lines;
• (e) back projecting said filtered data to form a precursor of said image;
• and
• (f) repeating steps a, b, c, d, e, until an exact image of the object is completed.

A method of computing images derived from computer tomography scan with detectors, comprising the steps of:

• (a) collecting cone beam (CB) data from a detector during a scan of an object;
• (b) identifying three families of lines on a plane DP(s) intersecting the cone beam, wherein s is value of the parameter describing the scan path and corresponding to the current source position, and the three families of lines include:
• (bi) a first family of lines parallel to {dot over (y)}(s), where
• {dot over (y)}(s) is the direction of the scan tangent at the current source position;
• (bii) a second family of lines tangent to Γ1 and Γ−1, where
• Γ1 is the projection of the scan turn defined by s<q<s+2π onto the plane DP(s);
• Γ−1 is the projection of the scan turn defined by s−2π<q<s onto the plane DP(s);
• q is the parameter along the scan path which describes the point being projected;
• (biii) a third family of lines tangent to Γ2 and Γ−2, where
• Γ2 is the projection of the scan turn defined by s+2π<q<s+4π onto the plane DP(s);
• Γ−2 is the projection of the scan turn defined by s−4π<q<s−2π onto the plane DP(s);
• (c) preprocessing and shift invariant filtering said data along said lines of said three families;
• (d) back projecting said filtered data to form a precursor of said image;
• and
• (e) repeating steps a, b, c, and d until an image of the object is completed.

A method of computing images derived from computer tomography scan with detectors, comprising the steps of:

• (a) collecting cone beam data from a detector during a scan of an object;
• (b) identifying three families of lines on a plane DP(s) intersecting the cone beam, wherein s is value of a parameter describing the scan path and corresponding to the current source position, and the three families of lines include:
• (bi) a first family of lines parallel to {dot over (y)}(s), where
• {dot over (y)}(s) is the direction of the scan tangent at the current source position;
• (bii) a second family of lines tangent to Γ1 and Γ−1, where
• Γ1 is the projection of the scan turn defined by s<q<s+2π onto the plane DP(s);
• Γ−1 is the projection of the scan turn defined by s−2π<q<s onto the plane DP(s);
• q is the parameter along the scan path which describes the point being projected;
• (biii) a third family of lines on the plane DP(s) that have at least three points of intersection s1, s2, s3 with Γ±1 and Γ±2 , where
• Γ2 is the projection of the scan turn defined by s+2π<q<s+4π onto the plane DP(s);
• Γ−2 is the projection of the scan turn defined by s−4π<q<s−2π onto the plane DP(s);
• (c) preprocessing and shift invariant filtering said data along said lines of said three families;
• (d) back projecting said filtered data to form a precursor of said image;
• and
• (e) repeating steps a, b, c, and d until an image of the object is completed.