Reprojection and backprojection methods and algorithms for implementation thereof

A method of image processing comprising:

• projecting edges of each pixel of a pixel grid, which is intersected by a ray projected from a source to a detector, in a predetermined linear sequence of pixels in the pixel grid, onto a predetermined line that passes through the grid;
• projecting the edges of each bin of a detector onto the predetermined line;
• and
• determining the contribution of each pixel to a bin of the detector array or vice versa in accordance with the projections of the pixel edges and the detector bin edges on the predetermined line.

A method of image processing comprising:

• establishing a pixel grid containing image pixels, which are arranged in image rows and columns;
• continuously mapping respective transitions between image pixels and detector-bins of a detector which has detected radiation from a source comprising:
• projecting detector bin transitions onto a predetermined line;
• projecting the pixel transitions onto the predetermined line;
• and
• weighting one of the detector bins and pixels with segment lengths on the predetermined line, based on distances between adjacent projections.

A computer readable medium encoded with a program executable by a computer for processing an image, said program being configured to instruct the computer to:

• project pixels in a pixel grid onto a detector having a plurality of bins, or vice versa;
• dynamically adjust a dimension of a square window for one of a pixel and a detector bin so that adjacent windows form a continuous shadow over one of the detector bins of the detector and the image pixels;
• and
• determine the effect of each pixel on each bin of the detector or vice versa.

A computer readable medium encoded with a program executable by a computer for processing an image, said program being configured to instruct the computer to:

• project edges of each pixel of a pixel grid, that is intersected by a ray projected from a source to a detector, in a predetermined linear sequence of pixels in the pixel grid, onto a predetermined line that passes through the grid;
• project the edges of each bin of a detector onto the predetermined line;
• and
• determine the contribution of each pixel to a bin of the detector array or vice versa in accordance with the projections of the pixel edges and the detector bin edges on the predetermined line.

A computer readable medium encoded with a program executable by a computer for processing an image, said program being configured to instruct the computer to:

• establish a pixel grid containing image pixels, which are arranged in image rows and columns;
• continuously map respective transitions between image pixels and detector-bins of a detector, which has detected radiation from a source by:
• projecting detector bin transitions onto a predetermined line;
• projecting the pixel transitions onto the predetermined line;
• and
• weighting one of the detector bins and pixels with segment lengths on the predetermined line, based on distances between adjacent projections.