Rotate and slant projector for fast fully-3d iterative tomographic reconstruction

A method of iterative fully-3D reconstruction of an image by positron emission tomography (PET) by a scanner having a plurality of detector elements comprising:

• estimating a resultant image volume, wherein said image volume is stored in an image matrix;
• rotating the image matrix into alignment with an azimuthal angle of a projection ray or line-of-response between detector elements in a same transaxial plane of the scanner, wherein said projection ray or line-of-response is perpendicular to an axis of symmetry of the scanner;
• re-sampling said image volume at said azimuthal angle by slanting said image matrix to each axial angle of oblique projection rays or lines of response at that azimuthal angle, wherein each said oblique projection ray or line-of-response is between detector elements in different transaxial planes of the scanner such that columns of the image matrix align with a plurality of data collection directions;
• applying a coarse-depth compression factor to said image matrix such that rows of the image matrix are collapsed onto one another in accordance with the coarse-depth compression factor so depth information of the rotated image matrix is compressed;
• and
• projecting said image by summing the compressed columns of the image matrix.