Rotate and slant projector for fast fully-3D iterative tomographic reconstruction
Disclosed herein are embodiments of a rotate-and-slant projector that takes advantage of symmetries in the geometry to compute truly volumetric projections to multiple oblique sinograms in a computationally efficient manner. It is based upon the 2D rotation-based projector using the fast three-pass method of shears, and it conserves the 2D rotator computations for multiple projections to each oblique sinogram set. The projector is equally applicable to both conventional evenly-spaced projections and unevenly-spaced line-of-response (LOR) data (where the arc correction is modeled within the projector). The LOR-based version models the exact location of the direct and oblique LORs, and provides an ordinary Poisson reconstruction framework. Speed optimizations of various embodiments of the projector include advantageously utilizing data symmetries such as the vertical symmetry of the oblique projection process, a coarse-depth compression, and array indexing schemes which maximize serial memory access.
1. 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.
2. The method of claim 1 , wherein said scanner is comprised of a plurality of substantially adjacent rings of detector elements in its axial direction.
3. The method of claim 1 , wherein said scanner is a PET scanner and said PET scanner includes said projector.