Image reconstruction based on accelerated method using polar symmetries

An image reconstruction system for reconstructing an image based on image projection data, the system having N tubes of response (TORs) with Nφ axial translation symmetries and Nθ in-plane rotation symmetries between the TORs, the system comprising:

• a memory;
• and
• one or more processors coupled to the memory, the one or more processors being configured to execute computer program instructions stored therein, the computer program instructions including:
• acquiring image projection data and generating a measurement data vector in response;
• ordering the measured image projection data according to one or more symmetries of the image reconstruction system, wherein the measured image projection data associated with TORs having axial or translation symmetry are stored in contiguous memory locations;
• obtaining a first image estimate data based on the measured image projection data;
• obtaining a system matrix mapping each of the measured image projection data to pixels of an image, wherein the pixels are positioned according to a polar or cylindrical coordinate grid, wherein each matrix coefficient stored in the memory is associated with a TOR and pixel combination which has no axial nor translation symmetry to other TOR and pixel combinations for which a matrix coefficient has been stored in the memory;
• iteratively computing an image estimate, wherein the iteratively computing includes:
• identifying a current image estimate stored in an image data vector;
• computing a measurement estimate data vector based on a first matrix-vector operation in a spatial domain between the system matrix and the current image estimate;
• computing a measurement correction vector based on the measurement estimate data vector and the measurement data vector;
• computing an image correction vector based on a second matrix-vector operation in the spatial domain between the system matrix and the measurement correction vector;
• and
• updating the current image estimate based on the image correction vector;
• and
• outputting a reconstructed image based on the updated image estimate.