Matrix Weighted Back-Projection Accelerates Tomographic Reconstruction

Tomography allows structure determination of an object from its projections. Weighted backprojection (WBP) is by far the standard method for tomographic reconstruction. The single-tilt acquisition geometry turns the 3D reconstruction problem into a set of independent 2D reconstruction problems of the slices that form the volume. These 2D reconstruction problems can be solved by WBP and modelled as sparse-matrix vector products, where the coefficient matrix are shared by the 2D problems. However, the standard implementation of WBP is based on recomputation of the coefficients when needed, because of the huge memory requirements. Modern computers now include enough memory to store the coefficients into a sparse matrix data structure. In this work, implementations of WBP based on matrix precomputation and efficient management of the memory hierarchy have been evaluated on modern architectures. The results clearly show that the matrix implementations significantly outperform the standard WBP.