A matrix approach to tomographic reconstruction and its implementation on GPUs.

Electron tomography allows elucidation of the molecular architecture of complex biological specimens. Weighted backprojection (WBP) is the standard reconstruction method in the field. In this work, three-dimensional reconstruction with WBP is addressed from a matrix perspective by formulating the problem as a set of sparse matrix-vector products, with the matrix being constant and shared by all the products. This matrix approach allows efficient implementations of reconstruction algorithms. Although WBP is computationally simple, the resolution requirements may turn the tomographic reconstruction into a computationally intensive problem. Parallel systems have traditionally been used to cope with such demands. Recently, graphics processor units (GPUs) have emerged as powerful platforms for scientific computing and they are getting increasing interest. In combination with GPU computing, the matrix approach for WBP exhibits a significant acceleration factor compared to the standard implementation.