Dynamic model generation for application of compressed sensing to cryo-electron tomography reconstruction

Cryo-electron tomography (cryo-ET), which produces three dimensional images at molecular resolution, is one of many applications that requires image reconstruction from projection measurements acquired with irregular measurement geometry. Although Fourier transform based reconstruction methods have been widely and successfully used in medical imaging for over 25 years, assumptions of regular measurement geometry and a band limited source cause direction sensitive artifacts when applied to cryo-ET. Iterative space domain methods such as compressed sensing could be applied to this severely underdetermined system with a limited range of projection angles and projection length, but progress has been hindered by the computational and storage requirements of the very large projection matrix of observation partials. In this paper we derive a method of dynamically computing the elements of the projection matrix accurately for continuous basis functions of limited extent with arbitrary beam width. Storage requirements are reduced by a factor of order 107 and there is no access overhead. This approach for limited angle and limited view measurement geometries is posed to enable dramatically improved reconstruction performance and is easily adapted to parallel computing architectures.