TERSE: a transmission and emission reconstruction environment for SPECT, has been developed at the University of Michigan by Jeff Fessler and Edward Ficaro, in a collaboration between the Department of Electrical Engineering and Computer Science (EECS) and the Division of Nuclear Medicine. TERSE consists of an X-windows graphical user interface to portions of the ASPIRE software libraries that have been optimized for SPECT imaging with simultaneous transmission and emission scans. Software components include: data structure for storing sparse matrices; subroutines for linear algebra operations with sparse matrices; programs for generating the “system matrices” for a wide variety of tomographic systems including parallel beam, fan beam, depth-dependent blurring, etc.; fast converging iterative algorithms for computing penalized likelihood and penalized weighted least squares estimates from noisy data; a variety of convex penalty functions are implemented. Unlike commercially available iterative reconstruction methods, TERSE is based on regularized statistical methods, and uses algorithms with guaranteed global convergence. This means the image properties, such as noise and spatial resolution, are more predictable and controllable than with the popular unregularized methods. The algorithms converge quickly to a stable image. The trade-off between resolution and noise is controlled directly by the user, not indirectly by the number of iterations, number of counts, etc.