Efficient computation for sequential forward observation selection in image reconstruction

In many applications of image reconstruction, the observation time is limited. With this limitation, it is necessary to choose the best combination of samples to guarantee the quality of the reconstructed image. Sequential forward selection (SFS) is a method to optimize the choice of observations, in which the samples are sequentially selected by using a matrix-based optimality criterion. With SFS, the previous selected sample can be observed while the next sample is selected. When the number of unknowns exceeds the number of observations during the selection process, the least squares criterion is undefined and the resulting SFS algorithm cannot be used. In this paper, we present a modified form of the criterion and develop an SFS algorithm for the new criterion. Then we develop an efficient computational strategy for this algorithm as well as the standard SFS algorithm and present some simulation results. The efficient algorithms show promise for optimizing MR imaging and MR spectroscopic imaging acquisition strategies