Sequential algorithms for observation selection

Some signal reconstruction problems allow for flexibility in the selection of observations and, hence, the signal formation equation. In such cases, we have the opportunity to determine the best combination of observations before acquiring the data. We present and analyze two classes of sequential algorithms to select observations-sequential backward selection (SBS) and sequential forward selection (SFS). Although both are suboptimal, they perform consistently well. We analyze the computational complexity of various forms of SBS and SFS and develop upper bounds on the sum of squared errors (SSE) of the solutions obtained by SBS and SFS.