New results on observation selection in signal reconstruction

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. In previous work, we defined a mean-squared error (MSE) selection criterion based on the known signal formation equation. Furthermore, we proposed the use of sequential backward selection (SBS) to optimize this criterion. Although SBS is suboptimal, it performs consistently well. In this paper, we analyze the performance of SBS and develop an upper bound on the MSE of the SBS-optimized solution. This upper bound provides analytical justification for the claim that SBS performs well in spite of being suboptimal. Furthermore, we derive a lower bound on the MSE of preliminary combinations of rows. This lower bound can be used as a point of reference for evaluating the upper performance bound of the SBS algorithm