Selection of observations in signal reconstruction

In many signal reconstruction problems, the data collection process is often computationally burdensome and expensive, which limits the amount of data that can be collected. In such cases, it is important to know the set of observations that will yield the best possible reconstruction of the signal so that only the most useful data are observed. This choice of observations must be made before actually expending resources to gather the data. If the mapping from the original signal to each observed data point is known, the mapping information can be used for choosing the best combination of observations. Two selection criteria based on the observation equation are defined. Efficient methods for optimizing these criteria with respect to the combination of observations are also proposed. Examples are presented that show that a reconstructed signal can be improved significantly by choosing observations according to these criteria.<>