New solutions to the wave equation have been shown to exhibit enhanced localization and energy fluence characteristics. The transmission and reception of these localized waves create unique problems, since they are essentially transient wave fronts inbothtime and space. Nonetheless, the ability to transmit wave energy through space with these interesting properties has many potential applications in a variety of applications areas. To realize their potential, new methods must be developed to analyze and process these waves. In this paper, approaches to design receiving arrays to reconstruct these special transient waves from noisy measurement data are discussed.