1. A method of constructing an image from a signal, comprising: interpreting the signal as a potential of a Schrödinger operator, wherein the signal contains at least a first component associated with a first set of functions and a second component associated with a second set of functions; decomposing the signal into first squared eigenfunctions associated with the first set of functions from second squared eigenfunctions associated with the second set of functions; reducing a design parameter of the Schrödinger operator; analyzing a first discrete spectrum of the Schrödinger operator for the first set of functions and a second discrete spectrum of the Schrödinger operator for the second set of functions; and combining the analysis of the first and second discrete spectra to construct the image.