The invention presents methods and instrumentation for measurement or imaging of a region of an object with waves of a general nature for example electromagnetic (EM) and elastic (EL) waves where the material parameters for wave propagation and scattering in the object depend on the wave field strength. The invention specially addresses suppression of 3rd order multiple scattering noise referred to as pulse reverberation noise and also suppression of linear scattering components to enhanced signal components from nonlinear scattering. The pulse reverberation noise is divided into three classes where the invention specially addresses Class I and Class II 3rd order multiple scattering that are generated from the same three scatterers but in opposite sequence. One specially addresses methods to achieve close to the same sensitivity to the Class I and II pulse reverberation noise which simplifies the suppression of both classes combined and methods for estimation of suppression of pulse reverberation noise that compensates for the difference between Class I and Class II noise. The methods are based on transmission of dual band pulse complexes composed of a low frequency (LF) pulse and a high frequency (HF) pulse where the LF pulse is used to nonlinearly manipulate the object parameters observed by the co propagating HF pulse. One or both of scattered and transmitted components from the HF pulse are picked up and further processed to suppress pulse reverberation noise and enhance nonlinear scattering components.
