Measurement or imaging of elastic wave nonlinear scatterers with a memory of scattering parameters comprises selecting LF pulses having characteristics to change the scattering parameters of nonlinear scatterers. A transmit time relation is selected so that the incident HF pulse propagates sufficiently close to the LF pulse that the effect of the incident LF pulse on its scatterer parameters is observed by the HF pulse. At least two elastic wave pulse complexes comprising a high frequency (HF) pulse and a selected low frequency (LF) pulse are transmitted towards the region. Received HF signals are combined to form nonlinear HF signals representing the scatterers with memory, with suppression of received HF signals from other scatterers. At least one of the received HF signals may be corrected by time delay correction and/or speckle correction with a speckle correction filter, determined by movement of the scattering object. Systems are also disclosed.