Abstract: Methods of acoustic imaging provide images with reduced reverberation noise and images of nonlinear scattering and propagation parameters of the object, and estimation methods of corrections for wave front aberrations produced by spatial variations in the acoustic propagation velocity. The methods are based on processing of the received signal from transmitted dual frequency band acoustic pulse complexes with overlapping high and low frequency pulses. The high frequency pulse is used for the image reconstruction and the low frequency pulse is used to manipulate the nonlinear scattering and/or propagation properties of the high frequency pulse. Through filtering in the pulse number coordinate and corrections for nonlinear propagation delays and optionally also amplitudes, a linear back scattering signal with suppressed pulse reverberation noise, a nonlinear back scattering signal, and quantitative nonlinear forward propagation and scattering parameters are extracted.