Image resolution is determined by the filtering properties of the inst
rumentation of the acoustic imaging system, i.e., by the passband for
temporal and spatial harmonics. The ray (longitudinal) resolution is d
etermined by the frequency interval in which the holograms are compute
d. Scatterer images can be obtained with longitudinal superresolution
(resolution exceeding the Rayleigh limit) by using either an iterative
method of adaptive extrapolation (modified Gershberg-Papoulis algorit
hm) or an autoregression model to extrapolate the echo-signal spectra.
In this article the adaptive extrapolation method is generalized to t
he two-dimensional case; it can then be used in the stage of hologram
reconstruction by projection in spectral space. This approach permits
scatterers to be imaged both with ray resolution and with wavefront su
perresolution. The efficiency of the investigated methods is tested in
experiments on the reconstruction of images of models of point and ex
tended inhomogeneities. The ray resolution is improved twofold in adap
tive extrapolation and fourfold in application to the autoregression m
odel of the echo-signal spectrum. The wavefront and ray resolutions ar
e enhanced fourfold and twofold, respectively, in experiments on image
processing by two-dimensional adaptive extrapolation. The application
of different extrapolation methods in different stages of the imaging
process improves the reliability of the results.