Abstract
The problem of restoring an image by its Fourier
transform is considered when the Fourier transform contains phase
distortions. The nature of these distortions and their values are
arbitrary. The criterion for the quality of the phase distortion
estimates is suggested. It can be used to select the image which
is mostly like the true one. The nature of the true image is also
arbitrary. The only condition for the true image is that it is
real and positive for all the points of the restored area. The
other condition for the task is that the recovered image is
calculated as the absolute value of the inverse Fourier
transform. The algorithm for the search of the compensating
phases satisfying the criterion is not considered for the general
case; however, the task of the radar imaging based on the wideband
signal and the time synthesis of the aperture is treated in
detail. The physical basis for the task is a wideband pulse
radar signal reflected by a moving object. As a result, a
two-dimensional aperture is synthesized along the range, due to
the super resolution, and along the velocity, according to
the motion of the object. The radar signals are received by a
single receiver. The image is reconstructed on the basis of these
signals by using the maximum likelihood technique. The method
uses the coherent processing of the signals. In practice, the
coherence can be destroyed (due to some atmospheric turbulence or
equipment instability, due to some inaccuracy in defining the
motion). We assume that the objects to be observed are located
at the far zone. For this task and on the basis of the suggested
criterion, we develop an approximate algorithm for searching the
best compensating phases in the radar signal. The quality of the
images is tested with the help of simulation.