The modern level of remote sensing system development requires special antennas with small dimensions and weight airborne location and with high spatial resolution. The possible way to solve the above compromise is to use the sparse arrays. However, the sparse arrays have considerable spatial ambiguity due to the high level of side lobes conditioned by the unfilled structure of antennas aperture. We propose to overcome this disadvantage by means of signal processing able to solve the problems of bandlimited extrapolation and interpolation simultaneously. The signal processing is generally based on the inverse problem solution that is mainly accomplished by aid of Tikhonov regularization approach. However, such approach is not able to solve the above mentioned problem due to its linearity.

In this paper we propose to use the nonlinear iterative methods of inverse problem solution in radiometry imaging systems with sparse antenna arrays. The nonlinearity of the method is provided by the parametric constrains on the solution that leads to the spectrum extrapolation and interpolation. To prevent image edges smooth the adaptive regularization is used in contrast to Tikhonov regularization where regularization parameter is constant one for all image regions.