When geophysical variables are estimated from remotely sensed electromagnetic data, severe difficulties are often encountered because of the ill-posed nature of the problem, so that the use of effective processing becomes essential. The inversion of radiometric data in the retrieval of atmospheric temperature profiles is considered and the use of the Kalman filter algorithm is analyzer to assess its performance from the point of view of accuracy of estimates and spatial resolution. The sensitivity to experimental errors is pointed out and the use of adaptive filtering to reduce the inaccuracy of data 0' examined. With regard to spectra of radiometric flucturtions, the performance of recently proposed spectr2l estimation techniques, amenable to the originally proposed maximum entropy method, are considered. The estimate of line parameters to identify and follow th temporal evolution of atmospheric internal oscillations is discussed, as well as the accuracy of retrieval of the slopes of radiometric turbulent spectra. E.M. REMOTE SENSING AND IN VERSE PROBLEMS A large variety of relevant and beneficial applications is drawing interest onto passive electromagnetic sensing techniques. In meteorology, satellite-based infrared and microwave sensors measure atmospheric variables on a global scale [i], while ground-based radiometers have proven their capability in continuously profiling the troposphere [2]. The dramatic increase of retrieval accuracy attainable by the contemporary use of satellite and ground-based data [3] and the sensitivity of radiometric instruments to clear-air turbulence and to internal waves [4,5] appear to be of considerable practical importance. The electromagnetic remote sensing of the earth surface (land or sea) by infrared and microwave sensors points out new ramified directions of beneficial applications [6]. Microwave thermography is now enriching the medical instrumentation and efforts are being made towards quantitative determination of subcutaneous temperature distribution as an effective tool in diagnosis and curative treatment [7].Full exploitation of the many potentialities of passive electromagnetic nsing techniques is subject to the feasibility of an adequate information retrieval from radiometric data, that is from the electromagnetic power 1874 impinging on the instrument antenno. As a result of the radiative transfer theory [8], the power reaching the radiometer is in general a weighted integral of the electromagnetic power emitted and scattered inside the medium under observation. Once the space-time distribution of intensity of emission and/or scattering is determined, the properties of the medium to be sensed can be retrieved through convenient modelling of the electromagnetic interaction mechanisms. The sensing process, therefore, requires different radiometric measurements and the subsequent inversion of the corresponding set of data.In the significant case of temperature profile retrieval, a Fredhoim integral equation of the first kind V (Y) = ( W (Y, z) B (z) dz Jo (1) relate...