This paper addresses the problem of microwave tomographic imaging from far-
field monostatic measurements. In the first-order Born approximation, a sim
ple Fourier relationship exists between the measured data and dielectric co
ntrast of the object under test. For a lossy object, the contrast function
depends on frequency, and this prevents monostatic data from being used dir
ectly since multifrequency probing radiation must be used to get sufficient
information. To overcome this difficulty, we propose a data preprocessing
strategy that eliminates frequency from the function to be reconstructed. T
he Fourier data obtained through preprocessing could be immediately inverte
d to give a bandpass estimate of the unknown function. Despite the drawback
s inherent in this approach, in small-scale tomographic applications, the s
pace region occupied by the object under test, as well as the sign of the u
nknown function, are normally known. This extra information allows us to ap
ply a projected Landweber algorithm to uniquely reconstruct the unknown, th
us avoiding the above-mentioned drawbacks, We outline the preprocessing and
reconstruction techniques adopted, and show some preliminary results from
experimental and simulated data.