Efficient techniques for choosing the regularization parameter for microwave imaging

摘要

The usual procedure for the microwave imaging in spatial domain consists in discretizing the electric field integral equations in the form of two coupled matrix equations by applying the moment method[l]-[8]. The associated ill-conditioned systems of algebraic equations are solved iteratively by implementing a regularization technique at each iteration step. One of the difficulties in the procedure is the selection of the regularization parameter[1]-[8]. If this parameter is too big, too much useful information could be lost. If it is too small, a convergent solution might not be obtained. Based on the stochastic inversion algorithm, this paper presents three methods for the selection of this parameter. The first method is applicable to the situation when the upper bound of the object function variance and the upper bound of the measured data noise variance are known. The second method can be used if only the upper bound of the object function variance is detectable. If this information is not available, the third method can be employed to find the regularization parameter. The efficiency of these methods is illustrated by reconstructing two-dimensional dielectric objects with noiseless measured data and also with data containing noise.