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This paper investigates a regularization scheme in the recently proposed subspace-based optimization method for solving inverse scattering problems. The number of leading singular values of a current-to-field mapping operator is found to balance the accuracy and the stability of the solution. If the number of leading singular values is chosen as a large number, the noise is amplified in the inverse process. On the other hand, if this parameter is chosen to be a small number, the convergence of the optimization method will be slow. This paper investigates the method of choosing the number of leading singular values of the current-to-field mapping operator.