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In this literature, we carefully investigate the structure of single- andmulti-frequency imaging functions, that are usually employed in inversescattering problems. Based on patterns of the singular vectors of theMulti-Static Response (MSR) matrix, we establish a relationship between imagingfunctions and the Bessel function. This relationship indicates certainproperties of imaging functions and the reason behind enhancement in theimaging performance by multiple frequencies. Several numerical simulations witha large amount of noisy data are performed in order to support ourinvestigation.

Structure analysis of single- and multi-frequency subspace migrations in inverse scattering problems