Multifrequency Backscattering Tomography: Principles and Reconstruction Methods

Single-frequency diffraction tomography, though is well known in the literature, has its inherent problems, such as the limited resolution and image distortion due to the existence of “blind areas” of the object spectrum. The introduction of multi-frequency methods can improve the resolution and partly fill out the “blind areas” of the spectrum. The existing multi-frequency methods, such as the multi-frequency holography (prestack migration) or the wide band Born inversion, are time consuming procedures. The Multi-Frequency Backscattering Tomography (MFBT) is a fast method which uses only the backscattered waves (after plane wave decomposition) but meanwhile maintains the merit of multifrequency methods. Two reconstruction methods are presented: the backpropagation method and the direct Fourier transform method. In the latter method, the backpropagation of plane waves in the z-direction is implememted by FFT through a change of variable, this increases significantly the computation speed. Compared with the single-frequency diffraction tomography, the MFBT has a better resolution and image quality, and its reconstruction speed is faster by a factor N,/IogzN,, where N, is the number of grid points in z-direction. When N, is large, the time saving of MFBT is remarkable.