4I-6 Diffraction Ultrasonic Lamb Wave Tomography Using Nonuniform FFT

Combining the Fourier diffraction theorem and the nonuniform fast Fourier transform (NUFFT), this paper describes a new efficient approach for Lamb wave diffraction tomography. Frequency-domain sampling distribution corresponding to crosshole configuration and fan beam configuration is respectively studied. It shows that crosshole projection leaves large blank zones where there is no estimate of the Fourier transform of the object while fan beam method can be well applicable to the image reconstruction because of its uniform samples in frequency domain. In order to improve the accuracy of diffraction tomography, perfect reconstruction algorithms should be given. Here, a forward NUFFT is performed based upon min-max optimization criterion, and inverse NUFFT is obtained iteratively in this framework. Algebraic reconstruction technique (ART), conjugate gradient (CG) and steepest descent (SD) are respectively used to reconstruct image. Simulation examples with incomplete and very noisy projection data demonstrate the proposed algorithm has the advantage of better reconstruction accuracy compared to the traditional frequency interpolation method