Reflection mode diffraction tomography is expected to reconstruct a higher resolution image than transmission mode. Its image reconstruction problem, however, in the many cases of practical uses becomes ill-posed one. In this paper, a new reconstruction method of limited angle reflection mode diffraction tomography using maximum entropy method is proposed. Results of simulation showed that the method was able to reconstruct the better quality images than IR method poposed by Kak, et al.

An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.

This letter discusses the quality improvement of reconstructed images in diffraction tomography. An efficient iterative procedure based on the modified Newton-Kantorovich method and the Gerchberg-Papoulis algorithm is presented. The simulated results demonstrate the property of high-quality reconstruction even for cases where the first-order Born approximation fails.