A new method of test for goodness of fit of Laplace's distribution is being proposed in this paper. The new parameter H is defined by the two standard deviations which are estimated by the methods of moments and of maximum likelihood. If the number of data is large, the goodness of the Laplace's distribution is easily tested by the percentile of the normal distribution of the parameter H.

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.

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.