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 paper proposes a method to estimate the waveform of a specified sound source in a noisy and reverberant environment using a sensor array. Previously, we proposed an iterative method to estimate the waveform. However, in this method the effect of reflection sound reduces to 1/M, where M is the number of microphones. Therefore, to solve the reverberation problem, we propose a new method using inverse filters of the transfer functions from the sound sources to each microphone. First, the transfer function from each sound source to each microphone is measured by the cross-spectrum technique and each inverse filter is calculated by the QR method. Then the initially estimated waveform of a sound source is the averaged signal of the inverse filter outputs. Since this waveform still contains the effects of the other sound sources, the iterative technique is adopted to estimate the waveform more precisely, reducing the effects of the other sound and the reflection sound. Some computer simulations and experiments were carried out. The results show the effectiveness of our method.

Inverse filters can be designed in order to enhance the accuracy with which signals recorded in a given space can be reproduced in a given listening space. The problem is considered here of the design of an inverse filter matrix which enables K recorded signals to be accurately reproduced at K points in the listening space when transmitted via M loudspeaker channels. The analysis is sufficiently general to incorporate the case when the best (least squares) approximation is sought to the reproduction of K signals at L points in the space when LK. An analysis is presented which demonstrates that the approach suggested by the Multiple-Input/Output Inverse Filtering theorem of Miyoshi and Kaneda can be realised adaptively by using the Multiple Error LMS algorithm of Elliott et al.

Binaural effects in two measures are studied. One measure is the detectable limen of click sounds under lateralization of diotic or dichotic noise signals, and the other is phoneme articulation score under localization or lateralization of speech and noise signals. The experiments use a headphones system with listener's own head related transfer function (HRTF) filters. The HRTF filter coefficients are calculated individually from the impulse responses due to the listener's HRTF measured in a slightly sound reflective booth. The frequency response of the headphone is compensated for using an inverse filter calculated from the response at the subject's own ear canal entrance point. Considering the speech frequency band in tele-communication systems is not sufficiently wide, the bandwidth of the HRTF filter is limited below 6.2 kHz. However, the experiments of the localization simulation in the horizontal plane show that the sound image is mostly perceived outside the head in the simulated direction. Under simulation of localization or lateralization of speech and noise signals, the phoneme articulation score increases when the simulation spatially separates the phonemes from the noise signals while the total signal to noise ratio for both ears is maintained constant. This result shows the binaural effect in speech intelligibility under the noise disturbance condition, which is regarded as a part of the cocktail party effect.