Takeshi Mandai

Blind source separation of spatio-temporal mixed signals using time-frequency analysis

The cocktail party problem deals with the specialized human listening ability to focus ones listening attention on a single talker among a cacophony of conversations and background noise. The blind source separation problem corresponds to a way to enable computers to solve the cocktail party problem in a satisfactory manner. The simplest version of spatio-temporal mixture problem, which is a type of blind source separation problems, is solved using time-frequency analysis. The analytic wavelet transform is used to represent time-frequency information and a numerical simulation is given. †Dedicated to Professor Hideo Soga on the occasion of his 60th birthday.

Blind image source separations by wavelet analysis

The purpose of blind source separation is to separate and to estimate the original sources from the sensor array, without knowing the transmission channel characteristics. Besides methods based on independent component analysis which is one of the most powerful tools for blind source separation, several methods based on time-frequency analysis have been proposed. One of them is the quotient signal estimation method which can estimate the unknown number of sources. The notion of the continuous multiwavelet transform is introduced and three types of multiwavelets are presented. A new method using continuous multiwavelet transform, position-scale information matrices and self-organizing maps, is presented and applied to image source separations with noise. The performance of three multiwavelets are compared.

Image separation using the monogenic wavelet transform

The Riesz transforms and the monogenic signal are two-dimensional generalizations of the Hilbert transform and the analytic signal, respectively. The monogenic wavelet transformation is introduced and applied to solve blind source separation problems for images. The monogenic wavelet transformation is used to define spatial-scale information. Algorithms to solve the image separation problem are proposed.

Multistage blind source separations by wavelet analysis

The purpose of blind source separation is to separate the original sources from the sensor array, without knowing the transmission channel characteristics. Besides methods based on independent component analysis, several methods based on time-frequency analysis have been proposed. In this paper, a new method of multistage separation is proposed, which improves our formerly proposed methods using the time-scale information matrix based on the continuous multiwavelet transform.

An Estimation Method of Shift Parameters in Image Separation Problem

The simplest spatio-temporal mixing model of blind source separation for images is discussed. Shift parameters are estimated by total correlation functions of continuous wavelet transforms. An image separation algorithm using an annular sector multiwavelet is proposed.

BLIND SOURCE SEPARATION OF SPATIO-TEMPORAL MIXED SIGNALS USING PHASE INFORMATION OF ANALYTIC WAVELET TRANSFORM

The cocktail party problem deals with the specialized human listening ability to focus ones listening attention on a single talker among a cacophony of conversations and background noises. The blind source separation problem is how to enable computers to solve the cocktail party problem in a satisfactory manner. The simplest version of spatio-temporal mixture problem, which is a type of blind source separation problem, has been solved by a generalized version of the quotient signal estimation method based on the analytic wavelet transform, under the assumption that the time delays are integer multiples of the sampling period. The analytic wavelet transform is used to represent time-frequency information of observed signals. Without the above assumption, improved algorithms, utilizing phase information of the analytic wavelet transforms of the observed signals, are proposed. A series of numerical simulations is presented.

Image separation using N-tree wavelet transforms

N-tree discrete wavelet transforms based on the fractional Hilbert transforms of biorthogonal wavelets are proposed. Application of N-tree discrete wavelet transforms to separating mixtures of shifted images is considered. Some experimental results demonstrate the validity of the proposed method.

Fractional Hilbert Transforms of Biorthogonal Wavelets

We show that the fractional Hilbert transform preserves the biorthogonal wavelet property. For a naturally generated biorthogonal wavelet pair constructed from a given biorthogonal scaling pair, we propose a design to construct a better biorthogonal scaling pair for the naturally generated biorthogonal wavelet pair using the fractional Hilbert transform. We also propose a calculation method for low-pass and high-pass filters.

Filter coefficients of the fractional Hilbert transforms of biorthogonal wavelets

It is available to construct a discrete wavelet transform corresponding to an analytic wavelet transform. It is necessary to design good biorthogonal scaling functions which generate the Hilbert transforms of biorthogonal wavelets. In this paper, a design method of good scaling functions is proposed. We calculate the low-pass filter coefficients, which correspond to these scaling functions, directly from the original biorthogonal low-pass filter coefficients. In numerical experiments, it is shown that DWTs and IDWTs with twenty taps filter coefficients reconstruct signals with adequate precision.

System identification based on distribution theory and wavelet transform

A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.