Marcel Joho

Joint diagonalization of correlation matrices by using gradient methods with application to blind signal separation

Joint diagonalization of several correlation matrices is a powerful tool for blind signal separation. The paper addresses the blind signal separation problem for the case where the source signals are non-stationary and/or non-white, and the sensors are possibly noisy. We present cost functions for jointly diagonalizing several correlation matrices. The corresponding gradients are derived and used in gradient-based joint-diagonalization algorithms. Several variations are given, depending on the desired properties of the separation matrix, e.g., unitary separation matrix. These constraints are either imposed by adding a penalty term to the cost function or by projecting the gradient onto the desired manifold. The performance of the proposed joint-diagonalization algorithm is verified by simulating a blind signal separation application.

An FFT-based algorithm for multichannel blind deconvolution

A new update equation for the general multichannel blind deconvolution (MCBD) of a convolved mixture of source signals is derived. It is based on the update equation for blind source separation (BSS), which has been shown to be an alternative interpretation of the natural gradient applied to the minimization of some mutual information criterion. Computational complexity is held at a minimum by carrying out the separation/equalization task in the frequency domain. The algorithm is compared to similar known blind algorithms and its validity is demonstrated by simulations of real-world acoustic filters. In order to assess the performance of the algorithm, performance measures for multichannel blind deconvolution of signals are given in the paper.

Combined blind/nonblind source separation based on the natural gradient

It is a known fact that blind algorithms have convergence times of an order of magnitude longer than their nonblind counterparts. However, as shown in this letter, the knowledge of a subset of signals can greatly accelerate the convergence of blind source separation. The convergence behavior of the proposed algorithm is compared with the blind-only case.

Connecting partitioned frequency-domain filters in parallel or in cascade

The efficient implementation of connected filters is an important issue in signal processing. A typical example is the cascade of two filters, e.g., an adaptive filter with a time-invariant prefilter. The filtering and adaptation is carried out very efficiently in the frequency domain whenever filters with many coefficients are required. This is implemented as a block algorithm by using overlap-save or overlap-add techniques. However, in many real-time applications also, a short latency time through the system is required, which leads to a degradation of the computational efficiency. Partitioned frequency-domain adaptive filters, also known as multidelay adaptive filters, provide an efficient way for the filtering and adaptation with long filters maintaining short processing delays. This paper shows a computationally efficient way of implementing two or more partitioned frequency-domain filters in cascade or in parallel when their filter lengths are large. The methods presented require only one fast Fourier transform (FFT) and one inverse fast Fourier transform per input and output port, respectively. The FFT size can be even smaller than the length of the filters, The filters can be either time invariant or adaptive.

Blind separation of signals with mixed kurtosis signs using threshold activation functions

A parameterized activation function in the form of an adaptive threshold for a single-layer neural network, which separates a mixture of signals with any distribution (except for Gaussian), is introduced. This activation function is particularly simple to implement, since it neither uses hyperbolic nor polynomial functions, unlike most other nonlinear functions used for blind separation. For some specific distributions, the stable region of the threshold parameter is derived, and optimal values for best separation performance are given. If the threshold parameter is made adaptive during the separation process, the successful separation of signals whose distribution is unknown is demonstrated and compared against other known methods.

On the design of the target-signal filter in adaptive beamforming

This brief deals with the improvement of jammer suppression for adaptive broadband beamforming. The analysis is carried out with a two-microphone Griffiths-Jim beamformer and a single jammer signal. By examining the derived optimal filter, a design strategy for the constant target-signal filter in the main channel of the adaptive beamformer is given. This leads to a substantial reduction in the required filter length of the adaptive filter, while maintaining the same jammer suppression. Furthermore, a faster rate of convergence can be achieved, as there are fewer filter coefficients that have to be adapted. The brief concludes with measurement results from a real-time implementation of an adaptive beamformer, showing that the proposed design method is effective, even when more than two microphones are used.

Adaptive beamforming with partitioned frequency-domain filters

In this paper an adaptive broadband beamformer is presented which is based on a partitioned frequency-domain least-mean-square algorithm (PFDLMS). This block algorithm is known for its efficient computation and fast convergence even when the input signals are correlated. In applications where long filters are required but only a small processing delay is allowed, a frequency domain adaptive beamformer without partitioning demands a large FFT length despite the small block size. The FFT length can be shortened significantly by filter partitioning, without increasing the number of FFT operations. The weaker requirement on the FFT size makes the algorithm attractive for acoustical applications.

A simple threshold nonlinearity for blind separation of sub-Gaussian signals

A computationally simple nonlinearity in the form of a threshold device for the blind separation of sub-Gaussian signals is derived. Convergence is shown to be robust, fast, and comparable to that of more complex polynomial nonlinearities. Together with the known signum nonlinearity for super-Gaussian distributions, which basically is a threshold device with the threshold set to zero, the general threshold nonlinearity (with an appropriate threshold) can separate any non-Gaussian signals.

Elementary cost functions for blind separation of non-stationary source signals

Blind source separation (BSS) is a problem found in many applications related to acoustics or communications. This paper addresses the blind source separation problem for the case where the source signals are non-stationary and the sensors are noisy. To this end, we propose several useful elementary cost functions which can be combined to an overall cost function. The elementary cost functions might have different objectives, such as uncorrelated output signals or power normalization of the output signals. Additionally, the corresponding gradients with respect to the adjustable parameters are given. We discuss the design of an overall cost function and also give a simulation example.

Blind signal separation in noisy environments using a three-step quantizer

Independent component analysis in noisy channels needs special considerations, since standard solutions leadto a bias in the estimate of the parameters. We show three d approaches to mitigate the e2ects of additive noise in the transfer medium. A principal component subspace methodcan red uce the noise to more favorable levels, so that any following algorithm shows reduced bias e2ects. Although stochastic-gradient algorithms for maximum-likelihood solutions to the problem can easily be found, they are computationally prohibitive. A very successful approach is, therefore, to assume zero noise power for the derivation of the adaptive algorithm andsubsequently trying to compensate for any bias introd ucedby such a solution. The thresholdnonlinearity (three-step quantizer) is suitable for the blindseparation of a large class of sub-Gaussian d istributions. Stability regions are exploredfollowedby algorithmic extensions to suppress the bias in the estimation of the separation matrix. c � 2002 Elsevier Science B.V. All rights reserved.