Philippe Lemmerling

Detection of fast neuronal signals in the motor cortex from functional near infrared spectroscopy measurements using independent component analysis

Fast changes, in the range of milliseconds, in the optical properties of cerebral tissue are associated with brain activity and can be detected using noninvasive near-infrared spectroscopy (NIRS). These changes are assumed to be caused by changes in the light scattering properties of the neuronal tissue. The aim of this study was to develop highly sensitive data analysi algorithms to detect this fast signal, which is small compared with other physiological signals. A frequency-domain tissue oximeter, whose laser diodes were intensity modulated at 110 MHz, was used. The amplitude, mean intensity and phase of the modulated optical signal were measured at a sample rate of 96 Hz. The probe, consisting of four crossed source detector pairs was placed above the motor cortex, contralateral to the hand performing a tapping exercise consisting of alternating rest and tapping periods of 20 s each. An adaptive filter was used to remove the arterial pulsatility from the optical signals. Independent component analysis allowed further separation of a signal component containing the fast signal. In nine out of 14 subjects, a significant fast neuronal signal related to the finger tapping was found in the intensity signals. In the phase signals, indications of the fast signal were found in only two subjects.

Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem

In this paper we develop a fast algorithm for the basic deconvolution problem. First we show that the kernel problem to be solved in the basic deconvolution problem is a so-called structured total least squares problem. Due to the low displacement rank of the involved matrices and the sparsity of the generators, we are able to develop a fast algorithm. We apply the new algorithm on a deconvolution problem arising in a medical application in renography. By means of this example, we show the increased computational performance of our algorithm as compared to other algorithms for solving this type of structured total least squares problem. In addition, Monte-Carlo simulations indicate the superior statistical performance of the structured total least squares estimator compared to other estimators such as the ordinary total least squares estimator.

Fast algorithm for solving the Hankel/Toeplitz Structured Total Least Squares problem

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector. In this paper we consider the Toeplitz (Hankel) STLS problem (i.e., an STLS problem in which the Toeplitz (Hankel) structure needs to be preserved). A fast implementation of an algorithm for solving this frequently occurring STLS problem is proposed. The increased efficiency is obtained by exploiting the low displacement rank of the involved matrices and the sparsity of the associated generators.The fast implementation is compared to two other implementations of algorithms for solving the Toeplitz (Hankel) STLS problem. The comparison is carried out on a recently proposed speech compression scheme. The numerical results confirm the high efficiency of the newly proposed fast implementation: the straightforward implementations have a complexity of O((m+n)3) and O(m3) whereas the proposed implementation has a complexity of O(mn+n2).

On the equivalence of constrained total least squares and structured total least squares

Several extensions of the total least squares (TLS) method that are able to calculate a structured rank deficient approximation of a data matrix have been developed. The main result of this article is the demonstration of the equivalence of two of these approaches, namely, the constrained total least squares (CTLS) approach and the structured total least squares (STLS) approach. We also present a numerical comparison of both methods.

Perceptual audio modeling with exponentially damped sinusoids

This paper presents the derivation of a new perceptual model that represents speech and audio signals by a sum of exponentially damped sinusoids. Compared to a traditional sinusoidal model, the exponential sinusoidal model (ESM) is better suited to model transient segments that are readily found in audio signals.Total least squares (TLS) algorithms are applied for the automatic extraction of the modeling parameters in the ESM, i.e. the amplitude, phase, frequency and damping factors of a user-defined number of damped sinusoids. In order to turn the SNR optimization criterion of these TLS algorithms into a perceptual modeling strategy, we use the psychoacoustic model of MPEG-1 Layer 1 in a subband TLS-ESM scheme. This allows us to model each subband signal in accordance with its perceptual relevance, thereby lowering the number of required modeling components for a given modeling quality. Simulations and listening tests confirm that perceptual ESM achieves the same perceived quality as plain ESM while using substantially less components, and provide support for applying the new model in the fields of parametric audio processing and coding.

Block-row Hankel weighted low rank approximation

This paper extends the weighted low rank approximation (WLRA) approach to linearly structured matrices. In the case of Hankel matrices with a special block structure, an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. Copyright

Structured Total Least Squares

In this paper an overview is given of the Structured Total Least Squares (STLS) approach and its recent extensions. The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector.

Analysis of the Structured Total Least Squares Problem for Hankel/Toeplitz Matrices

The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) approach when structured matrices are involved and a similarly structured rank deficient approximation of that matrix is desired. In many of those cases the STLS approach yields a Maximum Likelihood (ML) estimate as opposed to, e.g., TLS.In this paper we analyze the STLS problem for Hankel matrices (the theory can be extended in a straightforward way to Toeplitz matrices, block Hankel and block Toeplitz matrices). Using a particular parametrisation of rank-deficient Hankel matrices, we show that this STLS problem suffers from multiple local minima, the properties of which depend on the parameters of the new parametrisation. The latter observation makes initial estimates an important issue in STLS problems and a new initialization method is proposed. The new initialization method is applied to a speech compression example and the results confirm the improved performance compared to other previously proposed initialization methods.

Brief Misfit versus latency

In this paper we present a framework that combines some ideas of the behavioral modeling approach and the prediction error modeling approach. It is shown that the proposed model selection procedure can be rephrased as an optimization problem that only depends on the model parameters. Experiments illustrate the potential of the so-called misfit versus latency framework.

Structured weighted low rank approximation

This paper extends the weighted low rank approximation (WLRA) approach towards linearly structured matrices. In the case of Hankel matrices an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. The correctness of the latter algorithm is verified on a benchmark problem. Finally the statistical accuracy and numerical efficiency of the proposed algorithm is compared with that of STLNB, a previously proposed algorithm for solving Hankel WLRA problems. Copyright