9:30, SPTM-P8.1
PIC-PROJECTION TECHNIQUE FOR DECREASING OF STATISTICAL ERROR IN SIGNALS RECONSTRUCTION PROBLEMS
A. KALYUZHNY, A. KOVTONYUK
As is well known, the problem of signal reconstruction may be reduced to estimation of coefficients of some signal decomposition. In the previous paper at ICASSP2000 we have shown, that optimal coordinate basis for this method must be formed from eigenfunctions of the Fisher's information operator (so-called PIC-basis). However direct usage of the PIC-basis is not always convenient. Therefore in the given paper we propose the combined technique, according to which any given basis (FFT, DCT, wavelet, filterbanks, etc) is replaced by its projection on the subspace generated by the PIC-basis. Such projective basis, keeping all advantages of the initial representation, allows to decrease a range of possible fluctuations of a signal estimate. The effectiveness of the proposed technique is illustrated by numerical examples from area of nonlinear tomography of a medium.

9:30, SPTM-P8.2
SEVERAL APPROACHES TO SIGNAL RECONSTRUCTION FROM SPECTRUM MAGNITUDES
A. BURIAN, J. SAARINEN, P. KUOSMANEN, C. RUSU
The problem of reconstructing a one-dimensional (1-D) signal from only the magnitude of its Fourier transform emerges when the phase of a signal is apparently lost or impractical to measure. Previous solutions usually employed an Iterative Fourier Transform (IFT) algorithm applied on a discrete approximation of a signal. The utilization of these algorithms is seriously limited by the unpredictability of their convergence. We propose several solutions to the phase retrieval problem. The first two proposed solutions uses relationships between the phase and the gain differences (GD), or gain samples (GS), in nepers. The last proposed solution uses a neural network (NN) for solving the problem. The NN incorporates a combination of the maximum entropy estimation algorithm with some additional nonlinear constraints. We compare our solutions by using some numerical examples. The performances under noisy conditions are also considered.

9:30, SPTM-P8.3
WAVELET-BASED DENOISING USING HIDDEN MARKOV MODELS
M. BORRAN, R. NOWAK
Hidden Markov models have been used in a wide variety of wavelet-based statistical signal processing applications. Typically, Gaussian mixture distributions are used to model the wavelet coefficients and the correlation between the magnitudes of the wavelet coefficients within each scale and/or across the scales is captured by a Markov tree imposed on the (hidden) states of the mixture. This paper investigates correlations directly among the wavelet coefficient amplitudes (sign x magnitude), instead of magnitudes alone. Our theoretical analysis shows that the coefficients display significant correlations in sign as well as magnitude, especially near strong edges. We propose a new wavelet-based HMM structure based on mixtures of one-sided exponential densities that exploits both sign and magnitude correlations. We also investigate the application of this for denoising the signals corrupted by additive white Gaussian noise. Using some examples with standard test signals, we show that our new method can achieve better mean squared error, and the resulting denoised signals are generally much smoother.

9:30, SPTM-P8.4
AUTOMATIC STOPPING CRITERION FOR ANISOTROPIC DIFFUSION
V. SOLO
We develop, apparently for the first time, an automatic criterion to choose when to stop the iteration in anisotropic diffusion signal reconstruction.

9:30, SPTM-P8.5
APPLICATION OF TREE-BASED SEARCHES TO MATCHING PURSUIT
S. COTTER, B. RAO
Matching Pursuit (MP) uses a greedy search to construct a subset of vectors, from a larger set, which will best represent a signal of interest. Here, we extend this search for the best subset by keeping the K vectors which maximize the selection criterion at each iteration. This is termed the MP:K algorithm and represents a suboptimal search through the tree of all possible subsets where each node is limited to having K children. As a more suboptimal search, we can use the M-L search to select a subset of dictionary vectors, leading to the MP:M-L algorithm. We compare the computation and storage requirements for three variants of the MP algorithm using these searches. Through simulations, the significantly improved performance obtained using the MP:K and MP:M-L algorithms is demonstrated. We conclude that the Modified Matching Pursuit (MMP) algorithm offers the best compromise between performance and complexity using these search techniques.

9:30, SPTM-P8.6
KALMAN FILTER ANALYSIS FOR QUASI-PERIODIC SIGNALS
K. NISHI
An Optimal filter for extracting quasi-periodic signals such as a voiced speech or instrumental sound from the noise-corrupted observation are proposed. They are derived through the Kalman-Bucy filter analysis in which the dynamics of amplitude and pitch fluctuations are described through the Ito stochastic differential equation. The Laplace analysis to the filter equation leads to three types of comb filters, i.e., constant-BW (-bandwidth) type, constant-Q type and those mixture type that have robustness to the amplitude fluctuation, pitch fluctuation and both of them, respectively. All-pole digital filters can be also realized for real-time processing. Examples of filter design are presented, and the performance of harmonics extraction is examined by comparison between the constant-BW type and constant-Q type.

9:30, SPTM-P8.7
SIGNAL-ADAPTIVE ROBUST TIME-VARYING WIENER FILTERS: BEST SUBSPACE SELECTION AND STATISTICAL ANALYSIS
G. MATZ, F. HLAWATSCH, A. RAIDL
We propose a signal-adaptive robust time-varying Wiener filter for nonstationary signal estimation/enhancement. This filter uses projections onto local cosine subspaces and a novel ``best subspace'' algorithm. It allows efficient on-line operation including stable on-line estimation of design parameters. A statistical analysis is provided, and a speech enhancement example is considered.

9:30, SPTM-P8.8
H INFINITY SMOOTHING FOR CONTINUOUS UNCERTAINS SYSTEMS
E. BLANCO, G. THOMAS, P. NEVEUX
Recently, a H infinity smoother has been developed and it gives good results for noise uncertainties. Nevertheless, when appear uncertain parameters, its performances decrease significantly. That’s why, in this paper, an estimator robust to noise uncertain properties and parameter uncertainties is presented. As we can find in litterature, the robust H infinty smoother for uncertain systems is developed as a combination of two robust H infinty filters. The robust performances, for both noise and parameter uncertainties, of this new approach are evaluated on a simple example.