Showing papers by "Jean-Christophe Pesquet published in 1995"
01 Jan 1995
TL;DR: This paper characterize the asymptotic statistics of the criteria to gain insight which can be used to improve on the performance of the analysis, and provides an alternative approach to Minimax methods for deriving various attributes of nonlinear wavelet packet estimates.
Abstract: Wavelet packets are a useful extension of wavelets providing an adaptive time- scale analysis. In using noisy observations of a signal of interest, the criteria for best bases representation are random variables. The search may thus be very sensitive to noise. In this paper, we characterize the asymptotic statistics of the criteria to gain insight which can in turn, be used to improve on the performance of the analysis. By way of a well-known information-theoretic principle, namely the Minimum Description Length, we provide an alternative approach to Minimax methods for deriving various attributes of nonlinear wavelet packet estimates.
71 citations
TL;DR: It is shown that wide-sense stationarity may be achieved by adequately selecting the analysis wavelet and that the latter possesses additional properties which are useful in the presence of other types of nonstationarities.
Abstract: Processing nonstationary signals is an important and challenging problem. We focus on the class of nonstationary processes with stationary increments of an arbitrary order, and place them in a multiscale framework. Unlike other related studies, we concentrate on the discrete-time analysis and derive a number of new results in addition to placing the related existing ones in the same framework. We extend the study to various parametric models for which we derive the resulting multiresolution description. We show that wide-sense stationarity may be achieved by adequately selecting the analysis wavelet. After generalizing the study to wavelet packet analysis, we show that the latter possesses additional properties which are useful in the presence of other types of nonstationarities. >
64 citations
09 May 1995
TL;DR: A M-band wavelet decomposition of second order random processes is investigated and an extension of results which are known for the dyadic wavelet transform is proposed.
Abstract: We investigate a M-band wavelet decomposition of second order random processes. In particular, we propose an extension of results which are known for the dyadic wavelet transform. The statistical properties of the M-band wavelet coefficients are listed and recursive relations are derived and used to compute their multiscale characteristics. Special attention is also paid to the multiscale analysis of linear parametric models.
23 Oct 1995
TL;DR: A segmentation algorithm based on morphological operations to extract the visually important regions of the displaced frame difference image is proposed which is well adapted to low resolution (QCIF format) sequences.
Abstract: In image sequence compression schemes based on motion compensation, some new information contained in the displaced frame difference image must be coded. As this is expensive to transmit, it is important, particularly at low bit rates, to code only the most important information. We propose a segmentation algorithm based on morphological operations to extract the visually important regions of the displaced frame difference image. This segmentation is combined with a coding scheme which is automatically optimized for a given bit rate constraint. As demonstrated by examples, this method is well adapted to low resolution (QCIF format) sequences.