Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Wavelet transform theory and its application in EMG signal processing

Abstract: Wavelet analysis is often very effective because it provides a simple approach for dealing with local aspects of a signal. The electromyogram (EMG) signals arising from muscle activities have become a useful tool for clinical diagnosis, rehabilitation medicine and sport medicine. In this paper, a time-frequency analysis based on the wavelet transform of the EMG signals is presented with a focus on 2 areas: de-noising and feature extraction.

Multiresolution modeling and estimation of multisensor data

Abstract: This paper presents a multiresolution multisensor data fusion scheme for dynamic systems to be observed by several sensors of different resolutions. A state projection equation is introduced to associate the states of a system at each resolution with others. This projection equation together with the state transition equation and the measurement equations at each of the resolutions construct a continuous-time model of the system. The model meets the requirements of Kalman filtering. In discrete time, the state transition is described at the finest resolution and the sampling frequencies of sensors decrease successively by a factor of two in resolution. We can build a discrete model of the system by using a linear projection operator to approximate the state space projection. This discrete model satisfies the requirements of discrete Kalman filtering, which actually offers an optimal estimation algorithm of the system. In time-invariant case, the stability of the Kalman filter is analyzed and a sufficient condition for the filtering stability is given. A Markov-process-based example is given to illustrate and evaluate the proposed scheme of multiresolution modeling and estimation with multiple sensors.

Differential methods for the identification of 2D and 3D motion models in image sequences

Abstract: This paper presents a detailed analysis of the differential approach for motion estimation in video image sequences. The models considered are defined either by a parametric approach, or by a physical approach (in terms of parameters of the pick-up equipment, movement and object structures). The relationships between the 2D and the 3D approaches are examined. The ambiguities inherent in a physical interpretation of a set of descriptors identified from image sequences are underlined. The critical points when using differential estimators are discussed, in particular, we study several classical image processing tools which improve the convergence rate of these estimators (hierarchical analysis, multiresolution, spatial interpolation of the luminance…). Definition and tuning of gains, initialization stage, cross-dependence between image segmentation and identification of the parameters associated to each region (as well as the duality between top-down and bottom-up approaches), which partly condition the behavior of the algorithms, are studied too. Results in terms of motion and segmentation maps, images predicted from one or several previous images by motion compensation, convergence curves of some of the proposed iterative algorithms illustrate this paper. Finally, we draw from these theoretical developments and the associated simulations some key elements for an effective implementation of a complete motion estimation scheme. We conclude by some perspectives for future work.

Joint wavelet-transform correlator for image feature extraction

Abstract: We describe a joint wavelet-transform correlator in which the wavelet function is combined with the input image as the input joint image to realize the wavelet transform of the objective image. The Haar wavelet and the Roberts filter are chosen as the wavelet functions to extract the features of the objective image. The relationship of the Haar wavelet and the Roberts filter is analyzed mathematically based on admissible condition of the wavelet. Computer simulations are provided to verify the theory and to illustrate the performance of this correlator.