Multiresolution Estimation Research Articles

Toward Multiresolution Estimation and Efficient Representation of Gravitational Fields

In this paper we demonstrate performance of several local and multi-resolution gravity models derived from existing spherical harmonic models. A model of this type was provided to USAFSC in 1997, and additional variants have been developed since then. We also begin to address the problem of estimating multi-resolution models directly from gravity measurements. We hope to demonstrate that it is reasonable to expect gravity models with greater accuracy and flexibility once the spherical harmonic basis has been eliminated from the process.

Multi-resolution estimation of fractal dimension from noisy images

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D=3-H. The signal-dependent nature of the speckle noise, however, prevents a correct estimation of fractal dimension from synthetic aperture radar (SAR) images. Here, we propose and assess a novel method to obtain D based on the multi-scale decomposition provided by the normalized Laplacian pyramid (LP), which is a bandpass representation obtained by dividing the layers of a LP by its expanded base band and is designed to force the noise to become signal independent. Extensive experiments on synthetic fractal textures, both noise free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well-established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.

Coding algorithm with region-based motion compensation

This paper describes a region-based coding algorithm developed by Thomson Multimedia and submitted to MPEG-4 tests of November 1995 and January 1996. In this algorithm, the segmentation into regions is based on an advanced motion analysis, successively achieving a multiresolution motion field estimation and a segmentation based on a Markovian statistical approach, which insures a good temporal coherence of segmentation maps and an identification of covered areas. Moreover, the accurate motion description allows intermediate frames interpolation which can increase the displayed frame rate. Simulation results and MPEG-4 tests of January 1996 have shown that the algorithm is as efficient as block-based coding algorithms like MPEG-1 or H.263 for the compression functionality, while offering temporal scalability by higher frame rates. Moreover, description of the scene in coherent motion regions may be seen as an intermediate step toward object-based functionalities.

Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry

A recently developed multiresolution estimation framework offers the possibility of highly efficient statistical analysis, interpolation, and smoothing of extremely large data sets in a multiscale fashion. This framework enjoys a number of advantages not shared by other statistically-based methods. In particular, the algorithms resulting from this framework have complexity that scales only linearly with problem size, yielding constant complexity load per grid point independent of problem size. Furthermore these algorithms directly provide interpolated estimates at multiple resolutions, accompanying error variance statistics of use in assessing resolutionlaccuracy tradeoffs and in detecting statistically significant anomalies, and maximum likelihood estimates of parameters such as spectral power law coefficients. Moreover, the efficiency of these algorithms is completely insensitive to irregularities in the sampling or spatial distribution of measurements and to heterogeneities in measurement errors or model parameters. For these reasons this approach has the potential of being an effective tool in a variety of remote sensing problems. In this paper, we demonstrate a realization of this potential by applying the multiresolution framework to a problem of considerable current interest-the interpolation and statistical analysis of ocean surface data from the TOPEXPOSEIDON altimeter

Probabilistic linear models for multiresolution estimation in gray-level images

A multiresolution analysis of digital gray-level images is presented. A gray-level multi-scale framework is determined from two main assumptions: the gray scale is binary at the finest spatial resolution, and the gray levels of composed regions are obtained additively. In order to interrelate the gray-level histograms of the same image at different resolutions, probabilistic linear models are developed, which are then applied for estimation. Linear-optimization theory is used as a way of constructing such models. A general procedure for image processing is sketched, based on gray-level estimation. A versatile algorithm for nonlinear filtering is derived. Some examples of prospective applications are given.