A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing

Daniel, Michael M.; Willsky, Alan S.

doi:10.1109/5.554216

Cited by 59 publications

(51 citation statements)

References 21 publications

(61 reference statements)

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“…Fig. 1(b) introduces some standard terminology associated with multiscale models [5]. The nodes at the bottom of the inverted tree are called the`leaf nodes' while the single node at the top is called the`root node'.…”

Section: Multiscale Modelsmentioning

confidence: 99%

“…1(a) [5]. The tree in this ®gure describes a one-dimensional random ®eld at four di erent spatial scales, each corresponding to a particular discrete representation of the random ®eld.…”

Section: Multiscale Modelsmentioning

confidence: 99%

“…Once we have de®ned a multiscale discretization we can apply the concept of recursive estimation over scale, in a manner which is similar but not identical to temporal recursion [4,5]. This is feasible if the values of the discretized variable at di erent scales are related by a Markov statistical model.…”

Section: Introductionmentioning

confidence: 99%

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A multiscale approach for estimating solute travel time distributions

Daniel

Willsky

McLaughlin

2000

Advances in Water Resources

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This paper uses a multiscale statistical framework to estimate groundwater travel times and to derive conditional travel time probability densities. In the applications of interest here travel time uncertainties depend primarily on uncertainties in hydraulic conductivity. These uncertainties can be reduced if the travel times are conditioned on scattered measurements of hydraulic conductivity and/or hydraulic head. In our approach the spatially discretized log hydraulic conductivity is modeled as a multiscale stochastic process, where each scale describes the process at a di erent spatial resolution. Related dependent variables such as hydraulic head and travel time are approximated by discrete linear functions of the log conductivity. The linearization makes it possible to incorporate these variables into e cient multiscale estimation and conditional simulation algorithms. We illustrate the application of these algorithms by considering two options for estimating travel time densities: (1) a Monte Carlo technique which only requires linearization of the groundwater¯ow equation and (2) a Gaussian approximation which also requires linearization of Darcy's law and an implicit particle tracking equation. Both options provide reasonable estimates of the travel time probability density in a synthetic experiment if the underlying log hydraulic conductivity variance is small (0.5). When this variance is increased (to 5.0), the Monte Carlo result is still quite good but the Gaussian approximation is unsatisfactory. The multiscale Monte Carlo option is a very competitive approach for estimating travel time since it provides accurate results over a wide range of conditions and it is more computationally e cient than competing alternatives. Ó

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Section: Multiscale Modelsmentioning

confidence: 99%

“…1(a) [5]. The tree in this ®gure describes a one-dimensional random ®eld at four di erent spatial scales, each corresponding to a particular discrete representation of the random ®eld.…”

Section: Multiscale Modelsmentioning

confidence: 99%

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A multiscale approach for estimating solute travel time distributions

Daniel

Willsky

McLaughlin

2000

Advances in Water Resources

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“…Ž . Dougherty 1996, McLaughlin and Townley 1996and Daniel and Willsky 1997 , the limitations still remain. Part of our contribution is to recognize that the difficulty is the Ž .…”

Section: Introductionmentioning

confidence: 99%

“…Numerous methods are able to work with a variety of data and model types in hydrology, meteorology, and oceanography such as those in Kitanidis and Vomvoris 1983, Hoeksema and Kitinidis 1984, Dagan 1985, Gelhar 1986 Neuman 1986a;b;c , Ghil 1989, Carrera and Glorioso 1991 , Yangxiao et al 1991, Bennett 1992, Sun and Yeh 1992, Courtier et al 1993 Daniel andWillsky 1997 andZimmerman et al 1998 . Many of the crucial issues in moving from theory to practice are well understood.…”

Section: Introductionmentioning

confidence: 99%