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new experimental approach to land analysis has recently been developed, based on the integration of information acquired on different scales; it enables the structure and the functionality of the vege...
We construct detectors for ‘geometric’ objects in noisy data. Examples include a detector for presence of a line segment of unknown length, position, and orientation in two-dimensional image data wi...
We are given a set of n points that appears uniformly distributed in the unit square [0,1]2. We wish to test whether the set actually is generated from a non-uniform distribution having a small frac...
We have developed tools for analysis of 3-D volumetric data which allow sensitive characterizations of point clouds containing ˉlamentary structures. Our approach involves multiscale X-ray transforms...
We describe a frameworkfor multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. The frameworkhas 5 key components.
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as: the sphere S2, the special orthogonal group SO(3), the positive definite ma...
A test of homogeneity tries to decide whether observations come from a single distribution or from a mixture of several distributions. A powerful theory has been developed for the case where the comp...
A special semiparametric model for a univariate density is introduced that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for t...
The use of multiscale statistics, that is, the simultaneous inference about various stretches of data via multiple localized statistics, is a natural and popular method for inference about, for exam...
We introduce a new multiscale Gaussian beam method for the numerical solution of the wave equation with smooth variable coefficients. The first computational question addressed in this paper is how to...
The Gaussian beam method is an asymptotic method for wave equations with highly oscillatory data. In a recent published paper by two of the authors, a multiscale Gaussian beam method was first propose...
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(x,ξ)f (ξ)dξ, where Φ(x, ξ) is a phase funct...
While peer-to-peer consensus algorithms have enviable robustness and locality for distributed estimation and computation problems, they have poor scaling behavior with network diameter. We show how de...
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
This paper considers the model problem of recovering a signal f(t) from noisy sampled measurements. The objects we wish to recover are chirps which are neither smoothly varying nor stationary but rath...

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