Peter C. Gibson

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A partition of unity on the d-dimensional integer lattice Z d is used to create a generalized discrete Gabor transform, with analysis and synthesis windows of smooth, desirable characteristics. Factorizing the partition of unity allows for different choices of analysis and synthesis windows, a transformation on general lattices in the time and frequence(More)
Nonstationary processes in seismic modeling may be represented numerically by Gabor multipliers and generalized frame operators. These numerical algorithms are based on a localized version of the Fourier transform and share many of the speed and accuracy benefits of the FFT, while modeling nonstationarity. We demonstrate applications to seismic(More)
We present recent results on the scattering of plane waves in piecewise constant layered media, introducing a new geometric perspective. It turns out that the classical inverse scattering problem generically decouples into two separate problems. One problem is to recover a line from the magnitudes of the projections onto the line of a set of lattice points.(More)
Operators that preserve minimum phase signals, or delayed minimum phase signals, have been shown to be important in practical signal processing contexts, and specifically in geophysical imaging, where one seeks to identify such operators using test signals. Which sets of test signals suffice to recover an unknown operator of the given type? In the present(More)
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