Multiresolution Nonparametric Intensity and Density Estimation

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PLATELETS FOR MULTISCALE ANALYSIS IN
PHOTON-LIMITED IMAGING
Rebecca Willett and Robert Nowak, ECE Department,
Rice University
Approximation Rates
Wedgelet Partitions
MPLE Algorithm
Photon-Limited Imaging

• Const Estimate

• Error decay rates
• Fourier O(m-1/2)
• Wavelets O(m-1)
• Wedgelets O(m-1)
• Platelets O(m-2)

• Wedge Estimate

Data

• Platelet Estimate

Haar Wavelet Partition
Original Image
Wedgelet Partition

• Wedged Platelet Estimate

Poissonian Observations Image Curves Inverse
Problems

• Inherit from finer scale

Nuclear Medicine
Platelets are localized atoms at various scales,
locations, and orientations that can produce
highly accurate, piecewise linear approximations
to images consisting of smooth regions separated
by smooth boundaries. Platelets generalize
Donohos wedgelets and are capable of concisely
representing both smooth surfaces and edges.
Platelet Approximations
Beyond Wavelets
Haar
Platelets
Wedgelets
Confocal Microscopy
Supported by NSF, ARO, and ONR http//www.ece.rice
.edu/willett/