TITLE:  The Accurate and Precise Estimation of Velocities and Associated
Uncertainties in Solar Image Sequences


Modern controversies in solar physics demand a statistically robust
technique for determining the ``optical flow'' perpendicular to the
line of sight from a sequence of solar images. Local Correlation
Tracking (LCT) is the de-facto standard for estimating optical flow in
solar image sequences. However, this technique has many documented
limitations. Perhaps the greatest limitations of LCT are the absence of
demonstrated accuracy, precision and a quantifiable local uncertainty
associated with the velocities derived from this technique, and the
introduction of artificial scales.  I will present a new technique that
represents a generalization of established wavelet interferometric
techniques to the multi-point data represented by solar image
sequences.

The new technique determines the velocity field based on a
statistically robust estimate of the local group velocity of
fluctuations. The analysis is localized in space through a wavevector
k(x,w,t) determined by spatio-temporal analysis of each individual
pixel over the entire image sequence. The temporal spectral analysis is
localized in time using the time-frequency localization properties of
the Morlet wavelet transform which provides an optimal balance of
temporal and frequency localization simultaneously. The velocity field
is computed from the mean of the phase velocity w/k averaged over all
frequencies.  The variance provides a statistically robust uncertainty
for this estimate. The magnitude of the variance directly indicates
when the local spectral components are moving with the same velocity,
i.e., the group velocity. The technique identifies when the concept of
a local velocity is correct, and can be extended to analyze turbulent
situations where it is not correct. This tool will be applicable to
estimating differential rotation, surface flows of meso- and
supergranuls, helicity injection, the convective structure of an
emerging flux region, systems of sunspots and pores, and many other
solar phenomena.

This work Supported by ONR