  Sparse sampling schemes have the potential to dramatically reduce image
acquisition time while simultaneously reducing radiation damage to samples.
However, for a sparse sampling scheme to be useful it is important that we are
able to reconstruct the underlying object with sufficient clarity using the
sparse measurements. In dynamic sampling, each new measurement location is
selected based on information obtained from previous measurements. Therefore,
dynamic sampling schemes have the potential to dramatically reduce the number
of measurements needed for high fidelity reconstructions. However, most
existing dynamic sampling methods for point-wise measurement acquisition tend
to be computationally expensive and are therefore too slow for practical
applications.
  In this paper, we present a framework for dynamic sampling based on machine
learning techniques, which we call a supervised learning approach for dynamic
sampling (SLADS). In each step of SLADS, the objective is to find the pixel
that maximizes the expected reduction in distortion (ERD) given previous
measurements. SLADS is fast because we use a simple regression function to
compute the ERD, and it is accurate because the regression function is trained
using data sets that are representative of the specific application. In
addition, we introduce a method to terminate dynamic sampling at a desired
level of distortion, and we extended the SLADS methodology to sample groups of
pixels at each step. Finally, we present results on computationally-generated
synthetic data and experimentally-collected data to demonstrate a dramatic
improvement over state-of-the-art static sampling methods.
