  This is an unabridged version of a journal manuscript that has been submitted
for publication [1]. (Due to length restrictions, we were forced to remove
substantial amounts of content from the version that was submitted to the
journal, including more detailed theoretical explanations, additional figures,
and a more comprehensive bibliography. This content remains intact in this
version of the document).
  Sensitivity map estimation is important in many multichannel MRI
applications. Subspace-based sensitivity map estimation methods like ESPIRiT
are popular and perform well, though can be computationally expensive and their
theoretical principles can be nontrivial to understand. In the first part of
this work, we present a novel theoretical derivation of subspace-based
sensitivity map estimation based on a linear-predictability/structured low-rank
modeling perspective. This results in an estimation approach that is equivalent
to ESPIRiT, but with distinct theory that may be more intuitive for some
readers. In the second part of this work, we propose and evaluate a set of
computational acceleration approaches (collectively known as PISCO) that can
enable substantial improvements in computation time (up to ~100x in the
examples we show) and memory for subspace-based sensitivity map estimation.
