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

Extended Version of "New Theory and Faster Computations for Subspace-Based Sensitivity Map Estimation in Multichannel MRI''