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

## TL;DR

This paper introduces a new theoretical perspective on subspace-based sensitivity map estimation in multichannel MRI, specifically ESPIRiT, and proposes computational acceleration methods called PISCO that significantly reduce computation time and memory usage.

## Contribution

It provides a novel theoretical derivation of sensitivity map estimation based on linear predictability and low-rank modeling, and introduces PISCO for fast, memory-efficient computations.

## Key findings

- Theoretical derivation offers an intuitive understanding of ESPIRiT.
- PISCO accelerates computations by up to 100 times.
- Memory usage is substantially reduced with PISCO.

## Abstract

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.