# Autocalibrating and Calibrationless Parallel Magnetic Resonance Imaging as a Bilinear Inverse Problem

## TL;DR

This paper discusses recent approaches to jointly estimate unknown coil sensitivities and images in MRI, formulating it as a bilinear inverse problem to improve undersampled image reconstruction.

## Contribution

It introduces and reviews methods for solving the bilinear inverse problem in MRI, enabling calibrationless and auto-calibrating image reconstruction.

## Key findings

- Enhanced image quality from undersampled data
- Reduced need for separate calibration scans
- Improved robustness to subject movement

## Abstract

Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming Fourier-encoding steps by undersampling. The receive sensitivities are a priori unknown and influenced by geometry and electric properties of the (moving) subject. For optimal results, they need to be estimated jointly with the image from the same undersampled measurement data. Formulated as an inverse problem, this leads to a bilinear reconstruction problem related to multi-channel blind deconvolution. In this work, we will discuss some recently developed approaches for the solution of this problem.