# Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting

## TL;DR

This paper introduces a shearlet-based compressed sensing method for fast 3D cardiac MRI that achieves high-quality images with shorter scan times by using iterative reweighting and a novel sparsifying transform.

## Contribution

The paper presents a new 3D shearlet-based compressed sensing reconstruction method with iterative reweighting for improved cardiac MRI imaging speed and quality.

## Key findings

- Lower relative errors compared to other methods
- Higher structural similarity especially at high undersampling
- Better depiction of cardiac anatomy and coronary arteries

## Abstract

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS). Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. Data is acquired with a 3D Radial Phase Encoding (RPE) trajectory and an iterative reweighting scheme is used during image reconstruction to ensure fast convergence and high image quality. In our in-vivo cardiac MRI experiments we show that the proposed method 3DShearCS has lower relative errors and higher structural similarity compared to the other reconstruction techniques especially for high undersampling factors, i.e. short scan times. In this paper, we further show that 3DShearCS provides improved depiction of cardiac anatomy (measured by assessing the sharpness of coronary arteries) and two clinical experts qualitatively analyzed the image quality.