# Sparse Elasticity Reconstruction and Clustering using Local Displacement Fields

## TL;DR

This paper presents a novel method for elasticity reconstruction using local displacement data, employing sparse reconstruction and clustering to improve spatial resolution and reduce the amount of required observational data.

## Contribution

It introduces a new online clustering scheme called a superelement and combines it with sparse reconstruction for high-resolution elasticity estimation.

## Key findings

- Elasticity distribution reconstructed with only 10% of the body observed
- Estimation error decreased by considering sparsity of elasticity distribution
- Method achieves higher spatial resolution in elasticity mapping

## Abstract

This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement is proposed to reduce the number of dimensions of the optimization parameters. Alternating the optimization of element boundaries and elasticity parameters enables the elasticity distribution to be estimated with a higher spatial resolution. The simulation experiments show that elasticity distribution is reconstructed based on observations of approximately 10% of the total body. The estimation error was improved when considering the sparseness of the elasticity distribution.