Sparse Elasticity Reconstruction and Clustering using Local Displacement Fields
This addresses elasticity reconstruction for applications like medical imaging or material science, but it is incremental as it builds on sparse reconstruction theory with a new clustering scheme.
The paper tackles the problem of reconstructing elasticity distributions in elastic bodies from sparse local displacement observations, achieving reconstruction with only about 10% observation coverage and reducing estimation error by leveraging sparsity.
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.