AN OPTIMIZATION APPROACH TO ELASTIC INVERSE PROBLEMS (2007)

Content Provider	CiteSeerX
Author	Rivas, Carlos E. Barbone, Paul E. Oberai, Assad A.
Abstract	Imaging the elastic modulus distributions of soft tissues requires the solution of an elastic inverse problem. A typical approach to formulating this inverse problem is as an optimization problem. We consider in particular formulating this inverse problem as a constrained optimization problem in which we minimize the objective functional (the data mismatch) with the partial differential equations of elasticity as constraints. The Lagrange multiplier method is applied resulting in a two-eld variational formulation that is often called a mixed formulation. The constrained optimization formulation differs from the output least squares method that appears frequently in the literature in which the inverse problem is formulated as an unconstrained optimization problem. Formulating this inverse problem as a constrained optimization problem has some advantages over formulating it as an unconstrained one since we can analyze the well posedness of this formulation by using some standards theorems. So we can verify that under some suitable conditions this inverse problem will converge reliably to a unique solution. Under some relatively strong mathematical conditions, this is true for the
File Format	PDF
Publisher Date	2007-01-01
Access Restriction	Open
Subject Keyword	Inverse Problem Optimization Approach Elastic Inverse Problem Constrained Optimization Problem Data Mismatch Two-eld Variational Formulation Elastic Modulus Distribution Partial Differential Equation Unconstrained Optimization Problem Mixed Formulation Elastic Inverse Problem Well Posedness Suitable Condition Particular Formulating Unique Solution Constrained Optimization Formulation Differs Lagrange Multiplier Method Soft Tissue Typical Approach Optimization Problem Standard Theorem Objective Functional Strong Mathematical Condition
Content Type	Text