Multi-criterion Optimization Approach to Ill-posed Inverse Problem with Visual Feature’s Recovery

Abstract

Ill-posed inverse problem is commonly existed in signal processing such as image reconstruction from projection, parameter estimation on electromagnetic field, and path optimization in IP network. Usually, the solution of an inverse problem is unstable, not unique or does not exit. Traditional approach to solve this problem is to estimate the solution by optimizing a regularized objective function. In some cases, recovery of visual features is most emphasized in that solution; thereof the distribution of residual errors has distinct influence on the quality of solution.

This paper analyzes ill-posed inverse problem with the case of image reconstruction from projections and discusses its fidelity based on various visual features in the estimated solution. Multi-criterion Optimization Approach, a new approach to solve the ill-posed inverse problems with good recovery of visual features, is presented with its theory basis and the experiment results. The solution stability and accuracy are analyzed using singular value decomposition (SVD), and main factors affecting the reconstruction quality are also discussed.