A multi-objective optimization framework for ill-posed inverse problems

Many image inverse problems are ill-posed for no unique solutions. Most of them have incommensurable or mixed-type objectives. In this study, a multi-objective optimization framework is introduced to model such ill-posed inverse problems. The conflicting objectives are designed according to the properties of ill-posedness and certain techniques. Multi-objective evolutionary algorithms have capability to optimize multiple objectives simultaneously and obtain a set of trade-off solutions. For that reason, we use multi-objective evolutionary algorithms to keep the trade-off between these objectives for image ill-posed problems. Two case studies of sparse reconstruction and change detection are implemented. In the case study of sparse reconstruction, the measurement error term and the sparsity term are optimized by multi-objective evolutionary algorithms, which aims at balancing the trade-off between enforcing sparsity and reducing measurement error. In the case study of image change detection, two conflicting objectives are constructed to keep the trade-off between robustness to noise and preserving the image details. Experimental results of the two case studies confirm the multi-objective optimization framework for ill-posed inverse problems in image processing is effective.