Bilevel Methods for Image Reconstruction

This review discusses methods for learning parameters image reconstruction problems using bilevel formulations. Image typically involves optimizing a cost function to recover vector of unknown variables that agrees with collected measurements and prior assumptions. State-of-the-art learn these assumptions from training data various machine techniques, such as methods. One can view the problem formalizing hyperparameter optimization, bridging based optimization methods, or method best suited specific task. More formally, attempt minimize an upper-level loss function, where in are themselves minimizers lower-level function. contains running example tuning coefficients sparsifying filters used regularizer. Such generalize popular total variation regularization method, learned closely related convolutional neural networks approaches rapidly gaining popularity. Here, is reconstruct regularizer filters; corresponding measure reconstructed quality on data. multiple perspectives motivate use make them more easily accessible different audiences. We then turn ways optimize problem, providing pros cons variety proposed approaches. Finally we overview applications reconstruction.