Wavelet/shearlet hybridized neural networks for biomedical image restoration

Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets

Stochastic Optimal Control with Neural Networks and Application to a Retailer Inventory Problem

Overwhelming computational requirements of classical dynamic programming algorithms render them inapplicable to most practical stochastic problems. To overcome this problem a neural network based Dynamic Programming (DP) approach is described in this study. The cost function which is critical in a dynamic programming formulation is approximated by a neural network according to some designed weight-update rule based on Temporal Difference(TD)learning. A Lyapunov based theory is developed to guarantee an upper error bound between the output of the cost neural network and the true cost. We illustrate this approach through a retailer inventory problem