Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems

Forward Dynamics Solutions to Multi - Modal Inverse Dynamics Problems

In human motion studies, inverse dynamics analysis is the standard technique used to gain insight into the net summation of all muscle activity at each joint. In the inverse dynamics method, the joint forces and joint moments of force are calculated from a prescribed movement. Since the segmental movements, in contrast to the internal forces, can be measured, this method is commonly applied for...

Consistent Discretization of Linear Inverse Problems using Sparse Stochastic Processes

We introduce a novel discretization paradigm and specify MAP estimators for linear inverse problems by using the theory of continuous-domain sparse stochastic processes. We characterize the complete class of admissible priors for the discretized version of the signal and show that the said class is restricted to the family of infinitely divisible distributions. We also explain the connections b...

Solutions to Space-Time Inverse Problems

Stochastic model reduction applied to inverse problems

This article describes the use of Gaussian Processes in model reduction techniques with application to inverse problems. Mainly, the work is focused on the proper construction of the model approximation, namely on training process based on minimal number of learning samples, by making use of automatic samples selection through computed standard deviation of model prediction. An example of appli...

Common solutions to pseudomonotone equilibrium problems

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....