2D Deconvolution Using Adaptive Kernel

Dirk Nille, Udo von Toussaint
2019 Proceedings (MDPI)  
An analysis tool using Adaptive Kernel to solve an ill-posed inverse problem for a 2D model space is introduced. It is applicable for linear and non-linear forward models, for example in tomography and image reconstruction. While an optimisation based on a Gaussian Approximation is possible, it becomes intractable for more than some hundred kernel functions. This is because the determinant of the Hessian of the system has be evaluated. The SVD typically used for 1D problems fails with
more » ... problem size. Alternatively Stochastic Trace Estimation can be used, giving a reasonable approximation. An alternative to searching for the MAP solution is to integrate using Marcov Chain Monte Carlo without the need to determine the determinant of the Hessian. This also allows to treat problems where a linear approximation is not justified.
doi:10.3390/proceedings2019033006 fatcat:qeu2blkcqfdjxhh5cc6x6as53q